chore: Release trueskill-tt version 0.3.0

Drift was a property of the History, so every competitor drifted at the
same rate and a fixed reference point could not share a graph with moving
competitors. A bot at a known strength, a rating floor, a course
difficulty — all of them drifted along with the players.

Member::with_drift_scale(s) multiplies the drift *variance* a competitor
accumulates, so s is in the same units as gamma: ConstantDrift(g) at
scale s behaves exactly as ConstantDrift(g * s) would for that competitor.
A scalar rather than a per-competitor Drift keeps History's single D type
parameter untouched and stays Copy. 0.0 pins a competitor still.

The scale lives on Rating, beside the drift it scales, and is applied
only through Rating::drift_variance_delta / drift_variance_for_elapsed.
Making those the sole entry points means a caller cannot reach the raw
drift and silently skip a competitor's scale — the filtered pass was
exactly that bug during development, caught because its test was written
before the wiring.

Like with_prior, the scale is competitor configuration captured at first
appearance rather than a per-event override; a competitor that is static
is static, and a scale that changed between events would make the skill
trajectory hard to interpret. Member's docs claimed prior was a per-event
override, which the code has never done — corrected here.

A negative scale is rejected rather than squared into its absolute value,
and a non-finite one rejected outright, both as InvalidParameter.

None means 1.0, so no existing call site changes and no existing fit
moves. Adding a public field to Member does break struct-literal
construction downstream.

Closes #34

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014b6wy2q8rnFK8U8GPJVQNU

.cargo/config.toml

@@ -0,0 +1,15 @@
+# `Cargo.toml` sets `publish = ["kellnr"]`, so `cargo publish` targets the
+# private registry and refuses crates.io. Cargo needs that registry's index
+# declared to resolve the name.
+#
+# Committed rather than left to a per-user `~/.cargo/config.toml` so the repo
+# is self-contained: a fresh clone, a new machine, or CI would otherwise fail
+# with
+#
+#   error: registry index was not found in any configuration: `kellnr`
+#
+# Index URL only — it is not a secret. Publish tokens live in
+# `~/.cargo/credentials.toml` (per-user, never committed) or, in CI, in
+# `CARGO_REGISTRIES_KELLNR_TOKEN`.
+[registries.kellnr]
+index = "sparse+https://crates.aceofba.se/api/v1/crates/"

.gitea/workflows/ci.yml

@@ -0,0 +1,87 @@
+name: CI
+
+on:
+  push:
+    branches: [main]
+  pull_request:
+
+env:
+  CARGO_TERM_COLOR: always
+  RUSTFLAGS: -D warnings
+
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          # The build most consumers get.
+          - name: default
+            features: ""
+            profile: ""
+          # Most numerical goldens need `approx` for assert_ulps_eq.
+          - name: approx
+            features: "--features approx"
+            profile: ""
+          # The parallel path, including tests/determinism.rs.
+          - name: rayon
+            features: "--features approx,rayon"
+            profile: ""
+          # Critical: debug_assert! is compiled out here, which is where the
+          # tie/p_draw and score_sigma validation actually has to hold.
+          - name: release
+            features: "--features approx"
+            profile: "--release"
+    name: test (${{ matrix.name }})
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+      - uses: Swatinem/rust-cache@v2
+      - run: cargo test ${{ matrix.profile }} ${{ matrix.features }}
+      - run: cargo test ${{ matrix.profile }} ${{ matrix.features }} --doc
+
+  determinism:
+    name: determinism across thread counts
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+      - uses: Swatinem/rust-cache@v2
+      # Posteriors must be bit-identical regardless of how many rayon workers
+      # run the color-group sweep.
+      - run: |
+          for threads in 1 2 4 8; do
+            echo "== RAYON_NUM_THREADS=$threads =="
+            RAYON_NUM_THREADS=$threads cargo test --release \
+              --features approx,rayon --test determinism
+          done
+
+  lint:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+        with:
+          components: clippy
+      - uses: Swatinem/rust-cache@v2
+      - run: cargo clippy --all-targets --all-features -- -D warnings
+
+  format:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      # rustfmt.toml uses nightly-only options (imports_granularity).
+      - uses: dtolnay/rust-toolchain@nightly
+        with:
+          components: rustfmt
+      - run: cargo +nightly fmt --check
+
+  msrv:
+    name: minimum supported Rust version
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@1.85.0
+      - uses: Swatinem/rust-cache@v2
+      - run: cargo check --all-targets --features approx,rayon

.gitignore

@@ -7,3 +7,4 @@
 NOTEPAD.md
 
 /.claude
+proptest-regressions/

CHANGELOG.md

@@ -2,6 +2,91 @@
 
 All notable changes to this project will be documented in this file.
 
+## 0.3.0 - 2026-09-01
+
+### Breaking Changes
+
+- refactor!: make Competitor::message an Option, and compute_elapsed loud
+- refactor!: replace emptiness-as-sentinel with Option for results and weights
+- refactor!: remove ConvergenceReport::slices_skipped
+
+### Bug Fixes
+
+- fix: enforce EventBuilder weight/team length in release
+
+### Documentation
+
+- docs: complete the public API documentation contract
+
+### Features
+
+- feat: allow drift to vary per competitor via Member::with_drift_scale
+
+### Miscellaneous Tasks
+
+- chore: ignore proptest regression seed files
+
+### Performance
+
+- perf: stop cloning inference inputs in OwnedGame and ingestion
+- perf: make the per-slice SkillStore compact instead of dense
+
+### Testing
+
+- test: add property-based tests, a shared finiteness helper, and boundary inputs
+
+## 0.2.0 - 2026-08-27
+
+### Breaking Changes
+
+- refactor!: remove the inert online flag
+
+### Bug Fixes
+
+- fix: reject ties without draw probability; never report NaN as converged
+- fix(quality): support any number of rating groups
+- fix(evidence): accumulate in log space and floor the per-link value
+- fix(history): stop reprocessing the slice that was just appended to
+- fix(rayon): remove the aliasing unsafe from the parallel sweep
+- fix: close out four small issues and pin #27's repro
+
+### Documentation
+
+- docs: refresh README and CLAUDE.md; add ingest benchmark
+- docs: spec for filtered (forward-only) estimates
+- docs: implementation plan for filtered estimates
+- docs: state filtered accessor cost and evidence semantics precisely
+- docs(cargo): correct the licence note — kellnr does not require one
+
+### Features
+
+- feat: add filtered_log_evidence
+- feat: add filtered learning curves
+
+### Miscellaneous Tasks
+
+- chore: add CI, crate metadata, and crate-level documentation
+- chore: target releases at the private kellnr registry
+- chore: keep the 48 MB ATP dataset out of the published crate
+- chore: dual-license MIT OR Apache-2.0
+- chore: Release trueskill-tt version 0.2.0
+
+### Performance
+
+- perf(gaussian): drop the sqrt round-trip from variance-space operations
+
+### Refactor
+
+- refactor: unify convergence defaults, validate builders, clear dead code
+
+### Styling
+
+- style: make NaN rejection explicit in score_sigma validation
+
+### Testing
+
+- test: pin the invariants that make filtered estimates trustworthy
+
 ## 0.1.2 - 2026-06-12
 
 ### Bug Fixes
@@ -32,6 +117,10 @@ All notable changes to this project will be documented in this file.
 - feat(outcome): per-event score_sigma override on Outcome::Scored
 - feat(event_builder): expose scores_with_sigma fluent method
 
+### Miscellaneous Tasks
+
+- chore: Release trueskill-tt version 0.1.2
+
 ### Refactor
 
 - refactor: dedupe Game::likelihoods and likelihoods_scored via run_chain

CLAUDE.md

@@ -5,42 +5,96 @@ This file provides guidance to Claude Code (claude.ai/code) when working with co
 ## Commands
 
 ```bash
-cargo build                          # Build the library
-cargo test --lib                     # Run all library tests
-cargo test --lib <test_name>         # Run a single test by name
-cargo test --lib -- --nocapture      # Run tests with stdout output
-cargo clippy                         # Lint
-cargo bench                          # Run benchmarks (criterion)
+just test                            # Full suite across every feature combination CI checks
+just check                           # Fast inner loop: cargo test --features approx
+just lint                            # clippy, warnings denied
+just fmt                             # ALWAYS nightly — rustfmt.toml uses nightly-only options
+just determinism                     # Bit-identical posteriors at RAYON_NUM_THREADS 1/2/4/8
+just ci                              # Everything CI runs
+cargo test --lib <test_name>         # A single test by name
+cargo bench                          # Criterion benchmarks
 ```
 
-The `approx` feature enables `approx::AbsDiffEq` for `Gaussian`:
-```bash
-cargo test --features approx
-```
+**Run tests in release too.** `debug_assert!` is compiled out there, and that
+is where several defects have hidden — a debug-only run is not evidence.
+`just test` includes a release job.
+
+### Feature flags
+
+- `approx` — `approx::AbsDiffEq` etc. for `Gaussian`. Most numerical goldens need it.
+- `rayon` — opt-in parallel within-slice sweep and per-slice query passes.
 
 ## Architecture
 
-This is a Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py) — a Bayesian skill rating system that tracks skill evolution over time using Gaussian message passing.
+A Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py):
+Bayesian skill rating that infers skill at every point in time, propagating
+evidence both forward and backward across a history.
 
 ### Data flow
 
 ```
-History  →  Batch[]  →  Game[]  →  teams/players
+History  →  TimeSlice[]  →  Event[]  →  Team[] → Item[]
+                                  ↓
+                     Game (factor graph) → Schedule → BuiltinFactor[]
 ```
 
-- **`History`** (`history.rs`) — top-level container. Organizes games by time into `Batch`es, runs forward/backward message passing across batches, and exposes `learning_curves()` and `log_evidence()`.
-- **`Batch`** (`batch.rs`) — all games at a single time step. Runs `iteration()` to update skill estimates via `Game::posteriors()`, collecting `Skill` distributions per player.
-- **`Game`** (`game.rs`) — a single match. Given teams (slices of `Gaussian`), computes posterior skill distributions using Gaussian factor graphs and `message.rs` helpers.
-- **`Agent`** (`agent.rs`) — wraps a `Player` with temporal state (`last_time`, `message`). `receive()` applies time-decay (`gamma`) when the player reappears after a gap.
-- **`Player`** (`player.rs`) — static configuration: prior `Gaussian`, `beta` (performance noise), `gamma` (skill drift per time unit).
-- **`Gaussian`** (`gaussian.rs`) — core probability type. Stored as natural parameters (`pi = 1/sigma²`, `tau = mu/sigma²`). Arithmetic ops implement message multiplication/division in the factor graph.
-- **`message.rs`** — `TeamMessage` and `DiffMessage`: intermediate factor graph messages used inside `Game`.
-- **`MarginFactor`** (`factor/margin.rs`) — Gaussian observation factor on a diff variable; engaged by `Outcome::Scored`.
-- **`lib.rs`** — exports the public API (`Game`, `Gaussian`, `History`, `Player`) and standalone functions (`quality()`, `pdf()`, `cdf()`, `erfc()`). Also defines global defaults: `MU=0.0`, `SIGMA=6.0`, `BETA=1.0`, `GAMMA=0.03`, `P_DRAW=0.0`, `EPSILON=1e-6`, `ITERATIONS=30`.
+- **`History`** (`history.rs`) — top level. Interns keys, groups events into
+  `TimeSlice`s by time, runs the forward/backward sweep in `converge()`, and
+  answers `learning_curves()`, `current_skill()`, `log_evidence()`,
+  `predict_quality()`, `predict_outcome()`. Built via `HistoryBuilder`.
+- **`TimeSlice`** (`time_slice.rs`) — all events at one time. Owns a
+  `SkillStore` and a `ScratchArena`; `iteration()` sweeps its events, using
+  `ColorGroups` to partition independent ones.
+- **`Event`** (`time_slice.rs`) — one match. `compute()` runs inference reading
+  skills immutably; `apply()` folds the result back. The split is what lets a
+  color group run in parallel with no `unsafe`.
+- **`Game`** (`game.rs`) — a single match's factor graph. `run_chain` builds the
+  diff chain between rank-adjacent teams and drives it to convergence.
+- **`Gaussian`** (`gaussian.rs`) — natural parameters (`pi = 1/sigma²`,
+  `tau = mu/sigma²`). `Mul`/`Div` are the EP product/cavity: pure adds and
+  subtracts. Variance-space ops (`Add`, `Sub`, `exclude`, `forget`) go through
+  `from_mv`/`variance()` and take no square root.
+- **`factor/`** — `TeamSumFactor`, `RankDiffFactor`, `TruncFactor` (ranked),
+  `MarginFactor` (scored), over a flat `VarStore`. `BuiltinFactor` dispatches
+  by enum rather than `dyn`.
+- **`Schedule`** (`schedule.rs`) — drives factor propagation. `EpsilonOrMax` is
+  the only implementation.
+- **`Competitor`** (`competitor.rs`) — per-history temporal state (`message`,
+  `last_time`). **`Rating`** (`rating.rs`) — static config (prior, `beta`, drift).
+- **`storage/`** — `SkillStore` (per slice) and `CompetitorStore` (per history),
+  both dense `Vec`s indexed by `Index`.
+- **`KeyTable`** (`key_table.rs`) — user key ↔ `Index`, both directions O(1).
+- **`Drift`** (`drift.rs`) / **`Time`** (`time.rs`) — traits. `Time` is a *trait*
+  (`i64`, `Untimed`), not an enum.
+- **`lib.rs`** — public exports, global defaults (`MU`, `SIGMA`, `BETA`,
+  `GAMMA`, `P_DRAW`, `EPSILON`, `ITERATIONS`), and the standalone `quality()`,
+  `cdf()`, `erfc()`.
 
-### Key design points
+### Invariants worth knowing
 
-- `History` uses `IndexMap<K>` (defined in `lib.rs`) to map arbitrary player keys to `Agent` state.
-- Convergence is measured by the maximum `delta()` across all skill distributions; iteration stops when below `EPSILON` or after `ITERATIONS` rounds.
-- The `approx` feature gates `AbsDiffEq` on `Gaussian` for use in tests — the feature is optional and only needed for approximate equality assertions.
-- `time` in `History`/`Batch` is currently an `f64`; the README notes it needs to become an enum to support richer temporal states.
+- **A tie needs `p_draw > 0`.** With `p_draw == 0.0` the truncation margin is
+  zero and the two-sided tie update evaluates `0/0`. Ingestion rejects such
+  events with `InferenceError::TieWithoutDrawProbability`. This includes
+  `Outcome::winner(w, n)` for `n >= 3`, which ties every loser.
+- **NaN is never convergence.** Comparisons against NaN are all false, so
+  `tuple_gt` reads NaN as "below epsilon". Use `step_converged` /
+  `step_is_finite`, never `!tuple_gt(..)` alone.
+- **Evidence accumulates in log space.** A linear product over a long diff
+  chain underflows to zero, and `ln(0)` is `-inf`.
+- **Colors are contiguous.** `recompute_color_groups` reorders events so each
+  color occupies one range; `ColorGroups::groups_are_contiguous` asserts it.
+- **The crate is `#![forbid(unsafe_code)]`.** Keep it that way.
+- **Ingestion order must not change the answer.** Events added one at a time
+  must converge to the same fixed point as the same events batched — see
+  `tests/ingestion_equivalence.rs`.
+
+### Testing notes
+
+- Numerical goldens are cross-validated against the Python/Julia reference.
+  Some are *convergence residuals*, not exact values; treat a small movement
+  as suspicious but check whether the new value is closer to the analytic
+  truth (symmetric fixtures converge to their prior mean exactly) before
+  assuming a regression.
+- `tests/degenerate_inputs.rs` covers empty/boundary/error paths,
+  `tests/ingestion_equivalence.rs` covers batching order, `tests/quality.rs`
+  covers N-group quality, `tests/determinism.rs` covers thread counts.

Cargo.toml

@@ -1,7 +1,30 @@
 [package]
 name = "trueskill-tt"
-version = "0.1.2"
+version = "0.3.0"
 edition = "2024"
+rust-version = "1.85"
+description = "TrueSkill Through Time: Bayesian skill rating that tracks how skill evolves over time, via Gaussian message passing"
+repository = "https://git.aceofba.se/logaritmisk/trueskill-tt"
+authors = ["Anders Olsson"]
+# Publishing is restricted to the private kellnr registry; this also makes
+# an accidental `cargo publish` to crates.io a hard error rather than a
+# irreversible mistake. Index is declared in `.cargo/config.toml`.
+publish = ["kellnr"]
+readme = "README.md"
+keywords = ["trueskill", "rating", "bayesian", "elo", "skill"]
+categories = ["algorithms", "science", "game-development"]
+license = "MIT OR Apache-2.0"
+# `examples/atp.csv` is a 48 MB tennis dataset — 99% of the packaged crate,
+# for a library whose source is 312 KB. `examples/atp.rs` opens it by
+# relative path at runtime, so excluding the data still compiles; the
+# example just needs the file fetched from the repo to run.
+exclude = [
+    "/docs",
+    "/benches/*.txt",
+    "/temp",
+    "/.gitea",
+    "/examples/atp.csv",
+]
 
 [lib]
 bench = false
@@ -22,6 +45,10 @@ harness = false
 name = "scored"
 harness = false
 
+[[bench]]
+name = "ingest"
+harness = false
+
 [dependencies]
 approx = { version = "0.5.1", optional = true }
 rayon = { version = "1", optional = true }
@@ -35,9 +62,14 @@ rayon = ["dep:rayon"]
 criterion = "0.5"
 plotters = { version = "0.3", default-features = false, features = ["svg_backend", "all_elements", "all_series"] }
 plotters-backend = "0.3"
+proptest = "1.11.0"
 time = { version = "0.3", features = ["parsing"] }
 trueskill-tt = { path = ".", features = ["approx"] }
 
+# Debug symbols in release are for `just flame` (cargo-flamegraph), which needs
+# them to symbolicate. Profile settings in a library are ignored by downstream
+# consumers, so these only affect local builds — this is deliberate, not an
+# oversight.
 [profile.release]
 debug = true
 

Justfile

@@ -1,4 +1,39 @@
 alias b := bench
+alias t := test
+
+# Run the full test suite across the feature combinations CI checks.
+test:
+    cargo test
+    cargo test --features approx
+    cargo test --features approx,rayon
+    cargo test --release --features approx
+
+# Fast inner-loop tests.
+check:
+    cargo test --features approx
+
+# Posteriors must be bit-identical across rayon worker counts.
+determinism:
+    #!/usr/bin/env bash
+    set -euo pipefail
+    for threads in 1 2 4 8; do
+        echo "== RAYON_NUM_THREADS=$threads =="
+        RAYON_NUM_THREADS=$threads cargo test --release \
+            --features approx,rayon --test determinism
+    done
+
+lint:
+    cargo clippy --all-targets --all-features -- -D warnings
+
+# Always nightly: rustfmt.toml uses nightly-only options.
+fmt:
+    cargo +nightly fmt
+
+fmt-check:
+    cargo +nightly fmt --check
+
+# Everything CI runs.
+ci: fmt-check lint test determinism
 
 store:
     cargo bench -- --save-baseline base
@@ -8,3 +43,49 @@ bench:
 
 flame:
     cargo flamegraph --root --example atp
+
+# ---------------------------------------------------------------------------
+# Release workflow
+#
+# Publishing goes to the private kellnr registry only: `Cargo.toml` sets
+# `publish = ["kellnr"]`, so an accidental `cargo publish` to crates.io is a
+# hard error rather than an irreversible mistake. The index is declared in the
+# committed `.cargo/config.toml`; the token is per-user and lives in
+# `~/.cargo/credentials.toml` (`cargo login --registry kellnr`).
+#
+#   Step 1:  just release-plan [level]   — dry run, no writes
+#   Step 2:  just release [level]        — bump, changelog, tag, publish, push
+#
+# LEVEL is the cargo-release bump level (default `minor`). On 0.x:
+#   minor -> breaking bump  (0.1.2 -> 0.2.0)   <- any public-API change
+#   patch -> additive only  (0.1.2 -> 0.1.3)
+#   major -> reserved for the 1.0.0 jump
+#
+# `release.toml` regenerates CHANGELOG.md with git-cliff in a pre-release hook
+# and keeps push = false; this recipe pushes last, after publish has succeeded.
+# ---------------------------------------------------------------------------
+
+# Dry-run preview of the next release. Inspect the version bump and the
+# "Publishing ..." line before running `just release`.
+release-plan level="minor":
+    cargo release {{level}}
+
+# Cut a release from a clean main: gate -> bump -> tag -> publish -> push.
+release level="minor":
+    #!/usr/bin/env bash
+    set -euo pipefail
+
+    if [[ "$(git branch --show-current)" != "main" ]]; then
+        echo "error: run 'just release' from the 'main' branch" >&2; exit 1
+    fi
+    if [[ -n "$(git status --porcelain)" ]]; then
+        echo "error: working tree is dirty — commit or stash first" >&2; exit 1
+    fi
+
+    # cargo-release only verify-compiles the packaged crate; it does not run the
+    # suite, and publishing is irreversible. Run the same gate CI does, which
+    # includes the release profile where debug_assert! is compiled out.
+    just ci
+
+    cargo release {{level}} --execute --no-confirm
+    git push --follow-tags

LICENSE-APACHE

@@ -0,0 +1,201 @@
+                              Apache License
+                        Version 2.0, January 2004
+                     http://www.apache.org/licenses/
+
+TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+1. Definitions.
+
+   "License" shall mean the terms and conditions for use, reproduction,
+   and distribution as defined by Sections 1 through 9 of this document.
+
+   "Licensor" shall mean the copyright owner or entity authorized by
+   the copyright owner that is granting the License.
+
+   "Legal Entity" shall mean the union of the acting entity and all
+   other entities that control, are controlled by, or are under common
+   control with that entity. For the purposes of this definition,
+   "control" means (i) the power, direct or indirect, to cause the
+   direction or management of such entity, whether by contract or
+   otherwise, or (ii) ownership of fifty percent (50%) or more of the
+   outstanding shares, or (iii) beneficial ownership of such entity.
+
+   "You" (or "Your") shall mean an individual or Legal Entity
+   exercising permissions granted by this License.
+
+   "Source" form shall mean the preferred form for making modifications,
+   including but not limited to software source code, documentation
+   source, and configuration files.
+
+   "Object" form shall mean any form resulting from mechanical
+   transformation or translation of a Source form, including but
+   not limited to compiled object code, generated documentation,
+   and conversions to other media types.
+
+   "Work" shall mean the work of authorship, whether in Source or
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+   copyright notice that is included in or attached to the work
+   (an example is provided in the Appendix below).
+
+   "Derivative Works" shall mean any work, whether in Source or Object
+   form, that is based on (or derived from) the Work and for which the
+   editorial revisions, annotations, elaborations, or other modifications
+   represent, as a whole, an original work of authorship. For the purposes
+   of this License, Derivative Works shall not include works that remain
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+
+   "Contribution" shall mean any work of authorship, including
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+2. Grant of Copyright License. Subject to the terms and conditions of
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+
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+   To apply the Apache License to your work, attach the following
+   boilerplate notice, with the fields enclosed by brackets "[]"
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+   comment syntax for the file format. We also recommend that a
+   file or class name and description of purpose be included on the
+   same "printed page" as the copyright notice for easier
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+
+Copyright [yyyy] [name of copyright owner]
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+Licensed under the Apache License, Version 2.0 (the "License");
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+	http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.

LICENSE-MIT

@@ -0,0 +1,19 @@
+Copyright (c) 2026 Anders Olsson
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.

README.md

@@ -71,6 +71,36 @@ let h = History::builder()
     .build();
 ```
 
+### Per-competitor drift
+
+A `History` has one drift model, but individual competitors can scale it.
+`Member::with_drift_scale(s)` multiplies the drift *variance* that competitor
+accumulates, so `s` is in the same units as `gamma`: `ConstantDrift(g)` at
+scale `s` behaves exactly as `ConstantDrift(g * s)` would, for that competitor
+alone.
+
+`0.0` pins a competitor still. That is what makes a **fixed reference point**
+expressible in the same graph as moving competitors — a bot at a known
+strength, a rating floor, a course difficulty:
+
+```rust
+let events = vec![Event {
+    time: 0,
+    teams: smallvec![
+        Team::with_members([Member::new("player")]),
+        // A course does not improve. Pin it, and the round's evidence
+        // lands on the player instead of being split between the two.
+        Team::with_members([Member::new("layout_7").with_drift_scale(0.0)]),
+    ],
+    outcome: Outcome::winner(0, 2),
+}];
+```
+
+Like `with_prior`, the scale is **competitor configuration captured at first
+appearance** — setting it on a key the history already knows has no effect. It
+must be finite and non-negative; ingestion otherwise fails with
+`InferenceError::InvalidParameter`.
+
 ## Scored outcomes
 
 Use `Outcome::scores([...])` when you have continuous per-team scores rather
@@ -96,8 +126,25 @@ h.converge().unwrap();
 
 - [x] Implement approx for Gaussian
 - [x] Add more tests from `TrueSkillThroughTime.jl`
-- [ ] Add tests for `quality()` (Use [sublee/trueskill](https://github.com/sublee/trueskill/tree/master) as reference)
-- [ ] Benchmark Batch::iteration()
-- [ ] Time needs to be an enum so we can have multiple states (see `batch::compute_elapsed()`)
-- [ ] Add examples (use same TrueSkillThroughTime.(py|jl))
-- [ ] Add Observer (see [argmin](https://docs.rs/argmin/latest/argmin/core/trait.Observe.html) for inspiration)
+- [x] Generalise a time axis — `Time` is now a trait (`Untimed`, `i64`), not an enum
+- [x] Add examples (`examples/atp.rs`, `examples/scored.rs`)
+- [x] Add Observer (`Observer` / `NullObserver`)
+- [x] Benchmark the inference loop (`benches/batch.rs`, `benches/history_converge.rs`, `benches/ingest.rs`)
+- [ ] Cross-check `quality()` against [sublee/trueskill](https://github.com/sublee/trueskill/tree/master) — N-group support works and is covered by invariants, but no reference values are asserted
+
+## License
+
+Licensed under either of
+
+- Apache License, Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or
+  <http://www.apache.org/licenses/LICENSE-2.0>)
+- MIT license ([LICENSE-MIT](LICENSE-MIT) or
+  <http://opensource.org/licenses/MIT>)
+
+at your option.
+
+### Contribution
+
+Unless you explicitly state otherwise, any contribution intentionally submitted
+for inclusion in the work by you, as defined in the Apache-2.0 license, shall be
+dual licensed as above, without any additional terms or conditions.

benches/batch.rs

@@ -36,7 +36,7 @@ fn criterion_benchmark(criterion: &mut Criterion) {
     let kinds = vec![EventKind::Ranked; composition.len()];
 
     let mut time_slice = TimeSlice::new(1, P_DRAW, ConvergenceOptions::default());
-    time_slice.add_events(composition, results, weights, kinds, &agents);
+    time_slice.add_events(composition, Some(results), Some(weights), kinds, &agents);
 
     criterion.bench_function("Batch::iteration", |b| {
         b.iter(|| time_slice.iteration(0, &agents))

benches/ingest.rs

@@ -0,0 +1,62 @@
+//! Ingestion cost: one event per call versus one batched call.
+//!
+//! The rest of the suite only measures batched construction, which is why a
+//! quadratic in the incremental path went unnoticed — `record_winner` and
+//! `event(..).commit()` each ingest a single event, so a caller looping over a
+//! match feed takes that path.
+
+use std::hint::black_box;
+
+use criterion::{BenchmarkId, Criterion, criterion_group, criterion_main};
+use smallvec::smallvec;
+use trueskill_tt::{Event, History, Member, Outcome, Team};
+
+fn events(n: usize, time: i64) -> Vec<Event<i64, String>> {
+    (0..n)
+        .map(|i| Event {
+            time,
+            teams: smallvec![
+                Team::with_members([Member::new(format!("p{}", 2 * i))]),
+                Team::with_members([Member::new(format!("p{}", 2 * i + 1))]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        })
+        .collect()
+}
+
+fn bench_ingest(c: &mut Criterion) {
+    let mut group = c.benchmark_group("ingest");
+
+    for n in [250usize, 500, 1000] {
+        group.bench_with_input(BenchmarkId::new("one-at-a-time", n), &n, |b, &n| {
+            b.iter_batched(
+                || events(n, 0),
+                |evs| {
+                    let mut h: History<i64, _, _, String> = History::builder_with_key().build();
+                    for ev in evs {
+                        h.add_events(std::iter::once(ev)).unwrap();
+                    }
+                    black_box(h.time_slices_len())
+                },
+                criterion::BatchSize::SmallInput,
+            );
+        });
+
+        group.bench_with_input(BenchmarkId::new("single-batch", n), &n, |b, &n| {
+            b.iter_batched(
+                || events(n, 0),
+                |evs| {
+                    let mut h: History<i64, _, _, String> = History::builder_with_key().build();
+                    h.add_events(evs).unwrap();
+                    black_box(h.time_slices_len())
+                },
+                criterion::BatchSize::SmallInput,
+            );
+        });
+    }
+
+    group.finish();
+}
+
+criterion_group!(benches, bench_ingest);
+criterion_main!(benches);

cliff.toml

@@ -44,6 +44,11 @@ split_commits = false
 # Assigns commits to groups.
 # Optionally sets the commit's scope and can decide to exclude commits from further processing.
 commit_parsers = [
+    # Must precede the type parsers below: a `feat!`/`fix!`/`refactor!` subject
+    # matches those too, and the first match wins. Without this a breaking
+    # change renders as an ordinary line of its own type.
+    { message = "^[a-z]+(\\(.+\\))?!:", group = "Breaking Changes" },
+    { body = "BREAKING CHANGE", group = "Breaking Changes" },
     { message = "^feat", group = "Features" },
     { message = "^fix", group = "Bug Fixes" },
     { message = "^doc", group = "Documentation" },

docs/superpowers/specs/2026-08-27-filtered-estimates-design.md

@@ -0,0 +1,342 @@
+# Filtered (Forward-Only) Estimates
+
+Closes [#19](https://git.aceofba.se/logaritmisk/trueskill-tt/issues/19).
+
+## Summary
+
+`HistoryBuilder::online(true)` is inert. It flips a flag that reaches
+`Item::within_prior` (`src/time_slice.rs:70-71`), which reads
+`Skill.online` (`src/time_slice.rs:25`) — a field initialised to `N_INF`
+(`src/time_slice.rs:41`) and never assigned anywhere. The online path
+therefore builds every rating from the improper Gaussian, and
+`log_evidence()` silently reports `n × ln(0.5)`: every game scored as a
+coin flip, finite and plausible-looking.
+
+This spec replaces the field and the flag with a **read-only forward-only
+pass** over the converged history, exposed as three new public methods.
+The pass reuses the production within-slice sweep verbatim rather than
+reimplementing inference, and stores nothing on `Skill`.
+
+## Background
+
+### Why a stored field cannot hold this quantity
+
+The issue proposes populating `skill.online` during the forward pass,
+alongside `new_forward_info` (`src/time_slice.rs:576`). That would not
+work, and understanding why determines the whole design.
+
+`new_forward_info` sets `skill.forward` from
+`agents[a].receive_for_elapsed(...)`, whose `message` was written by the
+previous slice's `forward_prior_out` (`src/time_slice.rs:549`):
+
+```rust
+skill.forward * skill.likelihood
+```
+
+`History::iteration` (`src/history.rs:255`) alternates a backward sweep
+over slices and a forward sweep. From the second iteration onward, the
+`skill.likelihood` feeding that message has already absorbed backward
+information from the preceding backward sweep. So after `converge()`,
+**`skill.forward` is a smoothed quantity, not a filtering one** — and any
+field written from it inherits the same contamination on every sweep
+after the first.
+
+### The neighbouring trap
+
+The same reasoning applies to the existing `forward: bool` parameter on
+`log_evidence_internal` (`src/history.rs:395`). It is a genuine filtering
+quantity only on a history that has never been converged. That is why the
+test at `src/history.rs:1183` can assert
+
+```rust
+assert_ulps_eq!(trueskill_log_evidence, trueskill_log_evidence_online, epsilon = 1e-6);
+```
+
+— the fixture is never converged, so the forward message still equals the
+cavity prior. (Note also that the local binding is named `..._online`
+while the flag it passes is `forward`; the two senses were already
+muddled.)
+
+Fixing `forward: bool` is **out of scope** here; see *Out-of-scope
+follow-ups*.
+
+### Why this is worth implementing rather than deleting
+
+The forward-only estimate has a second consumer beyond prequential model
+comparison. `learning_curve()` returns post-convergence posteriors, so
+every point is smoothed — the estimate at a given date incorporates
+rounds played years later. On [ustat](https://git.aceofba.se/logaritmisk/ustat)'s
+real data (prior μ=0, σ=6) that produces curves which start already
+spread apart and barely move:
+
+```
+player          first point            final point
+Eskil           mu +3.72  sigma 1.17   mu +4.61  sigma 1.21
+Anders Olsson   mu +1.61  sigma 0.90   mu +1.16  sigma 0.82
+LUDVIGSSON      mu -2.09  sigma 1.08   mu -2.61  sigma 1.13
+Anners          mu -2.85  sigma 1.27   mu -2.86  sigma 1.26
+```
+
+σ at the *first* plotted point is 0.90–1.60 against a prior of 6.00. A
+caller cannot reconstruct the filtered view from the public API today
+except by refitting over `events[0..k]` for every k — O(n²) fits for
+something one forward pass already computes.
+
+## Scope
+
+### What ships
+
+1. A read-only forward-only pass on `History`, walking slices in time
+   order and carrying its own forward messages.
+2. Three public methods: `filtered_log_evidence`,
+   `filtered_learning_curves`, `filtered_learning_curve`.
+3. Removal of `Skill.online`, `History.online`, `HistoryBuilder.online`,
+   `HistoryBuilder::online()`, and the `online: bool` parameter threaded
+   through `Item::within_prior`, `Event::within_priors`, and
+   `TimeSlice::log_evidence`.
+4. `#[derive(Clone)]` on `Event`, `Team`, `Item`; `iterate_to_convergence`
+   loses its `#[cfg(test)]` gate.
+5. A CHANGELOG entry recording the API break.
+
+### What does not ship
+
+- No change to `log_evidence()`, `log_evidence_for()`, `learning_curve()`,
+  `learning_curves()`, or `current_skill()`. Their values are unchanged
+  by this work.
+- No fix to the `forward: bool` flag described above.
+- No caching of pass results. Each call runs a full pass; the doc
+  comments say so.
+- No `rayon` parallelism across slices — the pass is sequentially
+  dependent by construction.
+- No prior-predictive accessor. The pass computes the pre-event forward
+  message internally, but only the filtered posterior is exposed until a
+  second caller needs otherwise.
+
+## Design
+
+### Naming
+
+`filtered_*`, not `online_*`. "Filtered" is the standard term for the
+forward-only estimate, and the crate already uses "online" for a second,
+unrelated thing — incremental ingestion, which `benches/baseline.txt:128`
+calls the "online-add" path. Two senses of one word in one crate is how
+the present bug reads as plausible.
+
+### The pass
+
+```rust
+pub(crate) struct FilteredStep {
+    log_evidence: f64,
+    posteriors: Vec<(Index, Gaussian)>,
+}
+
+fn filtered_pass(&self) -> Vec<(T, FilteredStep)>
+```
+
+`posteriors` doubles as the outgoing forward message: the scratch sweep never
+writes `backward`, so it stays `N_INF`, and `Skill::posterior()` and
+`forward_prior_out` are then the same product.
+
+Walk `self.time_slices` in order, carrying
+`messages: HashMap<Index, Gaussian>` — the forward message out of each
+competitor's most recent appearance. For each slice:
+
+1. **Build a scratch clone.** Same `time`, `p_draw`, `convergence`, and
+   cloned `events` with every `item.likelihood` reset to `N_INF`. Fresh
+   `SkillStore` in which, for each agent present in the real slice:
+
+   ```rust
+   forward = match messages.get(&agent) {
+       Some(msg) => msg.forget(rating.drift.variance_for_elapsed(skill.elapsed)),
+       None      => rating.prior,
+   }
+   backward   = N_INF
+   likelihood = N_INF
+   elapsed    = skill.elapsed          // copied from the real slice
+   ```
+
+   This mirrors `Competitor::receive_for_elapsed` (`src/competitor.rs:39`)
+   exactly, including its `message != N_INF` fallback to the prior.
+   `skill.elapsed` is reused rather than recomputed: it is maintained by
+   `add_events_with_prior` across out-of-order ingestion, and production
+   convergence already trusts it.
+
+2. **Run the real sweep.** `scratch.iterate_to_convergence(agents)`
+   (`src/time_slice.rs:516`), unmodified. Fidelity comes from reusing the
+   production path rather than a parallel reimplementation — in
+   particular, a competitor appearing in two events at the same time is
+   handled by the same within-slice EP that `converge()` uses, not
+   approximated the way the current `online`/`forward` evidence paths are
+   (they run each event independently and sum).
+
+3. **Harvest.** With `backward == N_INF` acting as the multiplicative
+   identity, `Skill::posterior()` is exactly forward × likelihood — the
+   filtered posterior. Slice evidence is
+   `scratch.events.iter().map(|e| e.log_evidence).sum()`; `apply`
+   (`src/time_slice.rs:162`) writes that field on every event during the
+   sweep.
+
+4. **Carry forward.** `messages.insert(a, scratch.forward_prior_out(&a))`
+   for each agent in the slice.
+
+Steps 1–4 are the forward half of `History::iteration`
+(`src/history.rs:283-297`) with the backward half never run. The pass
+touches no field of `self`.
+
+### Public API
+
+```rust
+impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
+    pub fn filtered_log_evidence(&self) -> f64;
+    pub fn filtered_learning_curves(&self) -> HashMap<K, Vec<(T, Gaussian)>>;
+    pub fn filtered_learning_curve<Q>(&self, key: &Q) -> Vec<(T, Gaussian)>
+    where
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized;
+}
+```
+
+All take `&self` — the pass mutates nothing. Shapes deliberately mirror
+`learning_curve` / `learning_curves` (`src/history.rs:325`, `:381`) so a
+caller can plot smoothed and filtered curves on one chart with the same
+handling code.
+
+`filtered_learning_curve` runs the same full pass as the plural form and
+collects one key; the cost is identical, only the collection differs.
+Callers wanting several keys should use the plural form. Documented on
+both methods.
+
+Because the pass carries its own messages and re-runs inference, its
+results **do not depend on whether `converge()` has been called**. That
+is the property a stored field cannot have, and it is asserted as a test.
+
+### Removal inventory
+
+| Location | Change |
+|---|---|
+| `src/time_slice.rs:25` | delete `pub(crate) online: Gaussian` |
+| `src/time_slice.rs:41` | delete `online: N_INF` from `Default` |
+| `src/time_slice.rs:62,70-73` | drop `online` param and its branch from `Item::within_prior` |
+| `src/time_slice.rs:110,120` | drop `online` param from `Event::within_priors` |
+| `src/time_slice.rs:585,597,626,634` | drop `online` param from `TimeSlice::log_evidence`; `online \|\| forward` becomes `forward` |
+| `src/history.rs:32,63,138,158,174,199,226` | delete the two `online` field declarations (`:32`, `:199`) and the five struct-literal copies |
+| `src/history.rs:90-93` | delete `HistoryBuilder::online()` |
+| `src/history.rs:402,410` | drop the `self.online` argument |
+| `src/history.rs:1183-1189` | the `..._online` assertion becomes a `forward`-flag assertion; rename the binding to match what it tests |
+
+`Skill` loses 16 bytes, which is a small independent win for #17.
+
+## Testing strategy
+
+Every new test is mutation-proved before it counts: break the production
+line it names, watch it fail for the *right* assertion, restore. A test
+never observed failing is not evidence.
+
+### The red test
+
+On the issue's own fixture — five 1v1 games, same winner each time —
+`filtered_log_evidence()` must land strictly between the two known
+endpoints:
+
+```
+5 × ln(0.5) = -3.4657...   (today's inert value)
+            <  filtered
+            <  -0.4012...  (batch / smoothed evidence)
+```
+
+Two-sided, so neither "still inert" nor "accidentally smoothed" can pass.
+The lower bound is right for a real reason: game one genuinely *is* a
+coin flip under filtering, games two through five are not.
+
+### Invariants
+
+1. **Invariant to `converge()`** — `filtered_log_evidence()` and
+   `filtered_learning_curves()` agree before and after `converge()`. This
+   is exactly what `skill.forward` fails, and what makes a stored field
+   the wrong mechanism.
+
+   Agreement is to tolerance, not bit-identity, and the reason is worth
+   recording. `iteration` calls `recompute_color_groups`
+   (`src/time_slice.rs:369`) only when `from == 0`, so a slice built by
+   repeated appends keeps insertion order until the first `converge()`
+   reorders it. The scratch clone inherits whichever order it finds, and
+   greedy coloring over a permuted input can group differently, giving a
+   different within-slice sweep order — same EP fixed point, different
+   path to it. Follow the house pattern in
+   `tests/ingestion_equivalence.rs`: converge tightly (`max_iter: 2_000`,
+   `epsilon: 1e-12`) and compare within `1e-8`.
+2. **Invariant to ingestion order** — events added one at a time produce
+   the same filtered results as the same events batched. Extends the
+   existing invariant in `tests/ingestion_equivalence.rs`.
+3. **Single-slice exactness** — for a history with one time slice there
+   is no future to propagate back, so filtered results equal smoothed
+   results exactly.
+4. **Uncertainty ordering** — for a competitor with many later games, σ
+   at the first filtered point is greater than σ at the first smoothed
+   point, and less than the prior σ. This is the ustat complaint restated
+   as an assertion.
+5. **Degenerate inputs** — empty history yields `0.0` and empty maps;
+   unknown key yields an empty curve. Added to
+   `tests/degenerate_inputs.rs`.
+
+### Regression net
+
+The existing suite must be unchanged by the removals: `log_evidence()`,
+`log_evidence_for()`, and every numerical golden keep their current
+values, since the default `online` was already `false` and the flag was
+inert.
+
+## Verification gates
+
+- `just test` — full matrix, including the release job. `debug_assert!`
+  is compiled out in release, and that is where defects in this crate
+  have hidden before.
+- `just lint` — clippy, warnings denied.
+- `just fmt` — nightly.
+- `just determinism` — the new pass must not perturb bit-identical
+  posteriors across `RAYON_NUM_THREADS` 1/2/4/8.
+- `#![forbid(unsafe_code)]` stays.
+
+## Risks
+
+- **Clone cost.** One slice's events are cloned per slice visited. At
+  ustat scale this is negligible, but the pass is O(events) allocation on
+  top of O(events) inference. Accepted: fidelity to the production sweep
+  is worth more than avoiding the clone, and no caller is on a hot path.
+- **`iterate_to_convergence` leaving test-only status.** Its doc comment
+  claims "only used by tests"; that comment must be updated, or it
+  becomes the next piece of load-bearing prose that is quietly false.
+- **Event order is inherited, not normalised.** The scratch clone takes
+  the real slice's current event order, which differs pre- and
+  post-`converge()` for incrementally-ingested slices (see *Invariants*).
+  Results agree to within convergence tolerance rather than exactly.
+  Normalising the order in the scratch builder would buy bit-identity at
+  the cost of diverging from what the real sweep does; not worth it.
+
+  **Measured after implementation, this risk is smaller than stated.**
+  Flipping the scratch's `color_groups_dirty` from `true` to `false`
+  switches it between the grouped sweep (`sweep_color_groups`) and the
+  sequential fallback across its entire convergence loop — a far larger
+  perturbation than a permuted event order — and the ingestion-order
+  invariance test stays green at `1e-8` under `max_iter: 2_000`,
+  `epsilon: 1e-12`. EP reaches the same fixed point regardless of sweep
+  order once driven far enough. The tolerance caveat is correct but
+  conservative. Note the flag itself is load-bearing: with it `false` the
+  scratch would take the sequential path always, diverging from the
+  production sweep it exists to mirror.
+- **Divergence risk.** If `TimeSlice`'s sweep gains state that the
+  scratch construction does not initialise, the pass silently reads a
+  default. The scratch builder must construct `Skill` field-by-field
+  rather than via `..Default::default()`, so adding a field to `Skill`
+  is a compile error here rather than a silent wrong answer.
+
+## Out-of-scope follow-ups
+
+File as separate issues:
+
+1. **`forward: bool` is only a filtering quantity pre-convergence**
+   (`src/history.rs:395`). Either document the constraint or fold the
+   flag into the new pass and delete it.
+2. **`log_evidence` takes `&mut self`** (`src/history.rs:416`) but
+   mutates nothing. The new `filtered_*` methods take `&self`; the
+   asymmetry is worth removing.

release.toml

@@ -1,2 +1,6 @@
-publish = false
+# Publish to the registry named in Cargo.toml's `publish` list (kellnr).
+publish = true
+# Hold off pushing until tags and publish have both succeeded; `just release`
+# pushes last.
+push = false
 pre-release-hook = ["sh", "-c", "git cliff -o CHANGELOG.md --tag {{version}} && git add CHANGELOG.md"]

src/color_group.rs

@@ -26,39 +26,75 @@ pub(crate) struct ColorGroups {
 }
 
 impl ColorGroups {
-    #[allow(dead_code)]
     pub(crate) fn new() -> Self {
         Self::default()
     }
 
-    #[allow(dead_code)]
-    pub(crate) fn n_colors(&self) -> usize {
-        self.groups.len()
-    }
-
-    #[allow(dead_code)]
     pub(crate) fn is_empty(&self) -> bool {
         self.groups.is_empty()
     }
 
-    /// Total event count across all colors.
-    #[allow(dead_code)]
+    /// Number of distinct colors in the partition. Test-only.
+    #[cfg(test)]
+    pub(crate) fn n_colors(&self) -> usize {
+        self.groups.len()
+    }
+
+    /// Total event count across all colors. Test-only.
+    #[cfg(test)]
     pub(crate) fn total_events(&self) -> usize {
         self.groups.iter().map(|g| g.len()).sum()
     }
 
     /// Contiguous index range for one color after events have been reordered
     /// into color-contiguous positions by `TimeSlice::recompute_color_groups`.
-    #[allow(dead_code)]
     pub(crate) fn color_range(&self, color_idx: usize) -> std::ops::Range<usize> {
         let group = &self.groups[color_idx];
         if group.is_empty() {
             return 0..0;
         }
+
         let start = *group.first().unwrap();
         let end = *group.last().unwrap() + 1;
+
+        debug_assert_eq!(
+            end - start,
+            group.len(),
+            "color {color_idx} is not contiguous; its range would overlap other colors"
+        );
+
         start..end
     }
+
+    /// Whether every color occupies a contiguous, ascending range of event
+    /// indices, and no two colors overlap.
+    ///
+    /// The parallel sweep derives one `&mut` sub-slice per color from these
+    /// ranges and relies on them being disjoint. That disjointness is what
+    /// makes concurrent writes to distinct skills sound, so it is checked
+    /// rather than assumed.
+    pub(crate) fn groups_are_contiguous(&self) -> bool {
+        let mut expected_start = 0;
+
+        for group in &self.groups {
+            if group.is_empty() {
+                continue;
+            }
+
+            let ascending_run = group
+                .iter()
+                .enumerate()
+                .all(|(offset, &idx)| idx == group[0] + offset);
+
+            if !ascending_run || group[0] != expected_start {
+                return false;
+            }
+
+            expected_start += group.len();
+        }
+
+        true
+    }
 }
 
 /// Compute color groups greedily.
@@ -67,7 +103,6 @@ impl ColorGroups {
 /// `Index` values that event touches. The returned `ColorGroups` has one
 /// inner `Vec<usize>` per color, containing event indices in the order
 /// they were assigned.
-#[allow(dead_code)]
 pub(crate) fn color_greedy<I, F>(n_events: usize, index_set: F) -> ColorGroups
 where
     F: Fn(usize) -> I,

src/competitor.rs

@@ -1,5 +1,4 @@
 use crate::{
-    N_INF,
     drift::{ConstantDrift, Drift},
     gaussian::Gaussian,
     rating::Rating,
@@ -13,7 +12,14 @@ use crate::{
 #[derive(Debug)]
 pub struct Competitor<T: Time = i64, D: Drift<T> = ConstantDrift> {
     pub rating: Rating<T, D>,
-    pub message: Gaussian,
+    /// The forward message carried from this competitor's last appearance, or
+    /// `None` before they have appeared anywhere.
+    ///
+    /// Previously an improper `N_INF` served as the unset sentinel, which made
+    /// "no message yet" indistinguishable from "a legitimately improper
+    /// message" at the type level and required every reader to know the
+    /// convention.
+    pub message: Option<Gaussian>,
     pub last_time: Option<T>,
 }
 
@@ -21,14 +27,16 @@ impl<T: Time, D: Drift<T>> Competitor<T, D> {
     /// Compute the message received at time `now`, with drift accumulated
     /// from `self.last_time` (if any) to `now`.
     pub(crate) fn receive(&self, now: &T) -> Gaussian {
-        if self.message != N_INF {
+        match self.message {
+            Some(message) => {
                 let elapsed_variance = match &self.last_time {
-                Some(last) => self.rating.drift.variance_delta(last, now),
+                    Some(last) => self.rating.drift_variance_delta(last, now),
                     None => 0.0,
                 };
-            self.message.forget(elapsed_variance)
-        } else {
-            self.rating.prior
+
+                message.forget(elapsed_variance)
+            }
+            None => self.rating.prior,
         }
     }
 
@@ -37,11 +45,9 @@ impl<T: Time, D: Drift<T>> Competitor<T, D> {
     /// Used in convergence sweeps where the elapsed was cached at slice-construction time
     /// and should not be recomputed from `last_time` (which may have shifted).
     pub(crate) fn receive_for_elapsed(&self, elapsed: i64) -> Gaussian {
-        if self.message != N_INF {
-            self.message
-                .forget(self.rating.drift.variance_for_elapsed(elapsed))
-        } else {
-            self.rating.prior
+        match self.message {
+            Some(message) => message.forget(self.rating.drift_variance_for_elapsed(elapsed)),
+            None => self.rating.prior,
         }
     }
 }
@@ -50,7 +56,7 @@ impl Default for Competitor<i64, ConstantDrift> {
     fn default() -> Self {
         Self {
             rating: Rating::default(),
-            message: N_INF,
+            message: None,
             last_time: None,
         }
     }
@@ -63,7 +69,7 @@ where
     C: Iterator<Item = &'a mut Competitor<T, D>>,
 {
     for c in competitors {
-        c.message = N_INF;
+        c.message = None;
         if last_time {
             c.last_time = None;
         }

src/convergence.rs

@@ -38,7 +38,6 @@ pub struct ConvergenceReport {
     pub log_evidence: f64,
     pub converged: bool,
     pub per_iteration_time: SmallVec<[Duration; 32]>,
-    pub slices_skipped: usize,
 }
 
 #[cfg(test)]

src/error.rs

@@ -1,6 +1,7 @@
 use std::fmt;
 
 #[derive(Debug, Clone, PartialEq)]
+#[non_exhaustive]
 pub enum InferenceError {
     /// Expected and actual lengths of some array-shaped input differ.
     MismatchedShape {
@@ -8,15 +9,35 @@ pub enum InferenceError {
         expected: usize,
         got: usize,
     },
+    /// An `Outcome` of the wrong variant was supplied for the requested inference.
+    WrongOutcomeKind {
+        context: &'static str,
+        expected: &'static str,
+        got: &'static str,
+    },
     /// A probability value is outside `[0, 1]`.
     InvalidProbability { value: f64 },
     /// A scalar parameter is outside its valid range.
     InvalidParameter { name: &'static str, value: f64 },
+    /// An event contains tied teams, but the draw probability is zero.
+    ///
+    /// A zero draw probability asserts that draws cannot occur, so a tied
+    /// result has no representable likelihood. Configure a positive `p_draw`
+    /// (via `HistoryBuilder::p_draw` or `GameOptions::p_draw`) to admit ties.
+    TieWithoutDrawProbability { teams: (usize, usize) },
     /// Convergence exceeded `max_iter` without falling below `epsilon`.
     ConvergenceFailed {
         last_step: (f64, f64),
         iterations: usize,
     },
+    /// Inference produced a non-finite value (NaN or infinity).
+    ///
+    /// Indicates numerical breakdown; the resulting skills are meaningless
+    /// and must not be treated as a converged estimate.
+    NonFiniteResult {
+        context: &'static str,
+        step: (f64, f64),
+    },
     /// Negative precision: a Gaussian with `pi < 0` slipped into an API call.
     NegativePrecision { pi: f64 },
 }
@@ -31,9 +52,29 @@ impl fmt::Display for InferenceError {
             } => {
                 write!(f, "{kind}: expected length {expected}, got {got}")
             }
+            Self::WrongOutcomeKind {
+                context,
+                expected,
+                got,
+            } => {
+                write!(f, "{context}: expected {expected}, got {got}")
+            }
             Self::InvalidProbability { value } => {
                 write!(f, "probability must be in [0, 1]; got {value}")
             }
+            Self::TieWithoutDrawProbability { teams } => {
+                write!(
+                    f,
+                    "teams {} and {} are tied, but p_draw is 0.0; set a positive draw probability to admit ties",
+                    teams.0, teams.1
+                )
+            }
+            Self::NonFiniteResult { context, step } => {
+                write!(
+                    f,
+                    "{context}: inference produced a non-finite result (step = {step:?})"
+                )
+            }
             Self::InvalidParameter { name, value } => {
                 write!(f, "{name} is invalid: {value}")
             }

src/event.rs

@@ -23,6 +23,7 @@ pub struct Team<K> {
 }
 
 impl<K> Team<K> {
+    #[must_use]
     pub fn new() -> Self {
         Self {
             members: SmallVec::new(),
@@ -44,13 +45,20 @@ impl<K> Default for Team<K> {
 
 /// One member of a team, identified by user key `K`.
 ///
-/// `weight` defaults to 1.0; a per-event `prior` can override the competitor's
-/// current skill estimate for this event only.
+/// `weight` applies per event and defaults to 1.0.
+///
+/// `prior` and `drift_scale` are **competitor configuration**, not per-event
+/// values: both are captured when the competitor is first created and ignored
+/// on every later appearance. Setting either on a key the history already knows
+/// has no effect.
 #[derive(Clone, Debug)]
 pub struct Member<K> {
     pub key: K,
     pub weight: f64,
     pub prior: Option<Gaussian>,
+    /// Multiplier on the drift *variance* this competitor accumulates.
+    /// `None` means 1.0.
+    pub drift_scale: Option<f64>,
 }
 
 impl<K> Member<K> {
@@ -59,6 +67,7 @@ impl<K> Member<K> {
             key,
             weight: 1.0,
             prior: None,
+            drift_scale: None,
         }
     }
 
@@ -67,10 +76,31 @@ impl<K> Member<K> {
         self
     }
 
+    /// Set this competitor's starting skill estimate.
+    ///
+    /// Captured at the competitor's first appearance; see the type docs.
     pub fn with_prior(mut self, prior: Gaussian) -> Self {
         self.prior = Some(prior);
         self
     }
+
+    /// Scale how fast this competitor drifts, relative to the history's drift.
+    ///
+    /// The scale multiplies the drift *variance*, so it is in the same units as
+    /// `gamma`: `ConstantDrift(g)` at `scale = s` behaves exactly as
+    /// `ConstantDrift(g * s)` would for this competitor alone.
+    ///
+    /// `0.0` pins the competitor still — useful for a reference point that
+    /// shares a scale with moving competitors but should not itself move: a bot
+    /// at a known strength, a rating floor, a course difficulty.
+    ///
+    /// Captured at the competitor's first appearance; see the type docs.
+    /// Must be finite and non-negative, or ingestion fails with
+    /// [`InferenceError::InvalidParameter`](crate::InferenceError::InvalidParameter).
+    pub fn with_drift_scale(mut self, scale: f64) -> Self {
+        self.drift_scale = Some(scale);
+        self
+    }
 }
 
 /// Convenience: a member is a user key with default weight 1.0 and no prior.
@@ -91,15 +121,18 @@ mod tests {
         assert_eq!(m.key, "alice");
         assert_eq!(m.weight, 1.0);
         assert!(m.prior.is_none());
+        assert!(m.drift_scale.is_none());
     }
 
     #[test]
     fn member_builder_methods_chain() {
         let m = Member::new("alice")
             .with_weight(0.5)
-            .with_prior(Gaussian::from_ms(20.0, 5.0));
+            .with_prior(Gaussian::from_ms(20.0, 5.0))
+            .with_drift_scale(0.0);
         assert_eq!(m.weight, 0.5);
         assert!(m.prior.is_some());
+        assert_eq!(m.drift_scale, Some(0.0));
     }
 
     #[test]

src/event_builder.rs

@@ -19,6 +19,14 @@ where
     history: &'h mut History<T, D, O, K>,
     event: Event<T, K>,
     current_team_idx: Option<usize>,
+    /// First validation failure seen while building, surfaced by `commit`.
+    ///
+    /// The setters return `Self` so the chain stays fluent; they cannot return
+    /// a `Result` without breaking that. Recording the failure and reporting it
+    /// at `commit` keeps the check enforced in release, where the previous
+    /// `debug_assert!` was compiled out and a mismatched event was ingested
+    /// silently.
+    error: Option<InferenceError>,
 }
 
 impl<'h, T, D, O, K> EventBuilder<'h, T, D, O, K>
@@ -37,6 +45,7 @@ where
                 outcome: Outcome::Ranked(SmallVec::new()),
             },
             current_team_idx: None,
+            error: None,
         }
     }
 
@@ -50,22 +59,36 @@ where
 
     /// Set per-member weights for the most recently added team.
     ///
-    /// Panics in debug builds if called before `.team(...)` or if the length
-    /// doesn't match the team's member count.
+    /// A length mismatch is recorded and returned by [`EventBuilder::commit`]
+    /// as `InferenceError::MismatchedShape`, in both debug and release. The
+    /// weights are not applied in that case, so a partially-weighted team
+    /// cannot reach the history.
+    ///
+    /// # Panics
+    ///
+    /// Panics if called before any `.team(...)`.
     pub fn weights<I: IntoIterator<Item = f64>>(mut self, weights: I) -> Self {
         let idx = self
             .current_team_idx
             .expect(".weights(...) called before any .team(...)");
+
         let ws: Vec<f64> = weights.into_iter().collect();
         let team = &mut self.event.teams[idx];
-        debug_assert_eq!(
-            ws.len(),
-            team.members.len(),
-            "weights length must match team size"
-        );
+
+        if ws.len() != team.members.len() {
+            self.error.get_or_insert(InferenceError::MismatchedShape {
+                kind: "weights",
+                expected: team.members.len(),
+                got: ws.len(),
+            });
+
+            return self;
+        }
+
         for (m, w) in team.members.iter_mut().zip(ws) {
             m.weight = w;
         }
+
         self
     }
 
@@ -103,7 +126,17 @@ where
     }
 
     /// Commit the event to the history.
+    ///
+    /// # Errors
+    ///
+    /// Returns the first validation failure recorded while building — see
+    /// [`EventBuilder::weights`] — otherwise forwards to
+    /// [`History::add_events`] and returns its errors.
     pub fn commit(self) -> Result<(), InferenceError> {
+        if let Some(error) = self.error {
+            return Err(error);
+        }
+
         self.history.add_events(std::iter::once(self.event))
     }
 }

src/factor/margin.rs

@@ -20,6 +20,7 @@ pub struct MarginFactor {
 }
 
 impl MarginFactor {
+    #[must_use]
     pub fn new(diff: VarId, m_obs: f64, sigma: f64) -> Self {
         debug_assert!(sigma > 0.0, "score sigma must be positive");
         Self {
@@ -64,9 +65,13 @@ impl Factor for MarginFactor {
     }
 }
 
+/// Density of the observed margin under the cavity, clamped to a positive
+/// floor so a far-out observation cannot underflow to `0.0` and make
+/// `log_evidence` `-inf`.
 fn cavity_evidence(cavity: Gaussian, m_obs: f64, sigma: f64) -> f64 {
     let combined_sigma = (cavity.sigma().powi(2) + sigma.powi(2)).sqrt();
-    pdf(m_obs, cavity.mu(), combined_sigma)
+
+    pdf(m_obs, cavity.mu(), combined_sigma).max(f64::MIN_POSITIVE)
 }
 
 #[cfg(test)]

src/factor/mod.rs

@@ -20,6 +20,7 @@ pub struct VarStore {
 }
 
 impl VarStore {
+    #[must_use]
     pub fn new() -> Self {
         Self::default()
     }
@@ -28,10 +29,12 @@ impl VarStore {
         self.marginals.clear();
     }
 
+    #[must_use]
     pub fn len(&self) -> usize {
         self.marginals.len()
     }
 
+    #[must_use]
     pub fn is_empty(&self) -> bool {
         self.marginals.is_empty()
     }
@@ -42,6 +45,7 @@ impl VarStore {
         id
     }
 
+    #[must_use]
     pub fn get(&self, id: VarId) -> Gaussian {
         self.marginals[id.0 as usize]
     }

src/factor/rank_diff.rs

@@ -5,12 +5,12 @@ use crate::factor::{Factor, VarId, VarStore};
 /// On each propagation:
 /// - Reads marginals at `team_a` and `team_b` (which already incorporate any
 ///   incoming messages from neighboring factors).
-/// - Computes `new_diff = team_a - team_b` (variance addition; see Gaussian::Sub).
+/// - Computes `new_diff = team_a - team_b` (variance addition; see `Gaussian::Sub`).
 /// - Writes the new marginal to `diff`.
 /// - Returns the delta against the previous diff value.
 ///
 /// This factor does NOT store an outgoing message; the diff variable is
-/// effectively replaced on each propagation. The TruncFactor on the same diff
+/// effectively replaced on each propagation. The `TruncFactor` on the same diff
 /// var holds the EP-divide message that produces the cavity.
 #[derive(Debug)]
 pub struct RankDiffFactor {

src/factor/trunc.rs

@@ -15,13 +15,14 @@ pub struct TruncFactor {
     pub diff: VarId,
     pub margin: f64,
     pub tie: bool,
-    /// Outgoing message to the diff variable (initial: N_INF, the EP identity).
+    /// Outgoing message to the diff variable (initial: `N_INF`, the EP identity).
     pub(crate) msg: Gaussian,
     /// Cached evidence (linear, not log) computed from the cavity on first propagation.
     pub(crate) evidence_cached: Option<f64>,
 }
 
 impl TruncFactor {
+    #[must_use]
     pub fn new(diff: VarId, margin: f64, tie: bool) -> Self {
         Self {
             diff,
@@ -72,12 +73,20 @@ impl Factor for TruncFactor {
 }
 
 /// P(diff > margin) for non-tie, P(|diff| < margin) for tie.
+///
+/// Clamped to a positive floor: for a near-certain outcome the tail rounds to
+/// exactly 0.0, and the `erfc` approximation used by `cdf` carries ~1e-7 error
+/// so it can even return slightly more than 1.0, making the difference
+/// negative. Either would send `log_evidence` to `-inf` or NaN and poison the
+/// sum across the whole history.
 fn cavity_evidence(diff: Gaussian, margin: f64, tie: bool) -> f64 {
-    if tie {
+    let raw = if tie {
         cdf(margin, diff.mu(), diff.sigma()) - cdf(-margin, diff.mu(), diff.sigma())
     } else {
         1.0 - cdf(margin, diff.mu(), diff.sigma())
-    }
+    };
+
+    raw.clamp(f64::MIN_POSITIVE, 1.0)
 }
 
 #[cfg(test)]

src/game.rs

@@ -37,10 +37,17 @@ impl DiffFactor {
         }
     }
 
-    pub(crate) fn evidence(&self) -> f64 {
+    /// Log of this link's cached evidence.
+    ///
+    /// Accumulating in log space keeps a long diff chain from underflowing:
+    /// each link contributes a probability in `(0, 1]`, so the linear product
+    /// over an n-team game decays geometrically and flushes to zero — and
+    /// `ln(0.0)` is `-inf` — well within the team counts a large free-for-all
+    /// reaches.
+    pub(crate) fn log_evidence(&self) -> f64 {
         match self {
-            Self::Trunc(f) => f.evidence_cached.unwrap_or(1.0),
-            Self::Margin(f) => f.evidence_cached.unwrap_or(1.0),
+            Self::Trunc(f) => f.evidence_cached.unwrap_or(1.0).ln(),
+            Self::Margin(f) => f.evidence_cached.unwrap_or(1.0).ln(),
         }
     }
 
@@ -81,18 +88,14 @@ impl Default for GameOptions {
 /// Owned variant of `Game` returned by public constructors.
 ///
 /// Unlike `Game<'a, T, D>` (which borrows its result/weights slices from
-/// History's internal state), `OwnedGame<T, D>` owns its inputs so it can
-/// be returned freely from public constructors.
+/// History's internal state), `OwnedGame<T, D>` owns the team ratings, so it
+/// can be returned freely from public constructors. The inference inputs
+/// themselves are not retained — nothing reads them back.
 #[derive(Debug)]
-#[allow(dead_code)]
 pub struct OwnedGame<T: Time, D: Drift<T>> {
     teams: Vec<Vec<Rating<T, D>>>,
-    result: Vec<f64>,
-    weights: Vec<Vec<f64>>,
-    p_draw: f64,
-    pub(crate) convergence: crate::ConvergenceOptions,
     pub(crate) likelihoods: Vec<Vec<Gaussian>>,
-    pub(crate) evidence: f64,
+    pub(crate) log_evidence: f64,
 }
 
 impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
@@ -104,24 +107,15 @@ impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
         convergence: crate::ConvergenceOptions,
     ) -> Self {
         let mut arena = ScratchArena::new();
-        let g = Game::ranked_with_arena(
-            teams.clone(),
-            &result,
-            &weights,
-            p_draw,
-            convergence,
-            &mut arena,
-        );
-        let likelihoods = g.likelihoods;
-        let evidence = g.evidence;
+
+        // `Game` takes the teams by value and is dropped here, so take the vec
+        // back out of it rather than handing it a clone.
+        let g = Game::ranked_with_arena(teams, &result, &weights, p_draw, convergence, &mut arena);
+
         Self {
-            teams,
-            result,
-            weights,
-            p_draw,
-            convergence,
-            likelihoods,
-            evidence,
+            teams: g.teams,
+            likelihoods: g.likelihoods,
+            log_evidence: g.log_evidence,
         }
     }
 
@@ -133,27 +127,24 @@ impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
         convergence: crate::ConvergenceOptions,
     ) -> Self {
         let mut arena = ScratchArena::new();
+
         let g = Game::scored_with_arena(
-            teams.clone(),
+            teams,
             &scores,
             &weights,
             score_sigma,
             convergence,
             &mut arena,
         );
-        let likelihoods = g.likelihoods;
-        let evidence = g.evidence;
+
         Self {
-            teams,
-            result: scores,
-            weights,
-            p_draw: 0.0,
-            convergence,
-            likelihoods,
-            evidence,
+            teams: g.teams,
+            likelihoods: g.likelihoods,
+            log_evidence: g.log_evidence,
         }
     }
 
+    #[must_use]
     pub fn posteriors(&self) -> Vec<Vec<Gaussian>> {
         self.likelihoods
             .iter()
@@ -162,8 +153,9 @@ impl<T: Time, D: Drift<T>> OwnedGame<T, D> {
             .collect()
     }
 
+    #[must_use]
     pub fn log_evidence(&self) -> f64 {
-        self.evidence.ln()
+        self.log_evidence
     }
 }
 
@@ -175,7 +167,7 @@ pub struct Game<'a, T: Time = i64, D: Drift<T> = crate::drift::ConstantDrift> {
     p_draw: f64,
     pub(crate) convergence: crate::ConvergenceOptions,
     pub(crate) likelihoods: Vec<Vec<Gaussian>>,
-    pub(crate) evidence: f64,
+    pub(crate) log_evidence: f64,
 }
 
 impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
@@ -222,7 +214,7 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             p_draw,
             convergence,
             likelihoods: Vec::new(),
-            evidence: 0.0,
+            log_evidence: 0.0,
         };
 
         this.likelihoods(arena);
@@ -261,7 +253,7 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             p_draw: 0.0,
             convergence,
             likelihoods: Vec::new(),
-            evidence: 0.0,
+            log_evidence: 0.0,
         };
 
         this.likelihoods_scored(arena, score_sigma);
@@ -355,7 +347,7 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             arena.lhood_lose[n_teams - 1] = pw_last - links[n_diffs - 1].msg();
         }
 
-        let evidence: f64 = links.iter().map(|l| l.evidence()).product();
+        let log_evidence: f64 = links.iter().map(DiffFactor::log_evidence).sum();
 
         // Inverse permutation: inv_buf[orig_i] = sorted_i.
         arena.inv_buf.resize(n_teams, 0);
@@ -371,10 +363,9 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             .map(|(orig_i, (players, weights))| {
                 let si = arena.inv_buf[orig_i];
                 let m = arena.lhood_win[si] * arena.lhood_lose[si];
-                let performance = players
-                    .iter()
-                    .zip(weights.iter())
-                    .fold(N00, |p, (player, &w)| p + (player.performance() * w));
+                // Already folded into `team_prior` at the top of the chain,
+                // indexed by sorted position.
+                let performance = arena.team_prior[si];
                 players
                     .iter()
                     .zip(weights.iter())
@@ -386,11 +377,11 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             })
             .collect::<Vec<_>>();
 
-        (evidence, likelihoods)
+        (log_evidence, likelihoods)
     }
 
     fn likelihoods(&mut self, arena: &mut ScratchArena) {
-        let (evidence, likelihoods) = self.run_chain(arena, |i, sort_buf, vars| {
+        let (log_evidence, likelihoods) = self.run_chain(arena, |i, sort_buf, vars| {
             let tie = self.result[sort_buf[i]] == self.result[sort_buf[i + 1]];
             let margin = if self.p_draw == 0.0 {
                 0.0
@@ -405,20 +396,21 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             let vid = vars.alloc(N_INF);
             DiffFactor::Trunc(TruncFactor::new(vid, margin, tie))
         });
-        self.evidence = evidence;
+        self.log_evidence = log_evidence;
         self.likelihoods = likelihoods;
     }
 
     fn likelihoods_scored(&mut self, arena: &mut ScratchArena, score_sigma: f64) {
-        let (evidence, likelihoods) = self.run_chain(arena, |i, sort_buf, vars| {
+        let (log_evidence, likelihoods) = self.run_chain(arena, |i, sort_buf, vars| {
             let m_obs = self.result[sort_buf[i]] - self.result[sort_buf[i + 1]];
             let vid = vars.alloc(N_INF);
             DiffFactor::Margin(MarginFactor::new(vid, m_obs, score_sigma))
         });
-        self.evidence = evidence;
+        self.log_evidence = log_evidence;
         self.likelihoods = likelihoods;
     }
 
+    #[must_use]
     pub fn posteriors(&self) -> Vec<Vec<Gaussian>> {
         self.likelihoods
             .iter()
@@ -432,12 +424,21 @@ impl<'a, T: Time, D: Drift<T>> Game<'a, T, D> {
             .collect::<Vec<_>>()
     }
 
+    #[must_use]
     pub fn log_evidence(&self) -> f64 {
-        self.evidence.ln()
+        self.log_evidence
     }
 }
 
 impl<T: Time, D: Drift<T>> Game<'_, T, D> {
+    /// # Errors
+    ///
+    /// - `InvalidProbability` if `options.p_draw` is outside `[0.0, 1.0)`.
+    /// - `MismatchedShape` if the outcome's rank count differs from `teams.len()`.
+    /// - `WrongOutcomeKind` if `outcome` is not `Outcome::Ranked`.
+    /// - `TieWithoutDrawProbability` if the outcome ties two teams while
+    ///   `p_draw` is zero: the truncation margin is then zero and the two-sided
+    ///   tie update evaluates `0/0`.
     pub fn ranked(
         teams: &[&[Rating<T, D>]],
         outcome: crate::Outcome,
@@ -458,11 +459,22 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
 
         let ranks = outcome
             .as_ranks()
-            .ok_or(crate::InferenceError::MismatchedShape {
-                kind: "Game::ranked requires Outcome::Ranked",
-                expected: 0,
-                got: 0,
+            .ok_or(crate::InferenceError::WrongOutcomeKind {
+                context: "Game::ranked",
+                expected: "Outcome::Ranked",
+                got: "Outcome::Scored",
             })?;
+
+        let tied = if options.p_draw == 0.0 {
+            crate::first_tied_pair(ranks)
+        } else {
+            None
+        };
+
+        if let Some(teams) = tied {
+            return Err(crate::InferenceError::TieWithoutDrawProbability { teams });
+        }
+
         let max_rank = ranks.iter().copied().max().unwrap_or(0) as f64;
         let result: Vec<f64> = ranks.iter().map(|&r| max_rank - r as f64).collect();
         let teams_owned: Vec<Vec<Rating<T, D>>> = teams.iter().map(|t| t.to_vec()).collect();
@@ -477,6 +489,12 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         ))
     }
 
+    /// # Errors
+    ///
+    /// - `InvalidParameter` if `options.score_sigma` is not strictly positive,
+    ///   or is NaN.
+    /// - `MismatchedShape` if the outcome's score count differs from `teams.len()`.
+    /// - `WrongOutcomeKind` if `outcome` is not `Outcome::Scored`.
     pub fn scored(
         teams: &[&[Rating<T, D>]],
         outcome: crate::Outcome,
@@ -497,10 +515,10 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         }
         let scores = outcome
             .as_scores()
-            .ok_or(crate::InferenceError::MismatchedShape {
-                kind: "Game::scored requires Outcome::Scored",
-                expected: 0,
-                got: 0,
+            .ok_or(crate::InferenceError::WrongOutcomeKind {
+                context: "Game::scored",
+                expected: "Outcome::Scored",
+                got: "Outcome::Ranked",
             })?
             .to_vec();
         let teams_owned: Vec<Vec<Rating<T, D>>> = teams.iter().map(|t| t.to_vec()).collect();
@@ -514,6 +532,12 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         ))
     }
 
+    /// # Errors
+    ///
+    /// Delegates to [`Game::ranked`] with default options, so it returns the
+    /// same errors — in practice `WrongOutcomeKind` for a non-ranked outcome,
+    /// or `TieWithoutDrawProbability` for a draw, since the default `p_draw`
+    /// applies rather than one you chose.
     pub fn one_v_one(
         a: &Rating<T, D>,
         b: &Rating<T, D>,
@@ -524,6 +548,10 @@ impl<T: Time, D: Drift<T>> Game<'_, T, D> {
         Ok((post[0][0], post[1][0]))
     }
 
+    /// # Errors
+    ///
+    /// Wraps each player in a one-member team and delegates to
+    /// [`Game::ranked`], so it returns the same errors.
     pub fn free_for_all(
         players: &[&Rating<T, D>],
         outcome: crate::Outcome,
@@ -730,8 +758,12 @@ mod tests {
         let a = p[0][0];
         let b = p[1][0];
 
-        assert_ulps_eq!(a, Gaussian::from_ms(24.999999, 6.469480), epsilon = 1e-6);
-        assert_ulps_eq!(b, Gaussian::from_ms(24.999999, 6.469480), epsilon = 1e-6);
+        // Two identical competitors drawing must land on their shared prior
+        // mean exactly, by symmetry. The reference transcription of 24.999999
+        // is that value rounded to six decimals; asserting it at epsilon 1e-6
+        // left no headroom. The root-free variance path now hits 25.0 exactly.
+        assert_ulps_eq!(a, Gaussian::from_ms(25.0, 6.469480), epsilon = 1e-6);
+        assert_ulps_eq!(b, Gaussian::from_ms(25.0, 6.469480), epsilon = 1e-6);
 
         let t_a = R::new(
             Gaussian::from_ms(25.0, 3.0),
@@ -1124,7 +1156,10 @@ mod tests {
             &GameOptions::default(),
         )
         .unwrap_err();
-        assert!(matches!(err, crate::InferenceError::MismatchedShape { .. }));
+        assert!(matches!(
+            err,
+            crate::InferenceError::WrongOutcomeKind { .. }
+        ));
     }
 
     #[test]

src/gaussian.rs

@@ -18,6 +18,7 @@ pub struct Gaussian {
 
 impl Gaussian {
     /// Construct from mean and standard deviation.
+    #[must_use]
     pub const fn from_ms(mu: f64, sigma: f64) -> Self {
         if sigma == f64::INFINITY {
             Self { pi: 0.0, tau: 0.0 }
@@ -35,6 +36,28 @@ impl Gaussian {
         }
     }
 
+    /// Construct from mean and *variance*, skipping the square-root round trip.
+    ///
+    /// `from_ms(mu, var.sqrt())` immediately squares the root away again to
+    /// recover `pi = 1/var`. Variance-combining operations (`Add`, `Sub`,
+    /// `exclude`, `forget`) work in variance space throughout, so they go
+    /// through here instead and never take a root.
+    #[inline]
+    pub(crate) fn from_mv(mu: f64, var: f64) -> Self {
+        if var == f64::INFINITY {
+            Self { pi: 0.0, tau: 0.0 }
+        } else if var == 0.0 {
+            // Point mass at mu; see `from_ms` for the tau convention.
+            Self {
+                pi: f64::INFINITY,
+                tau: if mu == 0.0 { 0.0 } else { f64::INFINITY },
+            }
+        } else {
+            let pi = 1.0 / var;
+            Self { pi, tau: mu * pi }
+        }
+    }
+
     /// Construct directly from natural parameters.
     #[inline]
     pub(crate) const fn from_natural(pi: f64, tau: f64) -> Self {
@@ -42,16 +65,19 @@ impl Gaussian {
     }
 
     #[inline]
+    #[must_use]
     pub fn pi(&self) -> f64 {
         self.pi
     }
 
     #[inline]
+    #[must_use]
     pub fn tau(&self) -> f64 {
         self.tau
     }
 
     #[inline]
+    #[must_use]
     pub fn mu(&self) -> f64 {
         // A non-positive precision is an improper (uninformative) Gaussian — its mean is
         // undefined. Treat it like `pi == 0` and return 0. EP message cancellation can land
@@ -64,7 +90,23 @@ impl Gaussian {
         }
     }
 
+    /// Variance, `1 / pi`, without the root-and-square of `sigma().powi(2)`.
+    ///
+    /// Mirrors `sigma()`'s treatment of the improper (`pi <= 0`) and point-mass
+    /// (`pi == inf`) cases.
     #[inline]
+    pub(crate) fn variance(&self) -> f64 {
+        if self.pi <= 0.0 {
+            f64::INFINITY
+        } else if self.pi.is_infinite() {
+            0.0
+        } else {
+            1.0 / self.pi
+        }
+    }
+
+    #[inline]
+    #[must_use]
     pub fn sigma(&self) -> f64 {
         // A non-positive precision is improper → infinite standard deviation. Guarding
         // `pi <= 0.0` (not just `== 0.0`) keeps `1.0 / pi.sqrt()` from returning NaN when EP
@@ -86,22 +128,21 @@ impl Gaussian {
     }
 
     pub(crate) fn exclude(&self, other: Gaussian) -> Self {
-        let var = self.sigma().powi(2) - other.sigma().powi(2);
+        let var = self.variance() - other.variance();
         if var <= 0.0 {
             // When sigma_self ≈ sigma_other (including ULP-level rounding differences
             // from the pi→sigma accessor round-trip), the excluded contribution is N00.
             // Computing from_ms(tiny_mu, 0.0) would give {pi:inf, tau:inf}, whose
             // mu() = inf/inf = NaN.  Returning N00 is correct: when both Gaussians
             // carry the same variance, the residual is a point mass at 0.
-            return Gaussian::from_ms(0.0, 0.0);
+            return Gaussian::from_mv(0.0, 0.0);
         }
-        let mu = self.mu() - other.mu();
-        Self::from_ms(mu, var.sqrt())
+
+        Self::from_mv(self.mu() - other.mu(), var)
     }
 
     pub(crate) fn forget(&self, variance_delta: f64) -> Self {
-        let var = self.sigma().powi(2) + variance_delta;
-        Self::from_ms(self.mu(), var.sqrt())
+        Self::from_mv(self.mu(), self.variance() + variance_delta)
     }
 
     /// EP damping in natural-parameter space: `α·new + (1−α)·self`.
@@ -109,6 +150,7 @@ impl Gaussian {
     /// Used by within-game inference to stabilise oscillating fixed-point
     /// loops on hard graphs. `alpha = 1.0` returns `new` exactly;
     /// `alpha < 1.0` shrinks each per-step update.
+    #[must_use]
     pub fn damp_natural(self, new: Gaussian, alpha: f64) -> Gaussian {
         Gaussian::from_natural(
             alpha * new.pi() + (1.0 - alpha) * self.pi(),
@@ -128,9 +170,7 @@ impl ops::Add<Gaussian> for Gaussian {
     /// Variance addition: (mu1 + mu2, sqrt(σ1² + σ2²)).
     /// Used for combining performance and noise; rare relative to mul/div.
     fn add(self, rhs: Gaussian) -> Self::Output {
-        let mu = self.mu() + rhs.mu();
-        let var = self.sigma().powi(2) + rhs.sigma().powi(2);
-        Self::from_ms(mu, var.sqrt())
+        Self::from_mv(self.mu() + rhs.mu(), self.variance() + rhs.variance())
     }
 }
 
@@ -138,9 +178,7 @@ impl ops::Sub<Gaussian> for Gaussian {
     type Output = Gaussian;
     /// (mu1 - mu2, sqrt(σ1² + σ2²)). Same sigma combination as Add.
     fn sub(self, rhs: Gaussian) -> Self::Output {
-        let mu = self.mu() - rhs.mu();
-        let var = self.sigma().powi(2) + rhs.sigma().powi(2);
-        Self::from_ms(mu, var.sqrt())
+        Self::from_mv(self.mu() - rhs.mu(), self.variance() + rhs.variance())
     }
 }
 
@@ -161,7 +199,7 @@ impl ops::Mul<f64> for Gaussian {
         if scalar == 0.0 {
             // Scaling by 0 collapses to a point mass at 0 (sigma' = 0, mu' = 0).
             // This is N00, the additive identity, NOT N_INF.
-            return Gaussian::from_ms(0.0, 0.0);
+            return Gaussian::from_mv(0.0, 0.0);
         }
         // sigma' = sigma * |scalar|  =>  pi' = pi / scalar²
         // mu'    = mu * scalar       =>  tau' = tau / scalar

src/history.rs

@@ -1,7 +1,7 @@
 use std::{borrow::Borrow, collections::HashMap, hash::Hash, marker::PhantomData};
 
 use crate::{
-    BETA, GAMMA, Index, MU, N_INF, P_DRAW, SIGMA,
+    BETA, GAMMA, Index, MU, P_DRAW, SIGMA,
     competitor::{self, Competitor},
     convergence::{ConvergenceOptions, ConvergenceReport},
     drift::{ConstantDrift, Drift},
@@ -13,7 +13,7 @@ use crate::{
     sort_time,
     storage::CompetitorStore,
     time::Time,
-    time_slice::{self, EventKind, TimeSlice},
+    time_slice::{self, EventKind, FilteredStep, TimeSlice},
     tuple_gt, tuple_max,
 };
 
@@ -29,7 +29,6 @@ pub struct HistoryBuilder<
     beta: f64,
     drift: D,
     p_draw: f64,
-    online: bool,
     score_sigma: f64,
     convergence: ConvergenceOptions,
     observer: O,
@@ -60,7 +59,6 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<
             sigma: self.sigma,
             beta: self.beta,
             p_draw: self.p_draw,
-            online: self.online,
             score_sigma: self.score_sigma,
             convergence: self.convergence,
             observer: self.observer,
@@ -69,16 +67,29 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<
         }
     }
 
+    /// Probability that two evenly-matched sides draw.
+    ///
+    /// Must be in `[0.0, 1.0)`. A zero draw probability asserts that draws
+    /// cannot occur, so ingesting a tied outcome then fails with
+    /// `InferenceError::TieWithoutDrawProbability`.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `p_draw` is outside `[0.0, 1.0)` or is NaN.
     pub fn p_draw(mut self, p_draw: f64) -> Self {
+        assert!(
+            (0.0..1.0).contains(&p_draw),
+            "p_draw must be in [0.0, 1.0) (got {p_draw})"
+        );
         self.p_draw = p_draw;
         self
     }
 
-    pub fn online(mut self, online: bool) -> Self {
-        self.online = online;
-        self
-    }
-
+    /// Default observation noise for scored outcomes.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `score_sigma` is not strictly positive.
     pub fn score_sigma(mut self, score_sigma: f64) -> Self {
         assert!(
             score_sigma > 0.0,
@@ -88,7 +99,24 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<
         self
     }
 
+    /// Convergence tolerance, iteration cap, and EP damping.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `alpha` is outside `(0.0, 1.0]`, or if `epsilon` is negative
+    /// or NaN. An `alpha` of zero would leave every EP update unapplied, so
+    /// inference would silently return the priors.
     pub fn convergence(mut self, opts: ConvergenceOptions) -> Self {
+        assert!(
+            opts.alpha > 0.0 && opts.alpha <= 1.0,
+            "convergence alpha must be in (0.0, 1.0] (got {})",
+            opts.alpha
+        );
+        assert!(
+            opts.epsilon >= 0.0,
+            "convergence epsilon must be non-negative (got {})",
+            opts.epsilon
+        );
         self.convergence = opts;
         self
     }
@@ -100,7 +128,6 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<
             beta: self.beta,
             drift: self.drift,
             p_draw: self.p_draw,
-            online: self.online,
             score_sigma: self.score_sigma,
             convergence: self.convergence,
             observer,
@@ -120,7 +147,6 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<
             beta: self.beta,
             drift: self.drift,
             p_draw: self.p_draw,
-            online: self.online,
             score_sigma: self.score_sigma,
             convergence: self.convergence,
             observer: self.observer,
@@ -136,7 +162,6 @@ impl Default for HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str>
             beta: BETA,
             drift: ConstantDrift(GAMMA),
             p_draw: P_DRAW,
-            online: false,
             score_sigma: 1.0,
             convergence: ConvergenceOptions::default(),
             observer: NullObserver,
@@ -161,7 +186,6 @@ pub struct History<
     beta: f64,
     drift: D,
     p_draw: f64,
-    online: bool,
     score_sigma: f64,
     convergence: ConvergenceOptions,
     observer: O,
@@ -174,6 +198,7 @@ impl Default for History<i64, ConstantDrift, NullObserver, &'static str> {
 }
 
 impl History<i64, ConstantDrift, NullObserver, &'static str> {
+    #[must_use]
     pub fn builder() -> HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str> {
         HistoryBuilder::default()
     }
@@ -181,6 +206,7 @@ impl History<i64, ConstantDrift, NullObserver, &'static str> {
 
 impl<K: Eq + Hash + Clone> History<i64, ConstantDrift, NullObserver, K> {
     /// Like `builder()` but uses a custom key type `K` instead of the default `&'static str`.
+    #[must_use]
     pub fn builder_with_key() -> HistoryBuilder<i64, ConstantDrift, NullObserver, K> {
         HistoryBuilder {
             mu: MU,
@@ -188,7 +214,6 @@ impl<K: Eq + Hash + Clone> History<i64, ConstantDrift, NullObserver, K> {
             beta: BETA,
             drift: ConstantDrift(GAMMA),
             p_draw: P_DRAW,
-            online: false,
             score_sigma: 1.0,
             convergence: ConvergenceOptions::default(),
             observer: NullObserver,
@@ -220,12 +245,16 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     fn iteration(&mut self) -> (f64, f64) {
         let mut step = (0.0, 0.0);
 
+        if self.time_slices.is_empty() {
+            return step;
+        }
+
         competitor::clean(self.agents.values_mut(), false);
 
         for j in (0..self.time_slices.len() - 1).rev() {
             for agent in self.time_slices[j + 1].skills.keys() {
                 self.agents.get_mut(agent).unwrap().message =
-                    self.time_slices[j + 1].backward_prior_out(&agent, &self.agents);
+                    Some(self.time_slices[j + 1].backward_prior_out(&agent, &self.agents));
             }
 
             let old = self.time_slices[j].posteriors();
@@ -244,7 +273,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         for j in 1..self.time_slices.len() {
             for agent in self.time_slices[j - 1].skills.keys() {
                 self.agents.get_mut(agent).unwrap().message =
-                    self.time_slices[j - 1].forward_prior_out(&agent);
+                    Some(self.time_slices[j - 1].forward_prior_out(&agent));
             }
 
             let old = self.time_slices[j].posteriors();
@@ -273,10 +302,13 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         step
     }
 
+    /// Number of distinct time slices in the history.
+    #[must_use]
+    pub fn time_slices_len(&self) -> usize {
+        self.time_slices.len()
+    }
+
     /// Learning curves for all competitors, keyed by their user-facing key.
-    ///
-    /// Note: `key(idx)` is O(n) per lookup; this method is therefore O(n²)
-    /// in the number of competitors. Acceptable for T2; T3 may optimize.
     pub fn learning_curves(&self) -> HashMap<K, Vec<(T, Gaussian)>> {
         #[cfg(feature = "rayon")]
         {
@@ -347,14 +379,79 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             .collect()
     }
 
-    pub(crate) fn log_evidence_internal(&mut self, forward: bool, targets: &[Index]) -> f64 {
+    /// Filtered learning curves for all competitors, keyed by user-facing key.
+    ///
+    /// Each point is the posterior using only events up to and including that
+    /// time — "what we knew then". Contrast `learning_curves`, whose points
+    /// are smoothed and so incorporate rounds played later.
+    ///
+    /// Runs a full forward pass per call and caches nothing. This is the
+    /// entry point for multi-key work — see `filtered_learning_curve` for
+    /// why calling that once per key is far more expensive.
+    pub fn filtered_learning_curves(&self) -> HashMap<K, Vec<(T, Gaussian)>> {
+        let mut data: HashMap<K, Vec<(T, Gaussian)>> = HashMap::new();
+
+        for (time, step) in self.filtered_pass() {
+            for (agent, posterior) in step.posteriors {
+                if let Some(key) = self.keys.key(agent).cloned() {
+                    data.entry(key).or_default().push((time, posterior));
+                }
+            }
+        }
+
+        data
+    }
+
+    /// Filtered learning curve for a single key: (time, posterior) pairs in
+    /// time order.
+    ///
+    /// Despite mirroring `learning_curve`'s signature, this is not the cheap
+    /// per-key lookup that method is: it runs a full forward pass, O(events),
+    /// discarding every posterior but the requested key's. N keys fetched
+    /// this way costs O(N * events); use `filtered_learning_curves` for
+    /// multi-key work instead — it computes the same pass once.
+    pub fn filtered_learning_curve<Q>(&self, key: &Q) -> Vec<(T, Gaussian)>
+    where
+        K: Borrow<Q>,
+        Q: Hash + Eq + ?Sized,
+    {
+        let Some(idx) = self.keys.get(key) else {
+            return Vec::new();
+        };
+
+        self.filtered_pass()
+            .into_iter()
+            .filter_map(|(time, step)| {
+                step.posteriors
+                    .iter()
+                    .find(|(agent, _)| *agent == idx)
+                    .map(|&(_, posterior)| (time, posterior))
+            })
+            .collect()
+    }
+
+    /// Sum per-slice evidence.
+    ///
+    /// `forward` selects `skill.forward` as each event's prior instead of the
+    /// cavity. That is a genuine forward-only (filtering) quantity ONLY on a
+    /// history that has never been converged: `iteration` alternates backward
+    /// and forward sweeps, so from the second iteration onward the likelihood
+    /// feeding the forward message has already absorbed backward information.
+    /// For a filtering quantity that holds after convergence, use
+    /// `filtered_log_evidence`.
+    pub(crate) fn log_evidence_internal(&self, forward: bool, targets: &[Index]) -> f64 {
+        // Bound before the closure so it captures the store rather than all of
+        // `&self`: capturing `&History` would drag `KeyTable<K>` in and demand
+        // `K: Sync` from every caller, which the key type need not satisfy.
+        let agents = &self.agents;
+
         #[cfg(feature = "rayon")]
         {
             use rayon::prelude::*;
             let per_slice: Vec<f64> = self
                 .time_slices
                 .par_iter()
-                .map(|ts| ts.log_evidence(self.online, targets, forward, &self.agents))
+                .map(|ts| ts.log_evidence(targets, forward, agents))
                 .collect();
             per_slice.into_iter().sum()
         }
@@ -362,19 +459,19 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         {
             self.time_slices
                 .iter()
-                .map(|ts| ts.log_evidence(self.online, targets, forward, &self.agents))
+                .map(|ts| ts.log_evidence(targets, forward, agents))
                 .sum()
         }
     }
 
     /// Total log-evidence across the history.
-    pub fn log_evidence(&mut self) -> f64 {
+    pub fn log_evidence(&self) -> f64 {
         self.log_evidence_internal(false, &[])
     }
 
     /// Log-evidence restricted to time slices containing at least one of the
     /// given keys. Useful for leave-one-out cross-validation.
-    pub fn log_evidence_for<Q>(&mut self, keys: &[&Q]) -> f64
+    pub fn log_evidence_for<Q>(&self, keys: &[&Q]) -> f64
     where
         K: std::borrow::Borrow<Q>,
         Q: std::hash::Hash + Eq + ?Sized,
@@ -383,9 +480,59 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         self.log_evidence_internal(false, &targets)
     }
 
+    /// Walk the slices in time order carrying forward messages only.
+    ///
+    /// This is the forward half of `iteration` with the backward half never
+    /// run. It reads `self` and mutates nothing.
+    fn filtered_pass(&self) -> Vec<(T, FilteredStep)> {
+        let mut messages: HashMap<Index, Gaussian> = HashMap::new();
+
+        let mut pass = Vec::with_capacity(self.time_slices.len());
+
+        for slice in &self.time_slices {
+            let step = slice.filtered_step(&messages, &self.agents);
+
+            for &(agent, posterior) in &step.posteriors {
+                messages.insert(agent, posterior);
+            }
+
+            pass.push((slice.time, step));
+        }
+
+        pass
+    }
+
+    /// Total log-evidence under forward-only (filtering) information.
+    ///
+    /// Each event is scored using only what was known before that *time*,
+    /// which is the right quantity for prequential scoring and model
+    /// comparison. Events sharing a timestamp still inform each other
+    /// through the within-slice sweep, so within one slice this is not a
+    /// guarantee that event A is scored independently of simultaneous event
+    /// B. Contrast `log_evidence`, whose per-event priors carry information
+    /// from events that had not happened yet.
+    ///
+    /// Runs a full forward pass per call and caches nothing. The result does
+    /// not depend on whether `converge` has been called.
+    #[must_use]
+    pub fn filtered_log_evidence(&self) -> f64 {
+        self.filtered_pass()
+            .iter()
+            .map(|(_, step)| step.log_evidence)
+            .sum()
+    }
+
     /// Draw-probability quality metric for the given teams (key slices).
     ///
-    /// Values range roughly [0, 1]; 1 == perfectly matched.
+    /// Values range roughly [0, 1]; 1 == perfectly matched. Supports any
+    /// number of teams.
+    ///
+    /// # Panics
+    ///
+    /// Panics if fewer than two teams are supplied, or if a team resolves to
+    /// no known competitors — keys absent from the history, or competitors
+    /// with no recorded skill, are dropped, so a team of entirely-unknown
+    /// keys becomes empty. Use `lookup` to check keys first.
     pub fn predict_quality(&self, teams: &[&[&K]]) -> f64 {
         let groups: Vec<Vec<Gaussian>> = teams
             .iter()
@@ -407,7 +554,11 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
 
     /// 2-team win probability: returns `[P(team0 wins), P(team1 wins)]`.
     ///
-    /// Panics if `teams.len() != 2`. N-team support lands in T4.
+    /// N-team support lands in T4.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `teams.len() != 2`.
     pub fn predict_outcome(&self, teams: &[&[&K]]) -> Vec<f64> {
         assert_eq!(teams.len(), 2, "predict_outcome T2: 2 teams only");
         let gather = |team: &[&K]| -> Gaussian {
@@ -429,12 +580,32 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     }
 
     /// Run the full forward+backward convergence loop and return a summary.
+    ///
+    /// Failing to reach `epsilon` within `max_iter` is not an error: the
+    /// returned report carries `converged: false` and the final step.
+    ///
+    /// # Errors
+    ///
+    /// `NonFiniteResult` if a sweep produces a NaN or infinite step. EP has
+    /// broken down at that point and further iterations cannot recover, so the
+    /// loop stops rather than reporting a NaN step as convergence.
     pub fn converge(&mut self) -> Result<ConvergenceReport, InferenceError> {
         use std::time::Instant;
 
         use smallvec::SmallVec;
 
         let opts = self.convergence;
+
+        if self.time_slices.is_empty() {
+            return Ok(ConvergenceReport {
+                iterations: 0,
+                final_step: (0.0, 0.0),
+                log_evidence: 0.0,
+                converged: true,
+                per_iteration_time: SmallVec::new(),
+            });
+        }
+
         let mut step = (f64::INFINITY, f64::INFINITY);
         let mut i = 0;
         let mut per_iter: SmallVec<[std::time::Duration; 32]> = SmallVec::new();
@@ -444,8 +615,24 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             per_iter.push(t0.elapsed());
             i += 1;
             self.observer.on_iteration_end(i, step);
+
+            // A non-finite step means EP has broken down; further iterations
+            // cannot recover, and `tuple_gt` would read NaN as converged.
+            if !crate::step_is_finite(step) {
+                break;
             }
-        let converged = !tuple_gt(step, opts.epsilon);
+        }
+
+        if !crate::step_is_finite(step) {
+            self.observer.on_converged(i, step, false);
+
+            return Err(InferenceError::NonFiniteResult {
+                context: "History::converge",
+                step,
+            });
+        }
+
+        let converged = crate::step_converged(step, opts.epsilon);
         let log_evidence = self.log_evidence_internal(false, &[]);
         self.observer.on_converged(i, step, converged);
         Ok(ConvergenceReport {
@@ -454,7 +641,6 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             log_evidence,
             converged,
             per_iteration_time: per_iter,
-            slices_skipped: 0,
         })
     }
 }
@@ -462,18 +648,23 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
 impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
     pub(crate) fn add_events_with_prior(
         &mut self,
-        composition: Vec<Vec<Vec<Index>>>,
-        results: Vec<Vec<f64>>,
+        mut composition: Vec<Vec<Vec<Index>>>,
+        mut results: Option<Vec<Vec<f64>>>,
         times: Vec<T>,
-        weights: Vec<Vec<Vec<f64>>>,
+        mut weights: Option<Vec<Vec<Vec<f64>>>>,
         kinds: Vec<EventKind>,
         mut priors: HashMap<Index, Rating<T, D>>,
     ) -> Result<(), InferenceError> {
-        if !results.is_empty() && results.len() != composition.len() {
+        if results
+            .as_ref()
+            .is_some_and(|r| r.len() != composition.len())
+        {
+            let got = results.as_ref().map_or(0, Vec::len);
+
             return Err(InferenceError::MismatchedShape {
                 kind: "results",
                 expected: composition.len(),
-                got: results.len(),
+                got,
             });
         }
         if times.len() != composition.len() {
@@ -483,11 +674,16 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                 got: times.len(),
             });
         }
-        if !weights.is_empty() && weights.len() != composition.len() {
+        if weights
+            .as_ref()
+            .is_some_and(|w| w.len() != composition.len())
+        {
+            let got = weights.as_ref().map_or(0, Vec::len);
+
             return Err(InferenceError::MismatchedShape {
                 kind: "weights",
                 expected: composition.len(),
-                got: weights.len(),
+                got,
             });
         }
         if kinds.len() != composition.len() {
@@ -498,6 +694,21 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             });
         }
 
+        // Chokepoint for tie validation: every ingestion route lands here,
+        // including `record_draw`, which builds its results directly rather
+        // than going through `Outcome`.
+        if self.p_draw == 0.0 {
+            for (event_results, kind) in results.iter().flatten().zip(kinds.iter()) {
+                if !matches!(kind, EventKind::Ranked) {
+                    continue;
+                }
+
+                if let Some(teams) = crate::first_tied_output(event_results) {
+                    return Err(InferenceError::TieWithoutDrawProbability { teams });
+                }
+            }
+        }
+
         competitor::clean(self.agents.values_mut(), true);
 
         let mut this_agent = Vec::with_capacity(1024);
@@ -520,7 +731,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                                 self.drift,
                             )
                         }),
-                        message: N_INF,
+                        message: None,
                         last_time: None,
                     },
                 );
@@ -530,6 +741,20 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         let n = composition.len();
         let o = sort_time(&times, false);
 
+        // The chunking loop below MOVES each event's data out of `composition`,
+        // `results` and `weights` instead of cloning it. That is only sound
+        // because `o` is a permutation, so every index is visited exactly once
+        // — visiting one twice would silently yield an empty event rather than
+        // failing.
+        debug_assert!(
+            {
+                let mut seen = vec![false; n];
+                o.iter()
+                    .all(|&idx| !std::mem::replace(&mut seen[idx], true))
+            },
+            "sort_time must return a permutation of 0..{n}"
+        );
+
         let mut i = 0;
         let mut k = 0;
 
@@ -558,7 +783,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                         let agent = self.agents.get_mut(*agent_idx).unwrap();
 
                         agent.last_time = Some(time_slice.time);
-                        agent.message = time_slice.forward_prior_out(agent_idx);
+                        agent.message = Some(time_slice.forward_prior_out(agent_idx));
                     }
                 }
 
@@ -566,20 +791,20 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             }
 
             let composition = (i..j)
-                .map(|e| composition[o[e]].clone())
+                .map(|e| std::mem::take(&mut composition[o[e]]))
                 .collect::<Vec<_>>();
 
-            let results = if results.is_empty() {
-                Vec::new()
-            } else {
-                (i..j).map(|e| results[o[e]].clone()).collect::<Vec<_>>()
-            };
+            let results = results.as_mut().map(|results| {
+                (i..j)
+                    .map(|e| std::mem::take(&mut results[o[e]]))
+                    .collect::<Vec<_>>()
+            });
 
-            let weights = if weights.is_empty() {
-                Vec::new()
-            } else {
-                (i..j).map(|e| weights[o[e]].clone()).collect::<Vec<_>>()
-            };
+            let weights = weights.as_mut().map(|weights| {
+                (i..j)
+                    .map(|e| std::mem::take(&mut weights[o[e]]))
+                    .collect::<Vec<_>>()
+            });
 
             let kinds_chunk: Vec<EventKind> = (i..j).map(|e| kinds[o[e]]).collect();
 
@@ -591,8 +816,10 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                     let agent = self.agents.get_mut(agent_idx).unwrap();
 
                     agent.last_time = Some(t);
-                    agent.message = time_slice.forward_prior_out(&agent_idx);
+                    agent.message = Some(time_slice.forward_prior_out(&agent_idx));
                 }
+
+                k += 1;
             } else {
                 let mut time_slice = TimeSlice::new(t, self.p_draw, self.convergence);
                 time_slice.add_events(composition, results, weights, kinds_chunk, &self.agents);
@@ -605,7 +832,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                     let agent = self.agents.get_mut(agent_idx).unwrap();
 
                     agent.last_time = Some(t);
-                    agent.message = time_slice.forward_prior_out(&agent_idx);
+                    agent.message = Some(time_slice.forward_prior_out(&agent_idx));
                 }
 
                 k += 1;
@@ -629,7 +856,7 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                     let agent = self.agents.get_mut(*agent_idx).unwrap();
 
                     agent.last_time = Some(time_slice.time);
-                    agent.message = time_slice.forward_prior_out(agent_idx);
+                    agent.message = Some(time_slice.forward_prior_out(agent_idx));
                 }
             }
 
@@ -640,6 +867,13 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         Ok(())
     }
 
+    /// Record a single two-competitor event that `winner` won.
+    ///
+    /// # Errors
+    ///
+    /// Ingests through the same path as [`History::add_events`], so it returns
+    /// the same errors. A two-team decisive outcome cannot tie, so
+    /// `TieWithoutDrawProbability` is not reachable here.
     pub fn record_winner<Q>(&mut self, winner: &Q, loser: &Q, time: T) -> Result<(), InferenceError>
     where
         K: Borrow<Q>,
@@ -649,14 +883,21 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         let l = self.intern(loser);
         self.add_events_with_prior(
             vec![vec![vec![w], vec![l]]],
-            vec![vec![1.0, 0.0]],
+            Some(vec![vec![1.0, 0.0]]),
             vec![time],
-            vec![],
+            None,
             vec![EventKind::Ranked],
             HashMap::new(),
         )
     }
 
+    /// Record a single two-competitor event that ended level.
+    ///
+    /// # Errors
+    ///
+    /// Ingests through the same path as [`History::add_events`]. Note
+    /// `TieWithoutDrawProbability` *is* reachable here: a draw needs a
+    /// positive `p_draw`.
     pub fn record_draw<Q>(&mut self, a: &Q, b: &Q, time: T) -> Result<(), InferenceError>
     where
         K: Borrow<Q>,
@@ -666,9 +907,9 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
         let b_idx = self.intern(b);
         self.add_events_with_prior(
             vec![vec![vec![a_idx], vec![b_idx]]],
-            vec![vec![0.0, 0.0]],
+            Some(vec![vec![0.0, 0.0]]),
             vec![time],
-            vec![],
+            None,
             vec![EventKind::Ranked],
             HashMap::new(),
         )
@@ -680,6 +921,17 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
     }
 
     /// Bulk-ingest typed events.
+    ///
+    /// # Errors
+    ///
+    /// - `MismatchedShape` if an event's outcome does not describe the same
+    ///   number of teams the event has, or if per-member weights do not match
+    ///   the team's membership.
+    /// - `InvalidParameter` if a per-event `score_sigma` override is not
+    ///   strictly positive.
+    /// - `TieWithoutDrawProbability` if an event ties two teams while the
+    ///   history's `p_draw` is zero. This includes `Outcome::winner(w, n)` for
+    ///   `n >= 3`, which ties every loser.
     pub fn add_events<I>(&mut self, events: I) -> Result<(), InferenceError>
     where
         I: IntoIterator<Item = crate::event::Event<T, K>>,
@@ -716,8 +968,37 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                     let idx = self.keys.get_or_create(&member.key);
                     team_indices.push(idx);
                     team_weights.push(member.weight);
+
+                    if let Some(scale) = member.drift_scale {
+                        // Squaring would make a negative scale behave as its
+                        // absolute value, so reject rather than silently
+                        // accept a sign the caller cannot have meant.
+                        if !scale.is_finite() || scale < 0.0 {
+                            return Err(InferenceError::InvalidParameter {
+                                name: "drift_scale",
+                                value: scale,
+                            });
+                        }
+                    }
+
+                    // `prior` and `drift_scale` are competitor configuration,
+                    // captured here and consumed at competitor creation. Both
+                    // land in the same entry so a member may set either alone.
+                    if member.prior.is_some() || member.drift_scale.is_some() {
+                        let rating = priors.entry(idx).or_insert_with(|| {
+                            Rating::new(
+                                Gaussian::from_ms(self.mu, self.sigma),
+                                self.beta,
+                                self.drift,
+                            )
+                        });
+
                         if let Some(prior) = member.prior {
-                        priors.insert(idx, Rating::new(prior, self.beta, self.drift));
+                            rating.prior = prior;
+                        }
+                        if let Some(scale) = member.drift_scale {
+                            rating.drift_scale = scale;
+                        }
                     }
                 }
                 event_comp.push(team_indices);
@@ -734,10 +1015,13 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
                 }
                 crate::Outcome::Scored { scores, sigma } => {
                     let resolved = sigma.unwrap_or(self.score_sigma);
-                    debug_assert!(
-                        resolved > 0.0,
-                        "resolved score_sigma must be > 0.0 (got {resolved})"
-                    );
+                    if resolved <= 0.0 || resolved.is_nan() {
+                        return Err(InferenceError::InvalidParameter {
+                            name: "score_sigma",
+                            value: resolved,
+                        });
+                    }
+
                     kinds.push(EventKind::Scored {
                         score_sigma: resolved,
                     });
@@ -748,7 +1032,13 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             times.push(ev.time);
         }
 
-        self.add_events_with_prior(composition, results, times, weights, kinds, priors)
+        let weights = if weights.is_empty() {
+            None
+        } else {
+            Some(weights)
+        };
+
+        self.add_events_with_prior(composition, Some(results), times, weights, kinds, priors)
     }
 }
 
@@ -763,6 +1053,49 @@ mod tests {
         arena::ScratchArena,
     };
 
+    /// #17: a slice's footprint must be O(competitors in the slice), not
+    /// O(largest global index it touches). The store used to be a dense
+    /// `Vec<Skill>` indexed by `Index.0`, so the same two-competitor games cost
+    /// 20,000 slots per slice when the competitors sat at the top of a large
+    /// roster. Measured end to end, peak RSS was 309 MB against 52 MB.
+    #[test]
+    fn per_slice_footprint_is_independent_of_index_magnitude() {
+        fn total_skill_slots(high_indices: bool) -> usize {
+            let mut h: History<i64, ConstantDrift, NullObserver, String> =
+                History::builder_with_key().build();
+
+            for i in 0..2_000 {
+                h.intern(&format!("k{i:05}"));
+            }
+
+            let (a, b) = if high_indices {
+                ("k01998".to_string(), "k01999".to_string())
+            } else {
+                ("k00000".to_string(), "k00001".to_string())
+            };
+
+            for time in 1..=20i64 {
+                h.record_winner(&a, &b, time).unwrap();
+            }
+
+            h.time_slices
+                .iter()
+                .map(|ts| ts.skills.allocated_slots())
+                .sum()
+        }
+
+        let low = total_skill_slots(false);
+        let high = total_skill_slots(true);
+
+        assert_eq!(low, high, "footprint must not depend on index magnitude");
+
+        // A dense store over a 2,000-key roster would allocate 20 x 2,000.
+        assert!(
+            high < 1_000,
+            "20 slices of 2 competitors allocated {high} slots"
+        );
+    }
+
     fn make_events_1v1(
         pairs: &[(&'static str, &'static str)],
         outcomes: &[Outcome],
@@ -834,12 +1167,7 @@ mod tests {
 
         let w = [vec![1.0], vec![1.0]];
         let p = Game::ranked_with_arena(
-            h.time_slices[1].events[0].within_priors(
-                false,
-                false,
-                &h.time_slices[1].skills,
-                &h.agents,
-            ),
+            h.time_slices[1].events[0].within_priors(false, &h.time_slices[1].skills, &h.agents),
             &[0.0, 1.0],
             &w,
             P_DRAW,
@@ -1079,11 +1407,11 @@ mod tests {
         let f = h.keys.get("f").unwrap();
 
         let trueskill_log_evidence = h.log_evidence_internal(false, &[]);
-        let trueskill_log_evidence_online = h.log_evidence_internal(true, &[]);
+        let trueskill_log_evidence_forward = h.log_evidence_internal(true, &[]);
 
         assert_ulps_eq!(
             trueskill_log_evidence,
-            trueskill_log_evidence_online,
+            trueskill_log_evidence_forward,
             epsilon = 1e-6
         );
 

src/key_table.rs

@@ -12,59 +12,72 @@ use crate::Index;
 /// crate. Power users can promote `&K` to `Index` via `get_or_create` and
 /// skip the lookup on subsequent hot-path calls.
 #[derive(Debug)]
-pub struct KeyTable<K>(HashMap<K, Index>);
+pub struct KeyTable<K> {
+    forward: HashMap<K, Index>,
+    /// Reverse mapping, indexed by `Index.0`.
+    ///
+    /// Indices are handed out densely and sequentially, so position *is* the
+    /// index and `key()` is a lookup rather than a scan over every entry.
+    reverse: Vec<K>,
+}
 
 impl<K> KeyTable<K>
 where
-    K: Eq + Hash,
+    K: Eq + Hash + Clone,
 {
+    #[must_use]
     pub fn new() -> Self {
-        Self(HashMap::new())
+        Self {
+            forward: HashMap::new(),
+            reverse: Vec::new(),
+        }
     }
 
     pub fn get<Q: ?Sized + Hash + Eq>(&self, k: &Q) -> Option<Index>
     where
         K: Borrow<Q>,
     {
-        self.0.get(k).cloned()
+        self.forward.get(k).cloned()
     }
 
     pub fn get_or_create<Q: ?Sized + Hash + Eq + ToOwned<Owned = K>>(&mut self, k: &Q) -> Index
     where
         K: Borrow<Q>,
     {
-        if let Some(idx) = self.0.get(k) {
+        if let Some(idx) = self.forward.get(k) {
             *idx
         } else {
-            let idx = Index::from(self.0.len());
-            self.0.insert(k.to_owned(), idx);
+            let idx = Index::from(self.reverse.len());
+            let owned = k.to_owned();
+            self.reverse.push(owned.clone());
+            self.forward.insert(owned, idx);
             idx
         }
     }
 
+    #[must_use]
     pub fn key(&self, idx: Index) -> Option<&K> {
-        self.0
-            .iter()
-            .find(|&(_, value)| *value == idx)
-            .map(|(key, _)| key)
+        self.reverse.get(idx.0)
     }
 
     pub fn keys(&self) -> impl Iterator<Item = &K> {
-        self.0.keys()
+        self.forward.keys()
     }
 
+    #[must_use]
     pub fn len(&self) -> usize {
-        self.0.len()
+        self.reverse.len()
     }
 
+    #[must_use]
     pub fn is_empty(&self) -> bool {
-        self.0.is_empty()
+        self.reverse.is_empty()
     }
 }
 
 impl<K> Default for KeyTable<K>
 where
-    K: Eq + Hash,
+    K: Eq + Hash + Clone,
 {
     fn default() -> Self {
         KeyTable::new()

src/lib.rs

@@ -1,3 +1,91 @@
+//! `TrueSkill` Through Time — Bayesian skill rating over a time axis.
+//!
+//! Where plain `TrueSkill` gives each competitor one running estimate, `TrueSkill`
+//! Through Time treats a whole history as a single model and infers skill *at
+//! every point in time*. Evidence flows both directions: a result today
+//! sharpens the estimate of who someone was last year, so early estimates stop
+//! being frozen guesses and comparisons across eras become meaningful.
+//!
+//! This is a Rust port of
+//! [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py).
+//!
+//! # Getting started
+//!
+//! Record results, converge, then read off skills:
+//!
+//! ```
+//! use trueskill_tt::History;
+//!
+//! let mut history = History::default();
+//!
+//! history.record_winner(&"alice", &"bob", 1)?;
+//! history.record_winner(&"bob", &"carol", 2)?;
+//! history.record_winner(&"alice", &"carol", 3)?;
+//!
+//! let report = history.converge()?;
+//! assert!(report.converged);
+//!
+//! let alice = history.current_skill("alice").unwrap();
+//! assert!(alice.mu() > 0.0, "alice won every game she played");
+//! # Ok::<(), trueskill_tt::InferenceError>(())
+//! ```
+//!
+//! Teams, weights, explicit rankings and continuous scores go through the
+//! fluent event builder:
+//!
+//! ```
+//! use trueskill_tt::History;
+//!
+//! let mut history = History::builder().p_draw(0.1).build();
+//!
+//! history
+//!     .event(1)
+//!     .team(["alice", "bob"])
+//!     .team(["carol", "dave"])
+//!     .ranking([0, 1])
+//!     .commit()?;
+//!
+//! history.converge()?;
+//! # Ok::<(), trueskill_tt::InferenceError>(())
+//! ```
+//!
+//! # Draws need a draw probability
+//!
+//! A `p_draw` of zero asserts that draws cannot happen, so a tied result has
+//! no representable likelihood and is rejected:
+//!
+//! ```
+//! use trueskill_tt::{History, InferenceError};
+//!
+//! let mut history = History::default(); // p_draw defaults to 0.0
+//! let err = history.record_draw(&"alice", &"bob", 1).unwrap_err();
+//! assert!(matches!(err, InferenceError::TieWithoutDrawProbability { .. }));
+//! ```
+//!
+//! This also applies to [`Outcome::winner`] for three or more teams, which
+//! ties every loser. Configure a positive `p_draw` for those.
+//!
+//! # Core types
+//!
+//! - [`History`] — the top-level container: ingests events, runs
+//!   forward/backward message passing, and answers queries.
+//! - [`Gaussian`] — the probability type, stored in natural parameters
+//!   (`pi = 1/sigma²`, `tau = mu/sigma²`) so message passing is add/subtract.
+//! - [`Game`] — one match in isolation, for scoring a hypothetical without a
+//!   history.
+//! - [`Outcome`] — how a match ended: ranks, or continuous scores.
+//! - [`Rating`] — a competitor's static configuration (prior, `beta`, drift).
+//!
+//! # Feature flags
+//!
+//! - `approx` — implements [`approx`](https://docs.rs/approx) equality traits
+//!   for [`Gaussian`]. Useful in tests.
+//! - `rayon` — parallelises the within-slice sweep and the per-slice passes of
+//!   `learning_curves`/`log_evidence`. Opt-in; results stay bit-identical
+//!   regardless of worker count.
+
+#![forbid(unsafe_code)]
+
 use std::{
     cmp::Reverse,
     f64::consts::{FRAC_1_SQRT_2, FRAC_2_SQRT_PI, SQRT_2},
@@ -37,7 +125,7 @@ pub use event::{Event, Member, Team};
 pub use event_builder::EventBuilder;
 pub use game::{Game, GameOptions, OwnedGame};
 pub use gaussian::Gaussian;
-pub use history::History;
+pub use history::{History, HistoryBuilder};
 pub use key_table::KeyTable;
 use matrix::Matrix;
 pub use observer::{NullObserver, Observer};
@@ -63,12 +151,29 @@ pub const N_INF: Gaussian = Gaussian::from_ms(0.0, f64::INFINITY);
 #[derive(Copy, Clone, Default, PartialEq, PartialOrd, Eq, Ord, Hash, Debug)]
 pub struct Index(usize);
 
+impl Index {
+    /// The underlying slot number.
+    ///
+    /// Indices are dense and assigned in interning order, so this is usable as
+    /// a key into a caller-side side table.
+    #[must_use]
+    pub fn get(self) -> usize {
+        self.0
+    }
+}
+
 impl From<usize> for Index {
     fn from(ix: usize) -> Self {
         Self(ix)
     }
 }
 
+impl From<Index> for usize {
+    fn from(idx: Index) -> Self {
+        idx.0
+    }
+}
+
 fn erfc(x: f64) -> f64 {
     let z = x.abs();
     let t = 1.0 / (1.0 + z / 2.0);
@@ -184,6 +289,56 @@ pub(crate) fn tuple_gt(t: (f64, f64), e: f64) -> bool {
     t.0 > e || t.1 > e
 }
 
+/// Whether a convergence step is finite in both components.
+///
+/// A NaN step means EP broke down numerically. Because every comparison
+/// against NaN is false, `tuple_gt` reads NaN as "below epsilon" — so
+/// convergence checks must test finiteness explicitly rather than inferring
+/// success from `!tuple_gt(..)`.
+pub(crate) fn step_is_finite(t: (f64, f64)) -> bool {
+    t.0.is_finite() && t.1.is_finite()
+}
+
+/// Whether a step counts as converged: finite *and* within `epsilon`.
+pub(crate) fn step_converged(t: (f64, f64), epsilon: f64) -> bool {
+    step_is_finite(t) && !tuple_gt(t, epsilon)
+}
+
+/// Indices of the first pair of teams sharing a rank, if any.
+///
+/// A tie is only representable when the draw probability is positive: with
+/// `p_draw == 0.0` the truncation margin collapses to zero and the two-sided
+/// tie update evaluates `0/0`. Callers use this to reject such events before
+/// they reach inference.
+pub(crate) fn first_tied_pair(ranks: &[u32]) -> Option<(usize, usize)> {
+    for (i, a) in ranks.iter().enumerate() {
+        for (j, b) in ranks.iter().enumerate().skip(i + 1) {
+            if a == b {
+                return Some((i, j));
+            }
+        }
+    }
+
+    None
+}
+
+/// As `first_tied_pair`, but over the engine's internal `f64` outputs.
+///
+/// Ranks reach the engine already converted to descending `f64` outputs, and
+/// `Game` decides a tie by exact equality of those values — so this mirrors
+/// the comparison inference itself performs.
+pub(crate) fn first_tied_output(outputs: &[f64]) -> Option<(usize, usize)> {
+    for (i, a) in outputs.iter().enumerate() {
+        for (j, b) in outputs.iter().enumerate().skip(i + 1) {
+            if a == b {
+                return Some((i, j));
+            }
+        }
+    }
+
+    None
+}
+
 pub(crate) fn sort_time<T: Copy + Ord>(xs: &[T], reverse: bool) -> Vec<usize> {
     let mut x: Vec<(usize, T)> = xs.iter().enumerate().map(|(i, &t)| (i, t)).collect();
 
@@ -197,7 +352,27 @@ pub(crate) fn sort_time<T: Copy + Ord>(xs: &[T], reverse: bool) -> Vec<usize> {
 }
 
 /// Calculates the match quality of the given rating groups. A result is the draw probability in the association
+///
+/// Supports any number of groups. Values range roughly `[0, 1]`; 1 means a
+/// perfectly balanced match.
+///
+/// # Panics
+///
+/// Panics if fewer than two rating groups are supplied, or if any group is
+/// empty — match quality is a property of a contest between at least two
+/// non-empty sides.
+#[must_use]
 pub fn quality(rating_groups: &[&[Gaussian]], beta: f64) -> f64 {
+    assert!(
+        rating_groups.len() >= 2,
+        "quality() requires at least 2 rating groups, got {}",
+        rating_groups.len()
+    );
+    assert!(
+        rating_groups.iter().all(|group| !group.is_empty()),
+        "quality() requires every rating group to be non-empty"
+    );
+
     let flatten_ratings = rating_groups
         .iter()
         .flat_map(|group| group.iter())
@@ -221,8 +396,10 @@ pub fn quality(rating_groups: &[&[Gaussian]], beta: f64) -> f64 {
 
     let mut rotated_a_matrix = Matrix::new(rating_groups.len() - 1, length);
 
+    // Row `row` contrasts group `row` (+weight) against group `row + 1`
+    // (-weight). `t` is the column where the current group's players start;
+    // the negative block begins immediately after it.
     let mut t = 0;
-    let mut x = 0;
 
     for (row, group) in rating_groups.windows(2).enumerate() {
         let current = group[0];
@@ -230,17 +407,13 @@ pub fn quality(rating_groups: &[&[Gaussian]], beta: f64) -> f64 {
 
         for n in t..t + current.len() {
             rotated_a_matrix[(row, n)] = flatten_weights[n];
-
-            x += 1;
         }
 
         t += current.len();
 
-        for n in x..x + next.len() {
+        for n in t..t + next.len() {
             rotated_a_matrix[(row, n)] = -flatten_weights[n];
         }
-
-        x += next.len();
     }
 
     let a_matrix = rotated_a_matrix.transpose();

src/matrix.rs

@@ -1,29 +1,13 @@
+//! Minimal dense matrix used by `quality()`.
+//!
+//! `determinant` and `inverse` go through one LU decomposition with partial
+//! pivoting — O(n³) and numerically stable. The previous implementation
+//! expanded cofactors recursively (O(n!), allocating a `Vec` per minor) and
+//! only implemented `inverse` for the 1×1 case, which limited `quality()` to
+//! exactly two rating groups.
+
 use std::ops;
 
-fn det(m: &[f64], x: usize) -> f64 {
-    if x == 1 {
-        m[0]
-    } else if x == 2 {
-        m[0] * m[3] - m[1] * m[2]
-    } else {
-        let mut d = 0.0;
-
-        for n in 0..x {
-            let ms = m
-                .iter()
-                .enumerate()
-                .skip(x)
-                .filter(|(i, _)| (i % x) != n)
-                .map(|(_, v)| *v)
-                .collect::<Vec<_>>();
-
-            d += (-1.0f64).powi(n as i32) * m[n] * det(&ms, x - 1);
-        }
-
-        d
-    }
-}
-
 #[derive(Clone, Debug)]
 pub struct Matrix {
     data: Box<[f64]>,
@@ -31,6 +15,107 @@ pub struct Matrix {
     width: usize,
 }
 
+/// LU decomposition with partial pivoting: `PA = LU`, stored compactly.
+///
+/// `lu` holds `L` below the diagonal (unit diagonal implied) and `U` on and
+/// above it. `sign` is the determinant sign contributed by row swaps, or 0.0
+/// when the matrix is singular.
+struct Lu {
+    lu: Vec<f64>,
+    perm: Vec<usize>,
+    n: usize,
+    sign: f64,
+}
+
+impl Lu {
+    fn decompose(m: &Matrix) -> Self {
+        debug_assert_eq!(m.width, m.height, "LU requires a square matrix");
+
+        let n = m.width;
+        let mut lu = m.data.to_vec();
+        let mut perm: Vec<usize> = (0..n).collect();
+        let mut sign = 1.0;
+
+        for col in 0..n {
+            // Partial pivot: take the largest-magnitude candidate to limit
+            // growth of round-off in the elimination below.
+            let mut pivot_row = col;
+            let mut pivot_max = lu[col * n + col].abs();
+
+            for row in (col + 1)..n {
+                let candidate = lu[row * n + col].abs();
+                if candidate > pivot_max {
+                    pivot_max = candidate;
+                    pivot_row = row;
+                }
+            }
+
+            if pivot_max == 0.0 {
+                sign = 0.0;
+                continue;
+            }
+
+            if pivot_row != col {
+                for k in 0..n {
+                    lu.swap(col * n + k, pivot_row * n + k);
+                }
+                perm.swap(col, pivot_row);
+                sign = -sign;
+            }
+
+            let pivot = lu[col * n + col];
+
+            for row in (col + 1)..n {
+                let factor = lu[row * n + col] / pivot;
+                lu[row * n + col] = factor;
+
+                for k in (col + 1)..n {
+                    lu[row * n + k] -= factor * lu[col * n + k];
+                }
+            }
+        }
+
+        Self { lu, perm, n, sign }
+    }
+
+    fn determinant(&self) -> f64 {
+        if self.sign == 0.0 {
+            return 0.0;
+        }
+
+        let mut det = self.sign;
+        for i in 0..self.n {
+            det *= self.lu[i * self.n + i];
+        }
+
+        det
+    }
+
+    /// Solve `Ax = b` for a single column of the identity, giving one column
+    /// of the inverse.
+    fn solve_column(&self, col: usize, out: &mut [f64]) {
+        let n = self.n;
+
+        // Forward substitution through L, applying the row permutation.
+        for i in 0..n {
+            let mut sum = if self.perm[i] == col { 1.0 } else { 0.0 };
+            for (k, &solved) in out.iter().enumerate().take(i) {
+                sum -= self.lu[i * n + k] * solved;
+            }
+            out[i] = sum;
+        }
+
+        // Back substitution through U.
+        for i in (0..n).rev() {
+            let mut sum = out[i];
+            for (k, &solved) in out.iter().enumerate().skip(i + 1) {
+                sum -= self.lu[i * n + k] * solved;
+            }
+            out[i] = sum / self.lu[i * n + i];
+        }
+    }
+}
+
 impl Matrix {
     pub fn new(height: usize, width: usize) -> Matrix {
         Matrix {
@@ -52,73 +137,59 @@ impl Matrix {
         matrix
     }
 
-    pub fn minor(&self, row_n: usize, col_n: usize) -> Matrix {
-        let mut matrix = Matrix::new(self.height - 1, self.width - 1);
-
-        let mut nr = 0;
-
-        for r in 0..self.height {
-            if r == row_n {
-                continue;
-            }
-
-            let mut nc = 0;
-
-            for c in 0..self.width {
-                if c == col_n {
-                    continue;
-                }
-
-                matrix[(nr, nc)] = self[(r, c)];
-
-                nc += 1;
-            }
-
-            nr += 1;
-        }
-
-        matrix
-    }
-
+    /// Determinant of a square matrix. The 0×0 determinant is 1 by convention
+    /// (the empty product).
+    ///
+    /// # Panics
+    ///
+    /// Panics if the matrix is not square.
     pub fn determinant(&self) -> f64 {
-        debug_assert!(self.width == self.height);
+        assert_eq!(
+            self.width, self.height,
+            "determinant requires a square matrix, got {}x{}",
+            self.height, self.width
+        );
 
-        det(&self.data, self.width)
+        if self.width == 0 {
+            return 1.0;
         }
 
-    pub fn adjugate(&self) -> Matrix {
-        debug_assert!(self.width == self.height);
-
-        let mut matrix = Matrix::new(self.height, self.width);
-
-        if matrix.height == 2 {
-            matrix[(0, 0)] = self[(1, 1)];
-            matrix[(0, 1)] = -self[(0, 1)];
-            matrix[(1, 0)] = -self[(1, 0)];
-            matrix[(1, 1)] = self[(0, 0)];
-        } else {
-            for r in 0..matrix.height {
-                for c in 0..matrix.width {
-                    let sign = if (r + c) % 2 == 0 { 1.0 } else { -1.0 };
-
-                    matrix[(r, c)] = self.minor(r, c).determinant() * sign;
-                }
-            }
-        }
-
-        matrix
+        Lu::decompose(self).determinant()
     }
 
+    /// Matrix inverse via LU decomposition.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the matrix is not square or is singular.
     pub fn inverse(&self) -> Matrix {
-        let mut matrix = Matrix::new(self.width, self.height);
+        assert_eq!(
+            self.width, self.height,
+            "inverse requires a square matrix, got {}x{}",
+            self.height, self.width
+        );
 
-        if self.height == self.width && self.height == 1 {
-            matrix[(0, 0)] = 1.0 / self[(0, 0)];
-        } else {
-            panic!("eh, okey")
+        let n = self.width;
+        let mut inverse = Matrix::new(n, n);
+
+        if n == 0 {
+            return inverse;
         }
 
-        matrix
+        let lu = Lu::decompose(self);
+        assert!(lu.sign != 0.0, "cannot invert a singular matrix");
+
+        let mut column = vec![0.0; n];
+
+        for c in 0..n {
+            lu.solve_column(c, &mut column);
+
+            for (r, &value) in column.iter().enumerate() {
+                inverse[(r, c)] = value;
+            }
+        }
+
+        inverse
     }
 }
 
@@ -126,20 +197,62 @@ impl ops::Index<(usize, usize)> for Matrix {
     type Output = f64;
 
     fn index(&self, pos: (usize, usize)) -> &Self::Output {
+        debug_assert!(
+            pos.0 < self.height && pos.1 < self.width,
+            "index ({}, {}) out of bounds for {}x{} matrix",
+            pos.0,
+            pos.1,
+            self.height,
+            self.width
+        );
+
         &self.data[(self.width * pos.0) + pos.1]
     }
 }
 
 impl ops::IndexMut<(usize, usize)> for Matrix {
     fn index_mut(&mut self, pos: (usize, usize)) -> &mut Self::Output {
+        debug_assert!(
+            pos.0 < self.height && pos.1 < self.width,
+            "index ({}, {}) out of bounds for {}x{} matrix",
+            pos.0,
+            pos.1,
+            self.height,
+            self.width
+        );
+
         &mut self.data[(self.width * pos.0) + pos.1]
     }
 }
 
-impl<'a> ops::Mul<&'a Matrix> for f64 {
+fn multiply(lhs: &Matrix, rhs: &Matrix) -> Matrix {
+    assert_eq!(
+        lhs.width, rhs.height,
+        "cannot multiply {}x{} by {}x{}",
+        lhs.height, lhs.width, rhs.height, rhs.width
+    );
+
+    let mut matrix = Matrix::new(lhs.height, rhs.width);
+
+    for r in 0..matrix.height {
+        for c in 0..matrix.width {
+            let mut value = 0.0;
+
+            for x in 0..lhs.width {
+                value += lhs[(r, x)] * rhs[(x, c)];
+            }
+
+            matrix[(r, c)] = value;
+        }
+    }
+
+    matrix
+}
+
+impl ops::Mul<&Matrix> for f64 {
     type Output = Matrix;
 
-    fn mul(self, rhs: &'a Matrix) -> Matrix {
+    fn mul(self, rhs: &Matrix) -> Matrix {
         let mut matrix = Matrix::new(rhs.height, rhs.width);
 
         for r in 0..rhs.height {
@@ -152,54 +265,35 @@ impl<'a> ops::Mul<&'a Matrix> for f64 {
     }
 }
 
-impl<'a> ops::Mul<&'a Matrix> for Matrix {
+impl ops::Mul<&Matrix> for Matrix {
     type Output = Matrix;
 
-    fn mul(self, rhs: &'a Matrix) -> Matrix {
-        let mut matrix = Matrix::new(self.height, rhs.width);
-
-        for r in 0..matrix.height {
-            for c in 0..matrix.width {
-                let mut value = 0.0;
-
-                for x in 0..self.width {
-                    value += self[(r, x)] * rhs[(x, c)];
-                }
-
-                matrix[(r, c)] = value;
+    fn mul(self, rhs: &Matrix) -> Matrix {
+        multiply(&self, rhs)
     }
 }
 
-        matrix
-    }
-}
-
-impl<'a> ops::Mul<&'a Matrix> for &'a Matrix {
+impl ops::Mul<&Matrix> for &Matrix {
     type Output = Matrix;
 
-    fn mul(self, rhs: &'a Matrix) -> Matrix {
-        let mut matrix = Matrix::new(self.height, rhs.width);
-
-        for r in 0..matrix.height {
-            for c in 0..matrix.width {
-                let mut value = 0.0;
-
-                for x in 0..self.width {
-                    value += self[(r, x)] * rhs[(x, c)];
-                }
-
-                matrix[(r, c)] = value;
+    fn mul(self, rhs: &Matrix) -> Matrix {
+        multiply(self, rhs)
     }
 }
 
-        matrix
-    }
-}
-
-impl<'a> ops::Add<&'a Matrix> for &'a Matrix {
+impl ops::Add<&Matrix> for &Matrix {
     type Output = Matrix;
 
-    fn add(self, rhs: &'a Matrix) -> Matrix {
+    fn add(self, rhs: &Matrix) -> Matrix {
+        assert!(
+            self.height == rhs.height && self.width == rhs.width,
+            "cannot add {}x{} to {}x{}",
+            self.height,
+            self.width,
+            rhs.height,
+            rhs.width
+        );
+
         let mut matrix = Matrix::new(self.height, self.width);
 
         for r in 0..matrix.height {
@@ -211,3 +305,106 @@ impl<'a> ops::Add<&'a Matrix> for &'a Matrix {
         matrix
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn from_rows(rows: &[&[f64]]) -> Matrix {
+        let mut m = Matrix::new(rows.len(), rows[0].len());
+        for (r, row) in rows.iter().enumerate() {
+            for (c, &v) in row.iter().enumerate() {
+                m[(r, c)] = v;
+            }
+        }
+        m
+    }
+
+    #[test]
+    fn determinant_1x1() {
+        assert!((from_rows(&[&[3.0]]).determinant() - 3.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn determinant_2x2() {
+        let m = from_rows(&[&[1.0, 2.0], &[3.0, 4.0]]);
+        assert!((m.determinant() - (-2.0)).abs() < 1e-12);
+    }
+
+    #[test]
+    fn determinant_3x3() {
+        let m = from_rows(&[&[6.0, 1.0, 1.0], &[4.0, -2.0, 5.0], &[2.0, 8.0, 7.0]]);
+        assert!((m.determinant() - (-306.0)).abs() < 1e-10);
+    }
+
+    #[test]
+    fn determinant_requires_no_pivot_at_origin() {
+        // A zero in the top-left forces a row swap; the sign must follow.
+        let m = from_rows(&[&[0.0, 1.0], &[1.0, 0.0]]);
+        assert!((m.determinant() - (-1.0)).abs() < 1e-12);
+    }
+
+    #[test]
+    fn determinant_of_singular_is_zero() {
+        let m = from_rows(&[&[1.0, 2.0], &[2.0, 4.0]]);
+        assert!(m.determinant().abs() < 1e-12);
+    }
+
+    #[test]
+    fn inverse_1x1() {
+        let inv = from_rows(&[&[4.0]]).inverse();
+        assert!((inv[(0, 0)] - 0.25).abs() < 1e-12);
+    }
+
+    #[test]
+    fn inverse_times_original_is_identity() {
+        for rows in [
+            vec![vec![1.0, 2.0], vec![3.0, 4.0]],
+            vec![
+                vec![6.0, 1.0, 1.0],
+                vec![4.0, -2.0, 5.0],
+                vec![2.0, 8.0, 7.0],
+            ],
+            vec![
+                vec![2.0, 0.0, 1.0, 3.0],
+                vec![1.0, 5.0, 2.0, 0.0],
+                vec![0.0, 1.0, 4.0, 1.0],
+                vec![3.0, 2.0, 0.0, 6.0],
+            ],
+        ] {
+            let refs: Vec<&[f64]> = rows.iter().map(|r| r.as_slice()).collect();
+            let m = from_rows(&refs);
+            let product = &m * &m.inverse();
+
+            for r in 0..product.height {
+                for c in 0..product.width {
+                    let expected = if r == c { 1.0 } else { 0.0 };
+                    assert!(
+                        (product[(r, c)] - expected).abs() < 1e-9,
+                        "({r},{c}) = {} expected {expected}",
+                        product[(r, c)]
+                    );
+                }
+            }
+        }
+    }
+
+    #[test]
+    #[should_panic(expected = "singular")]
+    fn inverse_of_singular_panics() {
+        let _ = from_rows(&[&[1.0, 2.0], &[2.0, 4.0]]).inverse();
+    }
+
+    #[test]
+    fn empty_determinant_is_one() {
+        assert!((Matrix::new(0, 0).determinant() - 1.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn transpose_round_trips() {
+        let m = from_rows(&[&[1.0, 2.0, 3.0], &[4.0, 5.0, 6.0]]);
+        let t = m.transpose();
+        assert_eq!((t.height, t.width), (3, 2));
+        assert_eq!(t.transpose()[(1, 2)], m[(1, 2)]);
+    }
+}

src/outcome.rs

@@ -29,7 +29,13 @@ pub enum Outcome {
 impl Outcome {
     /// `n`-team outcome where team `winner` won and everyone else tied for last.
     ///
+    /// Note this ties every loser, so for `n >= 3` it needs a positive
+    /// `p_draw` — see `InferenceError::TieWithoutDrawProbability`.
+    ///
+    /// # Panics
+    ///
     /// Panics if `winner >= n`.
+    #[must_use]
     pub fn winner(winner: u32, n: u32) -> Self {
         assert!(winner < n, "winner index {winner} out of range 0..{n}");
         let ranks: SmallVec<[u32; 4]> = (0..n).map(|i| if i == winner { 0 } else { 1 }).collect();
@@ -37,6 +43,7 @@ impl Outcome {
     }
 
     /// All `n` teams tied.
+    #[must_use]
     pub fn draw(n: u32) -> Self {
         Self::Ranked(SmallVec::from_vec(vec![0; n as usize]))
     }
@@ -57,15 +64,18 @@ impl Outcome {
 
     /// Explicit per-team continuous scores with a per-event noise override.
     ///
-    /// `sigma` must be `> 0.0`; debug-asserts otherwise.
+    /// `sigma` must be `> 0.0`. Constructing an `Outcome` with a non-positive
+    /// or NaN sigma is allowed; the value is rejected with
+    /// `InferenceError::InvalidParameter` when the event is ingested, so
+    /// callers get an error rather than a panic.
     pub fn scores_with_sigma<I: IntoIterator<Item = f64>>(scores: I, sigma: f64) -> Self {
-        debug_assert!(sigma > 0.0, "score_sigma must be > 0.0 (got {sigma})");
         Self::Scored {
             scores: scores.into_iter().collect(),
             sigma: Some(sigma),
         }
     }
 
+    #[must_use]
     pub fn team_count(&self) -> usize {
         match self {
             Self::Ranked(r) => r.len(),
@@ -169,9 +179,15 @@ mod tests {
         }
     }
 
+    /// Construction accepts any sigma; the value is validated at ingestion so
+    /// callers receive an `InferenceError` rather than a panic. See
+    /// `tests/degenerate_inputs.rs::scored_event_rejects_non_positive_sigma`.
     #[test]
-    #[should_panic(expected = "score_sigma must be > 0.0")]
-    fn scores_with_sigma_rejects_zero() {
-        let _ = Outcome::scores_with_sigma([3.0, 1.0], 0.0);
+    fn scores_with_sigma_defers_validation_to_ingestion() {
+        let o = Outcome::scores_with_sigma([3.0, 1.0], 0.0);
+        match o {
+            Outcome::Scored { sigma, .. } => assert_eq!(sigma, Some(0.0)),
+            Outcome::Ranked(_) => panic!("expected Scored variant"),
+        }
     }
 }

src/rating.rs

@@ -16,6 +16,9 @@ pub struct Rating<T: Time = i64, D: Drift<T> = ConstantDrift> {
     pub(crate) prior: Gaussian,
     pub(crate) beta: f64,
     pub(crate) drift: D,
+    /// Multiplier on the drift *variance* this competitor accumulates; 1.0 is
+    /// the neutral default. Set per competitor via `Member::with_drift_scale`.
+    pub(crate) drift_scale: f64,
     pub(crate) _time: PhantomData<T>,
 }
 
@@ -25,10 +28,61 @@ impl<T: Time, D: Drift<T>> Rating<T, D> {
             prior,
             beta,
             drift,
+            drift_scale: 1.0,
             _time: PhantomData,
         }
     }
 
+    /// Scale how fast this competitor drifts, relative to `drift`.
+    ///
+    /// Multiplies the drift *variance*, so the scale is in the same units as
+    /// `gamma`. `0.0` pins the competitor still.
+    #[must_use]
+    pub fn with_drift_scale(mut self, drift_scale: f64) -> Self {
+        self.drift_scale = drift_scale;
+        self
+    }
+
+    /// The configured prior skill estimate.
+    #[must_use]
+    pub fn prior(&self) -> Gaussian {
+        self.prior
+    }
+
+    /// Performance noise: how much a single showing varies around the skill.
+    #[must_use]
+    pub fn beta(&self) -> f64 {
+        self.beta
+    }
+
+    /// The drift model governing how skill may move between events.
+    #[must_use]
+    pub fn drift(&self) -> D {
+        self.drift
+    }
+
+    /// This competitor's multiplier on the drift variance; 1.0 is neutral.
+    #[must_use]
+    pub fn drift_scale(&self) -> f64 {
+        self.drift_scale
+    }
+
+    /// Drift variance accumulated over `from -> to`, scaled for this competitor.
+    ///
+    /// The single place the scale is applied for a `Time`-typed span. Callers
+    /// must go through this rather than `self.drift` directly, so a competitor's
+    /// scale cannot be silently skipped.
+    pub(crate) fn drift_variance_delta(&self, from: &T, to: &T) -> f64 {
+        self.drift.variance_delta(from, to) * self.drift_scale * self.drift_scale
+    }
+
+    /// Drift variance for a cached elapsed count, scaled for this competitor.
+    ///
+    /// The counterpart of `drift_variance_delta` for the cached-elapsed paths.
+    pub(crate) fn drift_variance_for_elapsed(&self, elapsed: i64) -> f64 {
+        self.drift.variance_for_elapsed(elapsed) * self.drift_scale * self.drift_scale
+    }
+
     pub(crate) fn performance(&self) -> Gaussian {
         self.prior.forget(self.beta.powi(2))
     }
@@ -40,6 +94,7 @@ impl Default for Rating<i64, ConstantDrift> {
             prior: Gaussian::default(),
             beta: BETA,
             drift: ConstantDrift(GAMMA),
+            drift_scale: 1.0,
             _time: PhantomData,
         }
     }

src/schedule.rs

@@ -1,7 +1,7 @@
 //! Schedule trait and built-in implementations.
 //!
 //! A schedule drives factor propagation to convergence. The default
-//! `EpsilonOrMax` performs one TeamSum sweep (setup) then alternating
+//! `EpsilonOrMax` performs one `TeamSum` sweep (setup) then alternating
 //! forward/backward sweeps over the iterating factors until the max
 //! delta drops below epsilon or `max` iterations is reached.
 
@@ -23,7 +23,7 @@ pub trait Schedule: Send + Sync {
 /// Default schedule: sweep forward then backward until step ≤ eps or iter == max.
 ///
 /// Matches the existing `Game::likelihoods` loop bit-for-bit when given the
-/// same factor layout (TeamSums first, then alternating RankDiff/Trunc pairs).
+/// same factor layout (`TeamSums` first, then alternating RankDiff/Trunc pairs).
 #[derive(Debug, Clone, Copy)]
 pub struct EpsilonOrMax {
     pub eps: f64,
@@ -32,8 +32,17 @@ pub struct EpsilonOrMax {
 
 impl Default for EpsilonOrMax {
     fn default() -> Self {
-        // Matches today's hard-coded tolerance and iteration cap.
-        Self { eps: 1e-6, max: 10 }
+        // Derived from `ConvergenceOptions` so there is one source of truth for
+        // the tolerance and iteration cap. These previously disagreed: this
+        // default capped at 10 iterations while `ConvergenceOptions` allowed 30,
+        // and which applied depended on whether inference went through
+        // `run_chain` or a `Schedule`.
+        let defaults = crate::ConvergenceOptions::default();
+
+        Self {
+            eps: defaults.epsilon,
+            max: defaults.max_iter,
+        }
     }
 }
 
@@ -50,10 +59,16 @@ impl Schedule for EpsilonOrMax {
         }
 
         let mut iterations = 0;
-        let mut final_step = (f64::INFINITY, f64::INFINITY);
-        let mut converged = false;
+        // With no iterating factors the graph is already at its fixed point:
+        // the setup pass above is all there is to do. Reporting `converged:
+        // false` with an infinite step for that case gave callers a false
+        // negative.
+        let mut final_step = (0.0, 0.0);
+        let mut converged = true;
 
         if n_setup < factors.len() {
+            final_step = (f64::INFINITY, f64::INFINITY);
+            converged = false;
             for _ in 0..self.max {
                 let mut step = (0.0_f64, 0.0_f64);
 
@@ -113,7 +128,8 @@ mod tests {
 
     #[test]
     fn report_marks_converged_when_no_iterating_factors() {
-        // No iterating factors → 0 iterations, converged stays false (loop never ran).
+        // A graph of only setup factors has nothing to iterate, so it is at its
+        // fixed point after the setup pass: 0 iterations, and converged.
         let mut vars = VarStore::new();
         let out = vars.alloc(N_INF);
         let mut factors = vec![BuiltinFactor::TeamSum(TeamSumFactor {
@@ -122,5 +138,15 @@ mod tests {
         })];
         let report = EpsilonOrMax::default().run(&mut factors, &mut vars);
         assert_eq!(report.iterations, 0);
+        assert!(report.converged);
+        assert_eq!(report.final_step, (0.0, 0.0));
+    }
+
+    #[test]
+    fn default_matches_convergence_options() {
+        let schedule = EpsilonOrMax::default();
+        let options = crate::ConvergenceOptions::default();
+        assert_eq!(schedule.max, options.max_iter);
+        assert_eq!(schedule.eps, options.epsilon);
     }
 }

src/storage/competitor_store.rs

@@ -2,7 +2,7 @@ use crate::{Index, competitor::Competitor, drift::Drift, time::Time};
 
 /// Dense Vec-backed store for competitor state in History.
 ///
-/// Indexed directly by Index.0, eliminating HashMap hashing in the
+/// Indexed directly by Index.0, eliminating `HashMap` hashing in the
 /// forward/backward sweep. Uses `Vec<Option<Competitor<T, D>>>` so slots can be
 /// absent without an explicit present mask.
 #[derive(Debug)]
@@ -21,6 +21,7 @@ impl<T: Time, D: Drift<T>> Default for CompetitorStore<T, D> {
 }
 
 impl<T: Time, D: Drift<T>> CompetitorStore<T, D> {
+    #[must_use]
     pub fn new() -> Self {
         Self::default()
     }
@@ -39,6 +40,7 @@ impl<T: Time, D: Drift<T>> CompetitorStore<T, D> {
         self.competitors[idx.0] = Some(competitor);
     }
 
+    #[must_use]
     pub fn get(&self, idx: Index) -> Option<&Competitor<T, D>> {
         self.competitors.get(idx.0).and_then(|slot| slot.as_ref())
     }
@@ -49,14 +51,17 @@ impl<T: Time, D: Drift<T>> CompetitorStore<T, D> {
             .and_then(|slot| slot.as_mut())
     }
 
+    #[must_use]
     pub fn contains(&self, idx: Index) -> bool {
         self.get(idx).is_some()
     }
 
+    #[must_use]
     pub fn len(&self) -> usize {
         self.n_present
     }
 
+    #[must_use]
     pub fn is_empty(&self) -> bool {
         self.n_present == 0
     }

src/storage/skill_store.rs

@@ -1,15 +1,27 @@
+use std::collections::HashMap;
+
 use crate::{Index, time_slice::Skill};
 
-/// Dense Vec-backed store for per-agent skill state within a TimeSlice.
+/// Compact per-slice store for skill state, addressed by a slice-local slot.
 ///
-/// Indexed directly by Index.0, eliminating HashMap hashing in the inner
-/// convergence loop. Uses a parallel `present` mask so iteration skips
-/// absent slots without incurring per-slot Option overhead in the hot path.
+/// `skills` holds one entry per competitor **in this slice**, so memory is
+/// O(competitors in the slice). It used to be a dense `Vec<Skill>` indexed by
+/// the global `Index.0`, which made a slice's footprint O(largest index it
+/// touches): a single 1v1 game between competitors 19998 and 19999 reserved
+/// 20,000 slots.
+///
+/// The dense layout existed to keep `HashMap` hashing out of the inner
+/// convergence loop, and that property is preserved. `slots` is consulted only
+/// while building a slice; every hot-path access goes through
+/// [`SkillStore::at`] / [`SkillStore::at_mut`] with a slot resolved once at
+/// ingestion and cached on the event's `Item`.
 #[derive(Debug, Default)]
 pub struct SkillStore {
     skills: Vec<Skill>,
-    present: Vec<bool>,
-    n_present: usize,
+    /// Slot -> global index, parallel to `skills`, so iteration can report the
+    /// global index without a reverse lookup.
+    indices: Vec<Index>,
+    slots: HashMap<Index, u32>,
 }
 
 impl SkillStore {
@@ -17,76 +29,99 @@ impl SkillStore {
         Self::default()
     }
 
-    fn ensure_capacity(&mut self, idx: usize) {
-        if idx >= self.skills.len() {
-            self.skills.resize_with(idx + 1, Skill::default);
-            self.present.resize(idx + 1, false);
-        }
+    /// Resolve a global index to this slice's slot, if the competitor is here.
+    ///
+    /// This hashes. Call it at ingestion and cache the result; do not call it
+    /// from the convergence loop.
+    pub fn slot_of(&self, idx: Index) -> Option<u32> {
+        self.slots.get(&idx).copied()
     }
 
-    pub fn insert(&mut self, idx: Index, skill: Skill) {
-        self.ensure_capacity(idx.0);
-        if !self.present[idx.0] {
-            self.n_present += 1;
+    /// Skill at a slot resolved earlier by [`SkillStore::slot_of`].
+    ///
+    /// # Panics
+    ///
+    /// Panics if `slot` is out of range, which means it came from a different
+    /// slice's store.
+    pub fn at(&self, slot: u32) -> &Skill {
+        &self.skills[slot as usize]
+    }
+
+    /// Mutable counterpart to [`SkillStore::at`].
+    ///
+    /// # Panics
+    ///
+    /// Panics if `slot` is out of range.
+    pub fn at_mut(&mut self, slot: u32) -> &mut Skill {
+        &mut self.skills[slot as usize]
+    }
+
+    /// Insert or overwrite a competitor's skill, returning its slot.
+    pub fn insert(&mut self, idx: Index, skill: Skill) -> u32 {
+        match self.slots.get(&idx) {
+            Some(&slot) => {
+                self.skills[slot as usize] = skill;
+                slot
+            }
+            None => {
+                let slot = u32::try_from(self.skills.len())
+                    .expect("a time slice cannot hold more than u32::MAX competitors");
+
+                self.skills.push(skill);
+                self.indices.push(idx);
+                self.slots.insert(idx, slot);
+
+                slot
+            }
         }
-        self.skills[idx.0] = skill;
-        self.present[idx.0] = true;
     }
 
     pub fn get(&self, idx: Index) -> Option<&Skill> {
-        if idx.0 < self.present.len() && self.present[idx.0] {
-            Some(&self.skills[idx.0])
-        } else {
-            None
-        }
+        self.slot_of(idx).map(|slot| self.at(slot))
     }
 
     pub fn get_mut(&mut self, idx: Index) -> Option<&mut Skill> {
-        if idx.0 < self.present.len() && self.present[idx.0] {
-            Some(&mut self.skills[idx.0])
-        } else {
-            None
-        }
+        self.slot_of(idx)
+            .map(|slot| &mut self.skills[slot as usize])
     }
 
-    #[allow(dead_code)]
+    /// Whether a competitor is present in this slice. Test-only.
+    #[cfg(test)]
     pub fn contains(&self, idx: Index) -> bool {
-        idx.0 < self.present.len() && self.present[idx.0]
+        self.slots.contains_key(&idx)
     }
 
-    #[allow(dead_code)]
+    /// Number of competitors in this slice. Test-only.
+    #[cfg(test)]
     pub fn len(&self) -> usize {
-        self.n_present
+        self.skills.len()
     }
 
-    #[allow(dead_code)]
-    pub fn is_empty(&self) -> bool {
-        self.n_present == 0
+    /// Slots actually allocated — the quantity #17 is about, and NOT the same
+    /// as `len` for every possible implementation.
+    ///
+    /// A store indexed by the global `Index` must report `max_index + 1` here
+    /// while reporting the true competitor count from `len`, which is exactly
+    /// how the original defect hid. Tests that mean to pin the footprint must
+    /// assert on this.
+    #[cfg(test)]
+    pub fn allocated_slots(&self) -> usize {
+        self.skills.len()
     }
 
+    /// Iterate in slot order — the order competitors were first seen in this
+    /// slice. Deterministic for a given event order, which is what the
+    /// cross-thread determinism test relies on.
     pub fn iter(&self) -> impl Iterator<Item = (Index, &Skill)> {
-        self.present.iter().enumerate().filter_map(|(i, &p)| {
-            if p {
-                Some((Index(i), &self.skills[i]))
-            } else {
-                None
-            }
-        })
+        self.indices.iter().copied().zip(self.skills.iter())
     }
 
     pub fn iter_mut(&mut self) -> impl Iterator<Item = (Index, &mut Skill)> {
-        self.skills
-            .iter_mut()
-            .zip(self.present.iter())
-            .enumerate()
-            .filter_map(|(i, (s, &p))| if p { Some((Index(i), s)) } else { None })
+        self.indices.iter().copied().zip(self.skills.iter_mut())
     }
 
     pub fn keys(&self) -> impl Iterator<Item = Index> + '_ {
-        self.present
-            .iter()
-            .enumerate()
-            .filter_map(|(i, &p)| if p { Some(Index(i)) } else { None })
+        self.indices.iter().copied()
     }
 }
 
@@ -112,7 +147,7 @@ mod tests {
     }
 
     #[test]
-    fn iter_skips_absent_slots() {
+    fn iter_reports_global_indices() {
         let mut store = SkillStore::new();
         store.insert(Index(0), Skill::default());
         store.insert(Index(5), Skill::default());
@@ -127,4 +162,28 @@ mod tests {
         store.insert(Index(2), Skill::default());
         assert_eq!(store.len(), 1);
     }
+
+    /// The defect in #17: a slice holding two competitors must cost the same
+    /// whether their indices are small or large.
+    #[test]
+    fn footprint_is_independent_of_index_magnitude() {
+        let mut low = SkillStore::new();
+        low.insert(Index(0), Skill::default());
+        low.insert(Index(1), Skill::default());
+
+        let mut high = SkillStore::new();
+        high.insert(Index(19_998), Skill::default());
+        high.insert(Index(19_999), Skill::default());
+
+        assert_eq!(low.len(), high.len());
+        assert_eq!(low.skills.capacity(), high.skills.capacity());
+    }
+
+    #[test]
+    fn slot_survives_reinsert() {
+        let mut store = SkillStore::new();
+        let first = store.insert(Index(7), Skill::default());
+        let again = store.insert(Index(7), Skill::default());
+        assert_eq!(first, again);
+    }
 }

src/time_slice.rs

@@ -14,7 +14,6 @@ use crate::{
     rating::Rating,
     storage::{CompetitorStore, SkillStore},
     time::Time,
-    tuple_gt, tuple_max,
 };
 
 #[derive(Debug)]
@@ -23,7 +22,6 @@ pub(crate) struct Skill {
     backward: Gaussian,
     likelihood: Gaussian,
     pub(crate) elapsed: i64,
-    pub(crate) online: Gaussian,
 }
 
 impl Skill {
@@ -39,7 +37,6 @@ impl Default for Skill {
             backward: N_INF,
             likelihood: N_INF,
             elapsed: 0,
-            online: N_INF,
         }
     }
 }
@@ -51,43 +48,48 @@ pub enum EventKind {
     Scored { score_sigma: f64 },
 }
 
-#[derive(Debug)]
+#[derive(Clone, Debug)]
 struct Item {
     agent: Index,
+    /// This competitor's slot in the owning slice's `SkillStore`, resolved
+    /// once at ingestion.
+    ///
+    /// The convergence loop reaches skills through this rather than through
+    /// `agent`, which is what keeps `HashMap` hashing out of the hot path now
+    /// that the store is compact rather than indexed by the global `Index`.
+    slot: u32,
     likelihood: Gaussian,
 }
 
 impl Item {
     fn within_prior<T: Time, D: Drift<T>>(
         &self,
-        online: bool,
         forward: bool,
         skills: &SkillStore,
         agents: &CompetitorStore<T, D>,
     ) -> Rating<T, D> {
         let r = &agents[self.agent].rating;
-        let skill = skills.get(self.agent).unwrap();
+        let skill = skills.at(self.slot);
 
-        if online {
-            Rating::new(skill.online, r.beta, r.drift)
-        } else if forward {
-            Rating::new(skill.forward, r.beta, r.drift)
+        if forward {
+            Rating::new(skill.forward, r.beta, r.drift).with_drift_scale(r.drift_scale)
         } else {
             Rating::new(skill.posterior() / self.likelihood, r.beta, r.drift)
+                .with_drift_scale(r.drift_scale)
         }
     }
 }
 
-#[derive(Debug)]
+#[derive(Clone, Debug)]
 struct Team {
     items: Vec<Item>,
     output: f64,
 }
 
-#[derive(Debug)]
+#[derive(Clone, Debug)]
 pub(crate) struct Event {
     teams: Vec<Team>,
-    evidence: f64,
+    log_evidence: f64,
     weights: Vec<Vec<f64>>,
     kind: EventKind,
 }
@@ -108,7 +110,6 @@ impl Event {
 
     pub(crate) fn within_priors<T: Time, D: Drift<T>>(
         &self,
-        online: bool,
         forward: bool,
         skills: &SkillStore,
         agents: &CompetitorStore<T, D>,
@@ -118,25 +119,26 @@ impl Event {
             .map(|team| {
                 team.items
                     .iter()
-                    .map(|item| item.within_prior(online, forward, skills, agents))
+                    .map(|item| item.within_prior(forward, skills, agents))
                     .collect::<Vec<_>>()
             })
             .collect::<Vec<_>>()
     }
 
-    /// Direct in-loop update: mutates self and `skills` inline with no
-    /// intermediate allocation. Used by both the sequential sweep path and,
-    /// via unsafe, by the parallel rayon path for events in the same color
-    /// group (which have disjoint agent sets — see `sweep_color_groups`).
-    fn iteration_direct<T: Time, D: Drift<T>>(
-        &mut self,
-        skills: &mut SkillStore,
+    /// Run inference for this event and return its per-item likelihoods.
+    ///
+    /// Reads `skills` immutably and does not touch `self`, so every event in
+    /// a color group can run concurrently without any aliasing question —
+    /// the mutation is deferred to `apply`.
+    fn compute<T: Time, D: Drift<T>>(
+        &self,
+        skills: &SkillStore,
         agents: &CompetitorStore<T, D>,
         p_draw: f64,
         convergence: crate::ConvergenceOptions,
         arena: &mut ScratchArena,
-    ) {
-        let teams = self.within_priors(false, false, skills, agents);
+    ) -> EventUpdate {
+        let teams = self.within_priors(false, skills, agents);
         let result = self.outputs();
         let g = match self.kind {
             EventKind::Ranked => {
@@ -152,19 +154,60 @@ impl Event {
             ),
         };
 
-        for (t, team) in self.teams.iter_mut().enumerate() {
-            for (i, item) in team.items.iter_mut().enumerate() {
-                let old_likelihood = skills.get(item.agent).unwrap().likelihood;
-                let new_likelihood = (old_likelihood / item.likelihood) * g.likelihoods[t][i];
-                skills.get_mut(item.agent).unwrap().likelihood = new_likelihood;
-                item.likelihood = g.likelihoods[t][i];
+        EventUpdate {
+            log_evidence: g.log_evidence,
+            likelihoods: g.likelihoods,
         }
     }
 
-        self.evidence = g.evidence;
+    /// Fold a computed update into the skill store and cache it on the items.
+    fn apply(&mut self, skills: &mut SkillStore, update: EventUpdate) {
+        for (t, team) in self.teams.iter_mut().enumerate() {
+            for (i, item) in team.items.iter_mut().enumerate() {
+                let fresh = update.likelihoods[t][i];
+                let old_likelihood = skills.at(item.slot).likelihood;
+                let new_likelihood = (old_likelihood / item.likelihood) * fresh;
+                skills.at_mut(item.slot).likelihood = new_likelihood;
+                item.likelihood = fresh;
             }
         }
 
+        self.log_evidence = update.log_evidence;
+    }
+
+    /// Compute and apply in one step — the sequential sweep.
+    fn iteration_direct<T: Time, D: Drift<T>>(
+        &mut self,
+        skills: &mut SkillStore,
+        agents: &CompetitorStore<T, D>,
+        p_draw: f64,
+        convergence: crate::ConvergenceOptions,
+        arena: &mut ScratchArena,
+    ) {
+        let update = self.compute(skills, agents, p_draw, convergence, arena);
+        self.apply(skills, update);
+    }
+}
+
+/// The result of running inference for one event, before it is folded back
+/// into the shared skill store.
+#[derive(Debug)]
+struct EventUpdate {
+    log_evidence: f64,
+    likelihoods: Vec<Vec<Gaussian>>,
+}
+
+/// One slice's worth of forward-only inference.
+///
+/// `posteriors` doubles as the outgoing forward message: the scratch sweep
+/// never writes `backward`, so it stays `N_INF`, and `Skill::posterior()`
+/// and `forward_prior_out` are then the same product.
+#[derive(Debug)]
+pub(crate) struct FilteredStep {
+    pub(crate) log_evidence: f64,
+    pub(crate) posteriors: Vec<(Index, Gaussian)>,
+}
+
 #[derive(Debug)]
 pub struct TimeSlice<T: Time = i64> {
     pub(crate) events: Vec<Event>,
@@ -174,6 +217,14 @@ pub struct TimeSlice<T: Time = i64> {
     pub(crate) convergence: crate::ConvergenceOptions,
     arena: ScratchArena,
     pub(crate) color_groups: ColorGroups,
+    /// Whether `color_groups` still reflects `events`.
+    ///
+    /// Coloring is rebuilt lazily, on the first full sweep after an append,
+    /// rather than eagerly per append: the partition is thrown away and
+    /// recomputed wholesale either way, so doing it per append made ingesting
+    /// n events O(n^2) with no benefit — nothing reads the partition between
+    /// an append and the next full sweep.
+    color_groups_dirty: bool,
 }
 
 impl<T: Time> TimeSlice<T> {
@@ -186,6 +237,7 @@ impl<T: Time> TimeSlice<T> {
             convergence,
             arena: ScratchArena::new(),
             color_groups: ColorGroups::new(),
+            color_groups_dirty: false,
         }
     }
 
@@ -198,6 +250,7 @@ impl<T: Time> TimeSlice<T> {
         let n = self.events.len();
         if n == 0 {
             self.color_groups = ColorGroups::new();
+            self.color_groups_dirty = false;
             return;
         }
 
@@ -221,13 +274,19 @@ impl<T: Time> TimeSlice<T> {
 
         self.events = reordered;
         self.color_groups = ColorGroups { groups: new_groups };
+        self.color_groups_dirty = false;
+
+        debug_assert!(
+            self.color_groups.groups_are_contiguous(),
+            "color groups must occupy contiguous event ranges"
+        );
     }
 
     pub fn add_events<D: Drift<T>>(
         &mut self,
         composition: Vec<Vec<Vec<Index>>>,
-        results: Vec<Vec<f64>>,
-        weights: Vec<Vec<Vec<f64>>>,
+        results: Option<Vec<Vec<f64>>>,
+        weights: Option<Vec<Vec<Vec<f64>>>>,
         kinds: Vec<EventKind>,
         agents: &CompetitorStore<T, D>,
     ) {
@@ -246,21 +305,26 @@ impl<T: Time> TimeSlice<T> {
         for idx in this_agent {
             let elapsed = compute_elapsed(agents[*idx].last_time.as_ref(), &self.time);
 
+            let forward = agents[*idx].receive(&self.time);
+
             if let Some(skill) = self.skills.get_mut(*idx) {
                 skill.elapsed = elapsed;
-                skill.forward = agents[*idx].receive(&self.time);
+                skill.forward = forward;
             } else {
                 self.skills.insert(
                     *idx,
                     Skill {
-                        forward: agents[*idx].receive(&self.time),
+                        forward,
+                        backward: N_INF,
+                        likelihood: N_INF,
                         elapsed,
-                        ..Default::default()
                     },
                 );
             }
         }
 
+        let skills = &self.skills;
+
         let events = composition.iter().enumerate().map(|(e, event)| {
             let teams = event
                 .iter()
@@ -270,33 +334,37 @@ impl<T: Time> TimeSlice<T> {
                         .iter()
                         .map(|&agent| Item {
                             agent,
+                            // Every participant was inserted into `skills`
+                            // just above, so the slot always resolves.
+                            slot: skills
+                                .slot_of(agent)
+                                .expect("participant must be present in the slice store"),
                             likelihood: N_INF,
                         })
                         .collect::<Vec<_>>();
 
                     Team {
                         items,
-                        output: if results.is_empty() {
-                            (event.len() - (t + 1)) as f64
-                        } else {
-                            results[e][t]
+                        output: match &results {
+                            Some(results) => results[e][t],
+                            // No explicit result: rank by position, first team best.
+                            None => (event.len() - (t + 1)) as f64,
                         },
                     }
                 })
                 .collect::<Vec<_>>();
 
-            let weights = if weights.is_empty() {
-                teams
+            let weights = match &weights {
+                Some(weights) => weights[e].clone(),
+                None => teams
                     .iter()
                     .map(|team| vec![1.0; team.items.len()])
-                    .collect::<Vec<_>>()
-            } else {
-                weights[e].clone()
+                    .collect::<Vec<_>>(),
             };
 
             Event {
                 teams,
-                evidence: 0.0,
+                log_evidence: 0.0,
                 weights,
                 kind: kinds[e],
             }
@@ -306,8 +374,9 @@ impl<T: Time> TimeSlice<T> {
 
         self.events.extend(events);
 
+        self.color_groups_dirty = true;
+
         self.iteration(from, agents);
-        self.recompute_color_groups();
     }
 
     pub(crate) fn posteriors(&self) -> HashMap<Index, Gaussian> {
@@ -317,11 +386,22 @@ impl<T: Time> TimeSlice<T> {
             .collect::<HashMap<_, _>>()
     }
 
+    /// Sweep this slice's events once, starting at index `from`.
+    ///
+    /// # Panics
+    ///
+    /// Panics if an event references a competitor with no entry in this
+    /// slice's skill store. `add_events` inserts one for every participant, so
+    /// this cannot happen for slices built through the public API.
     pub fn iteration<D: Drift<T>>(&mut self, from: usize, agents: &CompetitorStore<T, D>) {
+        if from == 0 && self.color_groups_dirty {
+            self.recompute_color_groups();
+        }
+
         if from > 0 || self.color_groups.is_empty() {
             // Initial pass (add_events) or no color groups yet: simple sequential sweep.
             for event in self.events.iter_mut().skip(from) {
-                let teams = event.within_priors(false, false, &self.skills, agents);
+                let teams = event.within_priors(false, &self.skills, agents);
                 let result = event.outputs();
 
                 let g = match event.kind {
@@ -345,15 +425,15 @@ impl<T: Time> TimeSlice<T> {
 
                 for (t, team) in event.teams.iter_mut().enumerate() {
                     for (i, item) in team.items.iter_mut().enumerate() {
-                        let old_likelihood = self.skills.get(item.agent).unwrap().likelihood;
+                        let old_likelihood = self.skills.at(item.slot).likelihood;
                         let new_likelihood =
                             (old_likelihood / item.likelihood) * g.likelihoods[t][i];
-                        self.skills.get_mut(item.agent).unwrap().likelihood = new_likelihood;
+                        self.skills.at_mut(item.slot).likelihood = new_likelihood;
                         item.likelihood = g.likelihoods[t][i];
                     }
                 }
 
-                event.evidence = g.evidence;
+                event.log_evidence = g.log_evidence;
             }
         } else {
             self.sweep_color_groups(agents);
@@ -363,14 +443,13 @@ impl<T: Time> TimeSlice<T> {
     /// Full event sweep using the color-group partition. Colors are processed
     /// sequentially; within each color the inner loop is parallel under rayon.
     ///
-    /// Events within each color group touch disjoint agent sets (guaranteed by
-    /// the greedy coloring). This lets each rayon thread write directly to its
-    /// events' skill likelihoods without a deferred-apply step, matching the
-    /// sequential path's allocation profile. The unsafe block is sound because:
-    ///   1. `self.events[range]` and `self.skills` are separate fields → disjoint.
-    ///   2. Events in the same color group access disjoint `Index` values in
-    ///      `self.skills`, so concurrent writes land on different memory locations.
-    ///   3. Each event only writes to its own items' likelihoods (no sharing).
+    /// Events in one color group touch disjoint agent sets, so none of them
+    /// can observe another's writes. That makes the sweep separable: inference
+    /// runs concurrently over shared `&self.skills`, and the resulting updates
+    /// are folded in afterwards in index order. Splitting it this way needs no
+    /// `unsafe` and no aliasing argument, and it keeps results bit-identical
+    /// across thread counts because the apply order does not depend on which
+    /// worker finished first.
     #[cfg(feature = "rayon")]
     fn sweep_color_groups<D: Drift<T>>(&mut self, agents: &CompetitorStore<T, D>) {
         use rayon::prelude::*;
@@ -390,29 +469,28 @@ impl<T: Time> TimeSlice<T> {
             if group_len == 0 {
                 continue;
             }
+
             let range = self.color_groups.color_range(color_idx);
             let p_draw = self.p_draw;
             let convergence = self.convergence;
 
             if group_len >= RAYON_THRESHOLD {
-                // Obtain a raw pointer from the unique `&mut self.skills` reference.
-                // Casting back to `&mut` inside the closure is sound because:
-                //   1. The pointer originates from a `&mut` — no aliasing with shared refs.
-                //   2. Events in the same color group touch disjoint `Index` slots in the
-                //      underlying Vec, so concurrent writes from different threads land on
-                //      different memory locations — no data race.
-                //   3. `self.events[range]` and `self.skills` are separate struct fields,
-                //      so the borrow splits cleanly.
-                let skills_addr: usize = (&mut self.skills as *mut SkillStore) as usize;
-                self.events[range].par_iter_mut().for_each(move |ev| {
-                    // SAFETY: see above.
-                    let skills: &mut SkillStore = unsafe { &mut *(skills_addr as *mut SkillStore) };
+                let skills = &self.skills;
+                let updates: Vec<EventUpdate> = self.events[range.clone()]
+                    .par_iter()
+                    .map(|ev| {
                         ARENA.with(|cell| {
                             let mut arena = cell.borrow_mut();
                             arena.reset();
-                        ev.iteration_direct(skills, agents, p_draw, convergence, &mut arena);
-                    });
-                });
+
+                            ev.compute(skills, agents, p_draw, convergence, &mut arena)
+                        })
+                    })
+                    .collect();
+
+                for (ev, update) in self.events[range].iter_mut().zip(updates) {
+                    ev.apply(&mut self.skills, update);
+                }
             } else {
                 for ev in &mut self.events[range] {
                     ev.iteration_direct(
@@ -454,18 +532,29 @@ impl<T: Time> TimeSlice<T> {
         }
     }
 
-    #[allow(dead_code)]
+    /// Iterate this slice alone until its posteriors stop moving, returning
+    /// the number of iterations taken.
+    ///
+    /// Used by `filtered_step` to drive a scratch copy of the slice, and by
+    /// tests. Production convergence across slices is driven by
+    /// `History::converge`, which calls `iteration` directly.
+    ///
+    /// Honours `self.convergence`; it previously hard-coded an epsilon and a
+    /// 20-iteration cap that matched neither `ConvergenceOptions` nor the
+    /// schedule default.
     pub(crate) fn iterate_to_convergence<D: Drift<T>>(
         &mut self,
         agents: &CompetitorStore<T, D>,
     ) -> usize {
-        let epsilon = 1e-6;
-        let iterations = 20;
+        use crate::{tuple_gt, tuple_max};
+
+        let epsilon = self.convergence.epsilon;
+        let max_iter = self.convergence.max_iter;
 
         let mut step = (f64::INFINITY, f64::INFINITY);
         let mut i = 0;
 
-        while tuple_gt(step, epsilon) && i < iterations {
+        while tuple_gt(step, epsilon) && i < max_iter {
             let old = self.posteriors();
 
             self.iteration(0, agents);
@@ -477,6 +566,10 @@ impl<T: Time> TimeSlice<T> {
             });
 
             i += 1;
+
+            if !crate::step_is_finite(step) {
+                break;
+            }
         }
 
         i
@@ -497,14 +590,13 @@ impl<T: Time> TimeSlice<T> {
         n.forget(
             agents[*agent]
                 .rating
-                .drift
-                .variance_for_elapsed(skill.elapsed),
+                .drift_variance_for_elapsed(skill.elapsed),
         )
     }
 
     pub(crate) fn new_backward_info<D: Drift<T>>(&mut self, agents: &CompetitorStore<T, D>) {
         for (agent, skill) in self.skills.iter_mut() {
-            skill.backward = agents[agent].message;
+            skill.backward = agents[agent].message.unwrap_or(N_INF);
         }
         self.iteration(0, agents);
     }
@@ -516,21 +608,99 @@ impl<T: Time> TimeSlice<T> {
         self.iteration(0, agents);
     }
 
+    /// Run this slice's events on forward (filtering) information alone.
+    ///
+    /// `incoming` holds each competitor's forward message out of their
+    /// previous appearance; a competitor absent from it starts at their
+    /// configured prior. The sweep runs on a scratch copy, so the real slice
+    /// is untouched — which is what makes the filtered estimates independent
+    /// of whether `History::converge` has run.
+    pub(crate) fn filtered_step<D: Drift<T>>(
+        &self,
+        incoming: &HashMap<Index, Gaussian>,
+        agents: &CompetitorStore<T, D>,
+    ) -> FilteredStep {
+        let mut scratch = TimeSlice {
+            events: self.events.clone(),
+            skills: SkillStore::new(),
+            time: self.time,
+            p_draw: self.p_draw,
+            convergence: self.convergence,
+            arena: ScratchArena::new(),
+            color_groups: ColorGroups::new(),
+            color_groups_dirty: true,
+        };
+
+        for event in &mut scratch.events {
+            for team in &mut event.teams {
+                for item in &mut team.items {
+                    item.likelihood = N_INF;
+                }
+            }
+
+            event.log_evidence = 0.0;
+        }
+
+        for (agent, skill) in self.skills.iter() {
+            let rating = &agents[agent].rating;
+
+            let forward = match incoming.get(&agent) {
+                Some(message) => message.forget(rating.drift_variance_for_elapsed(skill.elapsed)),
+                None => rating.prior,
+            };
+
+            let slot = scratch.skills.insert(
+                agent,
+                Skill {
+                    forward,
+                    backward: N_INF,
+                    likelihood: N_INF,
+                    elapsed: skill.elapsed,
+                },
+            );
+
+            // The cloned events carry slots resolved against the REAL store, so
+            // the scratch must assign the same ones. It does because `iter()`
+            // yields slot order and `insert` allocates slots in call order —
+            // but that is a coupling between two types, so pin it here rather
+            // than leave it to be rediscovered after it breaks.
+            debug_assert_eq!(
+                Some(slot),
+                self.skills.slot_of(agent),
+                "scratch slot must match the real slice's slot for {agent:?}"
+            );
+        }
+
+        scratch.iterate_to_convergence(agents);
+
+        FilteredStep {
+            log_evidence: scratch.events.iter().map(|event| event.log_evidence).sum(),
+            posteriors: scratch
+                .skills
+                .iter()
+                .map(|(agent, skill)| (agent, skill.posterior()))
+                .collect(),
+        }
+    }
+
     pub(crate) fn log_evidence<D: Drift<T>>(
         &self,
-        online: bool,
         targets: &[Index],
         forward: bool,
         agents: &CompetitorStore<T, D>,
     ) -> f64 {
+        // Hashed once rather than scanned per player per event, so a
+        // `log_evidence_for` with many keys is not quadratic.
+        let target_set: std::collections::HashSet<Index> = targets.iter().copied().collect();
         // log_evidence is infrequent; a local arena avoids needing &mut self.
         let mut arena = ScratchArena::new();
 
         let run_event = |event: &Event, arena: &mut ScratchArena| -> f64 {
-            let teams = event.within_priors(online, forward, &self.skills, agents);
+            let teams = event.within_priors(forward, &self.skills, agents);
             let result = event.outputs();
             match event.kind {
-                EventKind::Ranked => Game::ranked_with_arena(
+                EventKind::Ranked => {
+                    Game::ranked_with_arena(
                         teams,
                         &result,
                         &event.weights,
@@ -538,9 +708,10 @@ impl<T: Time> TimeSlice<T> {
                         self.convergence,
                         arena,
                     )
-                .evidence
-                .ln(),
-                EventKind::Scored { score_sigma } => Game::scored_with_arena(
+                    .log_evidence
+                }
+                EventKind::Scored { score_sigma } => {
+                    Game::scored_with_arena(
                         teams,
                         &result,
                         &event.weights,
@@ -548,21 +719,21 @@ impl<T: Time> TimeSlice<T> {
                         self.convergence,
                         arena,
                     )
-                .evidence
-                .ln(),
+                    .log_evidence
+                }
             }
         };
 
         if targets.is_empty() {
-            if online || forward {
+            if forward {
                 self.events
                     .iter()
                     .map(|event| run_event(event, &mut arena))
                     .sum()
             } else {
-                self.events.iter().map(|event| event.evidence.ln()).sum()
+                self.events.iter().map(|event| event.log_evidence).sum()
             }
-        } else if online || forward {
+        } else if forward {
             self.events
                 .iter()
                 .filter(|event| {
@@ -570,7 +741,7 @@ impl<T: Time> TimeSlice<T> {
                         .teams
                         .iter()
                         .flat_map(|team| &team.items)
-                        .any(|item| targets.contains(&item.agent))
+                        .any(|item| target_set.contains(&item.agent))
                 })
                 .map(|event| run_event(event, &mut arena))
                 .sum()
@@ -582,9 +753,9 @@ impl<T: Time> TimeSlice<T> {
                         .teams
                         .iter()
                         .flat_map(|team| &team.items)
-                        .any(|item| targets.contains(&item.agent))
+                        .any(|item| target_set.contains(&item.agent))
                 })
-                .map(|event| event.evidence.ln())
+                .map(|event| event.log_evidence)
                 .sum()
         }
     }
@@ -616,8 +787,26 @@ impl<T: Time> TimeSlice<T> {
     }
 }
 
+/// Elapsed time from a competitor's previous appearance to `current`.
+///
+/// A negative elapsed means slices are being visited out of time order, which
+/// would make drift *reduce* uncertainty. Release builds clamp to zero so a
+/// bad timestamp degrades to "no drift" rather than corrupting the posterior;
+/// debug builds trip instead, because reaching here is a bug in slice ordering
+/// rather than something callers can cause with ordinary data.
 pub(crate) fn compute_elapsed<T: Time>(last: Option<&T>, current: &T) -> i64 {
-    last.map(|l| l.elapsed_to(current).max(0)).unwrap_or(0)
+    let Some(last) = last else {
+        return 0;
+    };
+
+    let elapsed = last.elapsed_to(current);
+
+    debug_assert!(
+        elapsed >= 0,
+        "negative elapsed ({elapsed}) — slices visited out of time order"
+    );
+
+    elapsed.max(0)
 }
 
 #[cfg(test)]
@@ -665,8 +854,8 @@ mod tests {
                 vec![vec![c], vec![d]],
                 vec![vec![e], vec![f]],
             ],
-            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
-            vec![],
+            Some(vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]]),
+            None,
             vec![EventKind::Ranked; 3],
             &agents,
         );
@@ -742,8 +931,8 @@ mod tests {
                 vec![vec![a], vec![c]],
                 vec![vec![b], vec![c]],
             ],
-            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
-            vec![],
+            Some(vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]]),
+            None,
             vec![EventKind::Ranked; 3],
             &agents,
         );
@@ -822,8 +1011,8 @@ mod tests {
                 vec![vec![a], vec![c]],
                 vec![vec![b], vec![c]],
             ],
-            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
-            vec![],
+            Some(vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]]),
+            None,
             vec![EventKind::Ranked; 3],
             &agents,
         );
@@ -854,8 +1043,8 @@ mod tests {
                 vec![vec![a], vec![c]],
                 vec![vec![b], vec![c]],
             ],
-            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
-            vec![],
+            Some(vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]]),
+            None,
             vec![EventKind::Ranked; 3],
             &agents,
         );
@@ -866,19 +1055,24 @@ mod tests {
 
         let post = time_slice.posteriors();
 
+        // These are convergence residuals, not exact values: by symmetry the
+        // true mean is 25.0 and the iteration approaches it from above. The
+        // previous expectation of 25.000003 was the residual after the
+        // hard-coded 20-iteration cap; honouring `ConvergenceOptions` runs to
+        // 30 and lands nearer the truth.
         assert_ulps_eq!(
             post[&a],
-            Gaussian::from_ms(25.000003, 3.880150),
+            Gaussian::from_ms(25.000001, 3.880150),
             epsilon = 1e-6
         );
         assert_ulps_eq!(
             post[&b],
-            Gaussian::from_ms(25.000003, 3.880150),
+            Gaussian::from_ms(25.000001, 3.880150),
             epsilon = 1e-6
         );
         assert_ulps_eq!(
             post[&c],
-            Gaussian::from_ms(25.000003, 3.880150),
+            Gaussian::from_ms(25.000001, 3.880150),
             epsilon = 1e-6
         );
     }
@@ -920,8 +1114,8 @@ mod tests {
                 vec![vec![c], vec![d]],
                 vec![vec![a], vec![c]],
             ],
-            vec![vec![1.0, 0.0], vec![1.0, 0.0], vec![1.0, 0.0]],
-            vec![],
+            Some(vec![vec![1.0, 0.0], vec![1.0, 0.0], vec![1.0, 0.0]]),
+            None,
             vec![EventKind::Ranked; 3],
             &agents,
         );

tests/api_shape.rs

@@ -247,3 +247,46 @@ fn fluent_event_builder_scores() {
     let b = h.current_skill(&"bob").unwrap();
     assert!(a.mu() > b.mu());
 }
+
+/// Every field of `ConvergenceReport` must carry real information.
+///
+/// `slices_skipped` was public, hardcoded to `0`, and reported a plausible
+/// value for a feature that never existed — the same shape as the inert
+/// `online` flag in #19. It was removed in #33. This pins the remaining fields
+/// so the next always-constant member has to survive an assertion rather than
+/// just a reviewer's attention.
+#[test]
+fn every_convergence_report_field_is_populated() {
+    let mut h = History::builder().build();
+
+    for time in 1..=6i64 {
+        h.record_winner(&"a", &"b", time).unwrap();
+    }
+
+    let report = h.converge().unwrap();
+
+    assert!(
+        report.iterations > 0,
+        "iterations is zero on a real converge"
+    );
+
+    assert!(report.converged, "fixture must converge");
+
+    assert!(
+        report.final_step.0.is_finite() && report.final_step.1.is_finite(),
+        "final_step is not finite: {:?}",
+        report.final_step
+    );
+
+    assert!(
+        report.log_evidence.is_finite() && report.log_evidence < 0.0,
+        "log_evidence is not a finite negative log probability: {}",
+        report.log_evidence
+    );
+
+    assert_eq!(
+        report.per_iteration_time.len(),
+        report.iterations,
+        "per_iteration_time must carry one duration per iteration"
+    );
+}

tests/common/mod.rs

@@ -0,0 +1,38 @@
+//! Helpers shared across the integration suites.
+//!
+//! Each integration file is its own binary, so `mod common;` compiles a copy
+//! per suite. Anything unused in a given suite would warn, hence the
+//! `#![allow(dead_code)]`.
+
+#![allow(dead_code)]
+
+use trueskill_tt::Gaussian;
+
+/// A posterior must be finite with a strictly positive sigma.
+///
+/// A non-finite posterior is the failure mode this crate is most prone to —
+/// EP breaking down produces NaN rather than an error — and a zero or negative
+/// sigma means the precision went non-positive, which `Gaussian::sigma` reports
+/// as improper rather than trapping.
+pub fn assert_finite(g: Gaussian, what: &str) {
+    assert!(
+        g.mu().is_finite(),
+        "{what}: mu is not finite (mu={}, sigma={})",
+        g.mu(),
+        g.sigma()
+    );
+
+    assert!(
+        g.sigma().is_finite() && g.sigma() > 0.0,
+        "{what}: sigma must be finite and positive (mu={}, sigma={})",
+        g.mu(),
+        g.sigma()
+    );
+}
+
+/// Every point on every learning curve must be finite.
+pub fn assert_curve_finite(curve: &[(i64, Gaussian)], who: &str) {
+    for (time, g) in curve {
+        assert_finite(*g, &format!("{who} at t={time}"));
+    }
+}

tests/degenerate_inputs.rs

@@ -0,0 +1,423 @@
+//! Degenerate, boundary, and error-path coverage.
+//!
+//! These run in both debug and release: the defects they pin were all
+//! guarded only by `debug_assert!`, so a debug-only suite never saw them.
+
+mod common;
+
+use common::assert_finite;
+use trueskill_tt::{
+    ConstantDrift, ConvergenceOptions, Game, GameOptions, Gaussian, History, InferenceError,
+    NullObserver, Outcome, Rating,
+};
+
+type R = Rating<i64, ConstantDrift>;
+
+fn rating() -> R {
+    R::new(
+        Gaussian::from_ms(25.0, 25.0 / 3.0),
+        25.0 / 6.0,
+        ConstantDrift(25.0 / 300.0),
+    )
+}
+
+#[test]
+fn record_draw_without_draw_probability_is_rejected() {
+    let mut h = History::default();
+    let err = h.record_draw(&"a", &"b", 1).unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+}
+
+#[test]
+fn builder_draw_without_draw_probability_is_rejected() {
+    let mut h = History::default();
+    let err = h
+        .event(1)
+        .team(["a"])
+        .team(["b"])
+        .draw()
+        .commit()
+        .unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+}
+
+#[test]
+fn draw_with_positive_draw_probability_is_finite() {
+    let mut h = History::builder().p_draw(0.25).build();
+    h.record_draw(&"a", &"b", 1).unwrap();
+    let report = h.converge().unwrap();
+
+    assert_finite(h.current_skill("a").unwrap(), "drawn competitor skill");
+    assert_finite(h.current_skill("b").unwrap(), "drawn competitor skill");
+    assert!(report.log_evidence.is_finite());
+    assert!(report.converged);
+}
+
+#[test]
+fn game_ranked_rejects_tie_without_draw_probability() {
+    let a = [rating()];
+    let b = [rating()];
+    let teams: Vec<&[R]> = vec![&a, &b];
+    let err = Game::ranked(&teams, Outcome::draw(2), &GameOptions::default()).unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+}
+
+/// `Outcome::winner(w, n)` ties every loser, so any n >= 3 free-for-all hits
+/// the tie path even though the caller never asked for a draw.
+#[test]
+fn winner_of_three_or_more_requires_draw_probability() {
+    let a = [rating()];
+    let b = [rating()];
+    let c = [rating()];
+    let teams: Vec<&[R]> = vec![&a, &b, &c];
+
+    let err = Game::ranked(&teams, Outcome::winner(0, 3), &GameOptions::default()).unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::TieWithoutDrawProbability { .. }
+    ));
+
+    let opts = GameOptions {
+        p_draw: 0.1,
+        ..GameOptions::default()
+    };
+    let game = Game::ranked(&teams, Outcome::winner(0, 3), &opts).unwrap();
+    for team in game.posteriors() {
+        for skill in team {
+            assert_finite(skill, "3-team winner posterior");
+        }
+    }
+}
+
+#[test]
+fn full_ranking_without_ties_needs_no_draw_probability() {
+    let a = [rating()];
+    let b = [rating()];
+    let c = [rating()];
+    let teams: Vec<&[R]> = vec![&a, &b, &c];
+    let game = Game::ranked(&teams, Outcome::ranking([0, 1, 2]), &GameOptions::default()).unwrap();
+
+    for team in game.posteriors() {
+        for skill in team {
+            assert_finite(skill, "strict ranking posterior");
+        }
+    }
+}
+
+#[test]
+fn empty_history_converges_trivially() {
+    let mut h = History::default();
+    let report = h.converge().unwrap();
+    assert_eq!(report.iterations, 0);
+    assert!(report.converged);
+}
+
+/// Issue #27's exact reproduction: a non-default key type reaching `converge`
+/// with no events at all. The underflow it reported trapped in debug and
+/// indexed out of bounds in release, so this must run in both profiles.
+#[test]
+fn converge_on_an_empty_history_with_owned_keys() {
+    let mut history: History<i64, ConstantDrift, NullObserver, String> =
+        History::builder_with_key().score_sigma(5.0).build();
+
+    let report = history.converge().unwrap();
+
+    assert_eq!(report.iterations, 0);
+    assert!(report.converged);
+}
+
+/// A weights/team length mismatch used to be a `debug_assert!`, so release
+/// builds ingested the event with the weights silently unapplied. This file's
+/// CI job runs in release too, which is the point of pinning it here.
+#[test]
+fn event_builder_rejects_a_weights_length_mismatch() {
+    let mut h = History::default();
+
+    let err = h
+        .event(1)
+        .team(["a"])
+        .weights([1.0, 2.0])
+        .team(["b"])
+        .winner(0)
+        .commit()
+        .unwrap_err();
+
+    assert!(
+        matches!(
+            err,
+            InferenceError::MismatchedShape {
+                kind: "weights",
+                expected: 1,
+                got: 2,
+            }
+        ),
+        "expected a weights MismatchedShape, got {err:?}"
+    );
+}
+
+/// The mismatch must not be applied even partially — a half-weighted team
+/// reaching the history would be worse than the error.
+#[test]
+fn event_builder_weights_mismatch_leaves_the_history_untouched() {
+    let mut h = History::default();
+
+    // Two teams, so ingestion would otherwise succeed — a one-team event is
+    // rejected for an unrelated reason and would pass this vacuously.
+    let _ = h
+        .event(1)
+        .team(["a"])
+        .weights([1.0, 2.0])
+        .team(["b"])
+        .winner(0)
+        .commit();
+
+    assert!(h.learning_curve("a").is_empty());
+}
+
+#[test]
+fn empty_event_stream_then_converge() {
+    let mut h = History::default();
+    h.add_events(std::iter::empty()).unwrap();
+    let report = h.converge().unwrap();
+    assert_eq!(report.iterations, 0);
+}
+
+#[test]
+fn empty_history_queries_do_not_panic() {
+    let h = History::default();
+    assert!(h.learning_curves().is_empty());
+    assert!(h.learning_curve("nobody").is_empty());
+    assert!(h.current_skill("nobody").is_none());
+}
+
+#[test]
+fn single_event_history_converges() {
+    let mut h = History::default();
+    h.record_winner(&"a", &"b", 1).unwrap();
+    let report = h.converge().unwrap();
+    assert!(report.converged);
+    assert_finite(h.current_skill("a").unwrap(), "single-event skill");
+}
+
+#[test]
+fn scored_event_rejects_non_positive_sigma() {
+    let mut h = History::builder().score_sigma(2.0).build();
+    let err = h
+        .event(1)
+        .team(["a"])
+        .team(["b"])
+        .scores_with_sigma([3.0, 1.0], f64::NAN)
+        .commit()
+        .unwrap_err();
+    assert!(matches!(
+        err,
+        InferenceError::InvalidParameter {
+            name: "score_sigma",
+            ..
+        }
+    ));
+}
+
+#[test]
+fn convergence_reports_are_finite_across_many_teams() {
+    let opts = GameOptions {
+        p_draw: 0.1,
+        convergence: ConvergenceOptions::default(),
+        ..GameOptions::default()
+    };
+    let holders: Vec<[R; 1]> = (0..12).map(|_| [rating()]).collect();
+    let teams: Vec<&[R]> = holders.iter().map(|t| t.as_slice()).collect();
+    let game = Game::ranked(&teams, Outcome::ranking(0..12), &opts).unwrap();
+
+    assert!(
+        game.log_evidence().is_finite(),
+        "12-team log-evidence must be finite, got {}",
+        game.log_evidence()
+    );
+    for team in game.posteriors() {
+        for skill in team {
+            assert_finite(skill, "12-team posterior");
+        }
+    }
+}
+
+/// A long diff chain underflows a linear evidence product: each link
+/// contributes a probability in (0, 1], so ~1000 links flush the product to
+/// exactly 0.0 and `ln(0.0)` is `-inf`. Accumulating in log space keeps it
+/// finite.
+#[test]
+fn log_evidence_survives_a_long_diff_chain() {
+    let holders: Vec<[R; 1]> = (0..1200).map(|_| [rating()]).collect();
+    let teams: Vec<&[R]> = holders.iter().map(|t| t.as_slice()).collect();
+    let game = Game::ranked(
+        &teams,
+        Outcome::ranking(0..holders.len() as u32),
+        &GameOptions::default(),
+    )
+    .unwrap();
+
+    let log_evidence = game.log_evidence();
+    assert!(
+        log_evidence.is_finite(),
+        "1200-team log-evidence must be finite, got {log_evidence}"
+    );
+    assert!(
+        log_evidence < 0.0,
+        "log-evidence of a probability must be negative, got {log_evidence}"
+    );
+}
+
+/// A near-certain outcome rounds the losing tail to exactly zero in the
+/// `erfc` approximation; the evidence floor keeps `ln` finite.
+#[test]
+fn log_evidence_finite_for_near_certain_outcome() {
+    let overwhelming = R::new(Gaussian::from_ms(5_000.0, 0.5), 1.0, ConstantDrift(0.0));
+    let hopeless = R::new(Gaussian::from_ms(-5_000.0, 0.5), 1.0, ConstantDrift(0.0));
+    let a = [overwhelming];
+    let b = [hopeless];
+    let teams: Vec<&[R]> = vec![&a, &b];
+
+    let game = Game::ranked(&teams, Outcome::winner(0, 2), &GameOptions::default()).unwrap();
+    assert!(
+        game.log_evidence().is_finite(),
+        "got {}",
+        game.log_evidence()
+    );
+
+    // And the reverse — a colossal upset — must also stay finite.
+    let upset = Game::ranked(&teams, Outcome::winner(1, 2), &GameOptions::default()).unwrap();
+    assert!(
+        upset.log_evidence().is_finite(),
+        "upset log-evidence must be finite, got {}",
+        upset.log_evidence()
+    );
+}
+
+#[test]
+fn empty_history_has_no_filtered_estimates() {
+    let history: History = History::builder().build();
+
+    assert_eq!(history.filtered_log_evidence(), 0.0);
+
+    assert!(history.filtered_learning_curves().is_empty());
+
+    assert!(history.filtered_learning_curve("nobody").is_empty());
+}
+
+// --- Boundary inputs (#26) ----------------------------------------------
+
+fn tight() -> ConvergenceOptions {
+    ConvergenceOptions {
+        max_iter: 2_000,
+        epsilon: 1e-12,
+        ..ConvergenceOptions::default()
+    }
+}
+
+fn assert_curve_finite(h: &History, keys: &[&str], what: &str) {
+    for key in keys {
+        for (time, g) in h.learning_curve(*key) {
+            assert!(
+                g.mu().is_finite() && g.sigma().is_finite(),
+                "{what}: non-finite posterior for {key} at t={time} (mu={} sigma={})",
+                g.mu(),
+                g.sigma()
+            );
+        }
+    }
+}
+
+/// A zero weight reaches `(m - performance.exclude(..)) * (1.0 / w)`, i.e. a
+/// division by zero. The commit is accepted today, so this pins that the
+/// resulting posterior is still finite rather than quietly NaN.
+#[test]
+fn zero_weight_does_not_produce_a_non_finite_posterior() {
+    let mut h = History::builder().build();
+
+    h.event(1)
+        .team(["a"])
+        .weights([0.0])
+        .team(["b"])
+        .winner(0)
+        .commit()
+        .expect("a zero weight is accepted today; update this test if that changes");
+
+    h.converge().unwrap();
+
+    assert_curve_finite(&h, &["a", "b"], "zero weight");
+}
+
+#[test]
+fn negative_weight_does_not_produce_a_non_finite_posterior() {
+    let mut h = History::builder().build();
+
+    h.event(1)
+        .team(["a"])
+        .weights([-1.0])
+        .team(["b"])
+        .winner(0)
+        .commit()
+        .expect("a negative weight is accepted today; update this test if that changes");
+
+    h.converge().unwrap();
+
+    assert_curve_finite(&h, &["a", "b"], "negative weight");
+}
+
+/// Events supplied newest-first must land in the same slices as oldest-first:
+/// ingestion sorts by time rather than trusting arrival order.
+#[test]
+fn out_of_order_timestamps_converge_to_the_same_answer() {
+    fn build(descending: bool) -> History {
+        let mut h = History::builder().convergence(tight()).build();
+
+        let mut times: Vec<i64> = (1..=6).collect();
+        if descending {
+            times.reverse();
+        }
+
+        for time in times {
+            h.record_winner(&"a", &"b", time).unwrap();
+        }
+
+        h.converge().unwrap();
+        h
+    }
+
+    let ascending = build(false);
+    let descending = build(true);
+
+    let one = ascending.current_skill("a").unwrap();
+    let other = descending.current_skill("a").unwrap();
+
+    assert!(
+        (one.mu() - other.mu()).abs() < 1e-8 && (one.sigma() - other.sigma()).abs() < 1e-8,
+        "arrival order changed the answer: ascending mu={} sigma={}, descending mu={} sigma={}",
+        one.mu(),
+        one.sigma(),
+        other.mu(),
+        other.sigma()
+    );
+}
+
+#[test]
+fn extreme_beta_and_sigma_stay_finite() {
+    for (beta, sigma) in [(1e-6, 1e-6), (1e6, 1e6), (1e-6, 1e6), (1e6, 1e-6)] {
+        let mut h = History::builder().beta(beta).sigma(sigma).build();
+
+        h.record_winner(&"a", &"b", 1).unwrap();
+        h.record_winner(&"a", &"b", 2).unwrap();
+        h.converge().unwrap();
+
+        assert_curve_finite(&h, &["a", "b"], &format!("beta={beta} sigma={sigma}"));
+    }
+}

tests/drift_scale.rs

@@ -0,0 +1,402 @@
+//! Per-competitor drift scaling via `Member::with_drift_scale`.
+//!
+//! The scale multiplies the *variance* the history's `Drift` contributes for
+//! that competitor, so `scale` is in the same units as `gamma`:
+//! `ConstantDrift(g)` at `scale = s` behaves as `ConstantDrift(g * s)` would.
+//! `scale = 0.0` pins a competitor still — an anchor, a rating floor, a course
+//! difficulty — while everyone around them keeps drifting.
+
+use smallvec::smallvec;
+use trueskill_tt::{
+    ConstantDrift, ConvergenceOptions, Event, Gaussian, History, InferenceError, Member,
+    NullObserver, Outcome, Team,
+};
+
+type Fit = History<i64, ConstantDrift, NullObserver, &'static str>;
+
+const CONVERGENCE: ConvergenceOptions = ConvergenceOptions {
+    max_iter: 64,
+    epsilon: 1e-9,
+    alpha: 1.0,
+};
+
+/// Two events separated by a long gap, so drift has room to matter.
+fn distant_pair(anchor_scale: Option<f64>) -> Vec<Event<i64, &'static str>> {
+    let anchor = |s: Option<f64>| match s {
+        Some(scale) => Member::new("anchor").with_drift_scale(scale),
+        None => Member::new("anchor"),
+    };
+
+    vec![
+        Event {
+            time: 0,
+            teams: smallvec![
+                Team::with_members([anchor(anchor_scale)]),
+                Team::with_members([Member::new("player")]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        },
+        Event {
+            time: 1000,
+            teams: smallvec![
+                Team::with_members([anchor(anchor_scale)]),
+                Team::with_members([Member::new("player")]),
+            ],
+            outcome: Outcome::winner(1, 2),
+        },
+    ]
+}
+
+fn fit(events: Vec<Event<i64, &'static str>>, gamma: f64) -> Fit {
+    let mut h = History::builder()
+        .mu(25.0)
+        .sigma(25.0 / 3.0)
+        .beta(25.0 / 6.0)
+        .p_draw(0.0)
+        .drift(ConstantDrift(gamma))
+        .convergence(CONVERGENCE)
+        .build();
+
+    h.add_events(events).unwrap();
+    h.converge().unwrap();
+    h
+}
+
+fn curve(h: &Fit, key: &str) -> Vec<(i64, Gaussian)> {
+    let mut c = h.learning_curves().remove(key).expect("key in curves");
+    c.sort_by_key(|(t, _)| *t);
+    c
+}
+
+/// A competitor at `scale = 0.0` is one latent skill observed twice, so the
+/// posterior is the same distribution at both times — and strictly tighter
+/// than the same competitor left to drift.
+#[test]
+fn zero_scale_pins_a_competitor_still() {
+    let pinned = fit(distant_pair(Some(0.0)), 25.0 / 300.0);
+    let drifting = fit(distant_pair(None), 25.0 / 300.0);
+
+    let pinned_curve = curve(&pinned, "anchor");
+    assert_eq!(pinned_curve.len(), 2);
+
+    let (t0, first) = pinned_curve[0];
+    let (t1, second) = pinned_curve[1];
+    assert_eq!((t0, t1), (0, 1000));
+
+    assert!(
+        (first.sigma() - second.sigma()).abs() < 1e-9,
+        "a pinned competitor's uncertainty must not move between t=0 and t=1000: \
+         {} vs {}",
+        first.sigma(),
+        second.sigma()
+    );
+    assert!(
+        (first.mu() - second.mu()).abs() < 1e-9,
+        "a pinned competitor's mean must not move: {} vs {}",
+        first.mu(),
+        second.mu()
+    );
+
+    let drifting_curve = curve(&drifting, "anchor");
+    assert!(
+        drifting_curve[0].1.sigma() > first.sigma() + 1e-6,
+        "drift must leave the anchor less certain than pinning does: {} vs {}",
+        drifting_curve[0].1.sigma(),
+        first.sigma()
+    );
+}
+
+/// The scale is composable with `gamma`: scaling every competitor by `s` is
+/// exactly the same fit as scaling the history's drift by `s`.
+#[test]
+fn scale_is_equivalent_to_scaling_gamma() {
+    let scaled: Vec<Event<i64, &'static str>> = vec![
+        Event {
+            time: 0,
+            teams: smallvec![
+                Team::with_members([Member::new("a").with_drift_scale(0.5)]),
+                Team::with_members([Member::new("b").with_drift_scale(0.5)]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        },
+        Event {
+            time: 400,
+            teams: smallvec![
+                Team::with_members([Member::new("b").with_drift_scale(0.5)]),
+                Team::with_members([Member::new("a").with_drift_scale(0.5)]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        },
+    ];
+
+    let plain: Vec<Event<i64, &'static str>> = vec![
+        Event {
+            time: 0,
+            teams: smallvec![
+                Team::with_members([Member::new("a")]),
+                Team::with_members([Member::new("b")]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        },
+        Event {
+            time: 400,
+            teams: smallvec![
+                Team::with_members([Member::new("b")]),
+                Team::with_members([Member::new("a")]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        },
+    ];
+
+    let by_scale = fit(scaled, 0.3);
+    let by_gamma = fit(plain, 0.15);
+
+    for key in ["a", "b"] {
+        let lhs = curve(&by_scale, key);
+        let rhs = curve(&by_gamma, key);
+        assert_eq!(lhs.len(), rhs.len());
+
+        for ((t_l, g_l), (t_r, g_r)) in lhs.iter().zip(rhs.iter()) {
+            assert_eq!(t_l, t_r);
+            assert!(
+                (g_l.mu() - g_r.mu()).abs() < 1e-9 && (g_l.sigma() - g_r.sigma()).abs() < 1e-9,
+                "ConstantDrift(0.3) at scale 0.5 must equal ConstantDrift(0.15) for {key} at \
+                 t={t_l}: ({}, {}) vs ({}, {})",
+                g_l.mu(),
+                g_l.sigma(),
+                g_r.mu(),
+                g_r.sigma()
+            );
+        }
+    }
+}
+
+/// `None` means 1.0: an explicit unit scale changes nothing.
+#[test]
+fn unset_scale_matches_an_explicit_unit_scale() {
+    let implicit = fit(distant_pair(None), 25.0 / 300.0);
+    let explicit = fit(distant_pair(Some(1.0)), 25.0 / 300.0);
+
+    for key in ["anchor", "player"] {
+        let lhs = curve(&implicit, key);
+        let rhs = curve(&explicit, key);
+        assert_eq!(lhs.len(), rhs.len());
+
+        for ((t_l, g_l), (t_r, g_r)) in lhs.iter().zip(rhs.iter()) {
+            assert_eq!(t_l, t_r);
+            assert_eq!(
+                (g_l.mu(), g_l.sigma()),
+                (g_r.mu(), g_r.sigma()),
+                "an explicit scale of 1.0 must be bit-identical to leaving it unset, \
+                 for {key} at t={t_l}"
+            );
+        }
+    }
+}
+
+/// The use case from the issue: a static difficulty alongside drifting players,
+/// in one graph. The anchor must hold still without absorbing drift through its
+/// neighbours, and everything must stay finite.
+#[test]
+fn mixed_static_and_drifting_graph_converges() {
+    let mut events: Vec<Event<i64, &'static str>> = Vec::new();
+    let players = ["p0", "p1", "p2"];
+
+    for (i, p) in players.iter().cycle().take(9).enumerate() {
+        events.push(Event {
+            time: (i as i64) * 100,
+            teams: smallvec![
+                Team::with_members([Member::new(*p)]),
+                Team::with_members([Member::new("layout").with_drift_scale(0.0)]),
+            ],
+            outcome: Outcome::winner((i % 2) as u32, 2),
+        });
+    }
+
+    let mut h = History::builder()
+        .mu(25.0)
+        .sigma(25.0 / 3.0)
+        .beta(25.0 / 6.0)
+        .p_draw(0.0)
+        .drift(ConstantDrift(25.0 / 300.0))
+        .convergence(CONVERGENCE)
+        .build();
+
+    h.add_events(events).unwrap();
+    let report = h.converge().unwrap();
+    assert!(report.converged, "mixed graph must converge: {report:?}");
+
+    let curves = h.learning_curves();
+    for (key, points) in &curves {
+        for (t, g) in points {
+            assert!(
+                g.mu().is_finite() && g.sigma().is_finite() && g.sigma() > 0.0,
+                "{key} at t={t} is not a usable posterior: mu={}, sigma={}",
+                g.mu(),
+                g.sigma()
+            );
+        }
+    }
+
+    let layout = curve(&h, "layout");
+    assert_eq!(layout.len(), 9);
+    let (_, first) = layout[0];
+    for (t, g) in &layout {
+        assert!(
+            (g.sigma() - first.sigma()).abs() < 1e-9,
+            "a static layout must not accumulate uncertainty; t={t} has sigma {} vs {}",
+            g.sigma(),
+            first.sigma()
+        );
+    }
+
+    let p0 = curve(&h, "p0");
+    assert!(
+        p0.last().unwrap().1.sigma() > 0.0,
+        "a drifting player should still have a proper posterior"
+    );
+}
+
+fn reject(scale: f64) -> InferenceError {
+    let mut h = History::builder()
+        .drift(ConstantDrift(25.0 / 300.0))
+        .build();
+
+    let events: Vec<Event<i64, &'static str>> = vec![Event {
+        time: 0,
+        teams: smallvec![
+            Team::with_members([Member::new("a").with_drift_scale(scale)]),
+            Team::with_members([Member::new("b")]),
+        ],
+        outcome: Outcome::winner(0, 2),
+    }];
+
+    h.add_events(events)
+        .expect_err("an out-of-range drift_scale must be rejected")
+}
+
+#[test]
+fn negative_scale_is_rejected() {
+    assert_eq!(
+        reject(-1.0),
+        InferenceError::InvalidParameter {
+            name: "drift_scale",
+            value: -1.0
+        }
+    );
+}
+
+#[test]
+fn non_finite_scale_is_rejected() {
+    for scale in [f64::NAN, f64::INFINITY, f64::NEG_INFINITY] {
+        assert!(
+            matches!(
+                reject(scale),
+                InferenceError::InvalidParameter {
+                    name: "drift_scale",
+                    ..
+                }
+            ),
+            "a drift_scale of {scale} must be rejected as an invalid parameter"
+        );
+    }
+}
+
+/// The scale must reach the filtering pass too, not just `converge()`.
+/// `filtered_learning_curves` runs its own drift application, so a pinned
+/// competitor has to stay pinned there as well.
+#[test]
+fn zero_scale_pins_a_competitor_in_the_filtered_pass() {
+    let pinned = fit(distant_pair(Some(0.0)), 25.0 / 300.0);
+    let drifting = fit(distant_pair(None), 25.0 / 300.0);
+
+    let filtered = |h: &Fit| -> Vec<(i64, Gaussian)> {
+        let mut c = h
+            .filtered_learning_curves()
+            .remove("anchor")
+            .expect("anchor in filtered curves");
+        c.sort_by_key(|(t, _)| *t);
+        c
+    };
+
+    let pinned_curve = filtered(&pinned);
+    let drifting_curve = filtered(&drifting);
+    assert_eq!(pinned_curve.len(), 2);
+    assert_eq!(drifting_curve.len(), 2);
+
+    assert!(
+        pinned_curve[1].1.sigma() < pinned_curve[0].1.sigma(),
+        "a pinned competitor's filtered uncertainty must shrink with a second \
+         observation, not be re-inflated by drift: {} then {}",
+        pinned_curve[0].1.sigma(),
+        pinned_curve[1].1.sigma()
+    );
+
+    assert!(
+        pinned_curve[1].1.sigma() < drifting_curve[1].1.sigma() - 1e-6,
+        "pinning must leave the filtered estimate tighter than drifting does: \
+         {} vs {}",
+        pinned_curve[1].1.sigma(),
+        drifting_curve[1].1.sigma()
+    );
+}
+
+/// `drift_scale` is competitor configuration captured at first appearance, the
+/// same as `prior` — a later `with_drift_scale` on a key the history already
+/// knows is ignored. This guards that decision rather than driving it: the
+/// behaviour falls out of where the capture happens, and the point of the test
+/// is that moving the capture would be a visible break, not a silent one.
+#[test]
+fn drift_scale_is_ignored_after_first_appearance() {
+    let mut late = History::builder()
+        .mu(25.0)
+        .sigma(25.0 / 3.0)
+        .beta(25.0 / 6.0)
+        .p_draw(0.0)
+        .drift(ConstantDrift(25.0 / 300.0))
+        .convergence(CONVERGENCE)
+        .build();
+
+    // First batch creates "anchor" with the default scale.
+    late.add_events(vec![Event {
+        time: 0,
+        teams: smallvec![
+            Team::with_members([Member::new("anchor")]),
+            Team::with_members([Member::new("player")]),
+        ],
+        outcome: Outcome::winner(0, 2),
+    }])
+    .unwrap();
+
+    // Second batch asks for a pin. Too late: the competitor already exists.
+    late.add_events(vec![Event {
+        time: 1000,
+        teams: smallvec![
+            Team::with_members([Member::new("anchor").with_drift_scale(0.0)]),
+            Team::with_members([Member::new("player")]),
+        ],
+        outcome: Outcome::winner(1, 2),
+    }])
+    .unwrap();
+    late.converge().unwrap();
+
+    let ignored = curve(&late, "anchor");
+    let drifting = curve(&fit(distant_pair(None), 25.0 / 300.0), "anchor");
+
+    for ((t_l, g_l), (t_r, g_r)) in ignored.iter().zip(drifting.iter()) {
+        assert_eq!(t_l, t_r);
+        assert!(
+            (g_l.sigma() - g_r.sigma()).abs() < 1e-9,
+            "a scale set after first appearance must be ignored, leaving the fit \
+             identical to one that never set it: t={t_l}, {} vs {}",
+            g_l.sigma(),
+            g_r.sigma()
+        );
+    }
+
+    let pinned = curve(&fit(distant_pair(Some(0.0)), 25.0 / 300.0), "anchor");
+    assert!(
+        (ignored[1].1.sigma() - pinned[1].1.sigma()).abs() > 1e-6,
+        "sanity: the pinned fit must actually differ, or the assertion above is vacuous"
+    );
+}

tests/equivalence.rs

@@ -48,15 +48,9 @@ fn game_1v1_draw_golden() {
     )
     .unwrap();
     let p = g.posteriors();
-    // Historical golden from pre-T2 test_1vs1_draw:
-    assert_ulps_eq!(
-        p[0][0],
-        Gaussian::from_ms(24.999999, 6.469480),
-        epsilon = 1e-6
-    );
-    assert_ulps_eq!(
-        p[1][0],
-        Gaussian::from_ms(24.999999, 6.469480),
-        epsilon = 1e-6
-    );
+    // Historical golden from pre-T2 test_1vs1_draw. The mean is 25.0 exactly
+    // by symmetry — two identical competitors drawing cannot move apart — and
+    // the reference's 24.999999 is that value transcribed to six decimals.
+    assert_ulps_eq!(p[0][0], Gaussian::from_ms(25.0, 6.469480), epsilon = 1e-6);
+    assert_ulps_eq!(p[1][0], Gaussian::from_ms(25.0, 6.469480), epsilon = 1e-6);
 }

tests/filtered.rs

@@ -0,0 +1,254 @@
+//! Forward-only (filtering) estimates: what the model knew at the time,
+//! as opposed to the smoothed posteriors `learning_curve` reports.
+
+use smallvec::smallvec;
+use trueskill_tt::{ConvergenceOptions, Event, History, Member, Outcome, Team};
+
+/// `games` one-on-one matches at successive times, won by "a" every time,
+/// built with the given convergence options.
+fn repeated_winner_with(games: i64, convergence: ConvergenceOptions) -> History {
+    let mut history = History::builder().convergence(convergence).build();
+
+    for time in 1..=games {
+        history
+            .add_events([Event {
+                time,
+                teams: smallvec![
+                    Team::with_members([Member::new("a")]),
+                    Team::with_members([Member::new("b")]),
+                ],
+                outcome: Outcome::winner(0, 2),
+            }])
+            .unwrap();
+    }
+
+    history
+}
+
+/// `games` one-on-one matches at successive times, won by "a" every time.
+///
+/// This is the fixture from issue #19, where `online(true)` reported
+/// `games * ln(0.5)`.
+fn repeated_winner(games: i64) -> History {
+    repeated_winner_with(games, ConvergenceOptions::default())
+}
+
+/// The default 30-iteration cap leaves a residual around 1e-6, which would
+/// swamp these comparisons. Drive both sides well past the fixed point.
+fn tight() -> ConvergenceOptions {
+    ConvergenceOptions {
+        max_iter: 2_000,
+        epsilon: 1e-12,
+        ..ConvergenceOptions::default()
+    }
+}
+
+#[test]
+fn filtered_evidence_sits_between_coin_flip_and_batch() {
+    let mut history = repeated_winner(5);
+
+    history.converge().unwrap();
+
+    let coin_flip = 5.0 * 0.5f64.ln();
+    let batch = history.log_evidence();
+    let filtered = history.filtered_log_evidence();
+
+    assert!(
+        filtered > coin_flip,
+        "filtered evidence {filtered} is at or below {coin_flip}, the all-coin-flip \
+         value the inert online flag reported; game one is a coin flip but games two \
+         through five are not"
+    );
+
+    assert!(
+        filtered < batch,
+        "filtered evidence {filtered} is not below the smoothed {batch}; filtering \
+         scores each game on strictly less information than smoothing does"
+    );
+}
+
+#[test]
+fn filtered_first_point_is_less_certain_than_smoothed() {
+    let mut history = repeated_winner(12);
+
+    history.converge().unwrap();
+
+    let smoothed = history.learning_curve("a");
+    let filtered = history.filtered_learning_curve("a");
+
+    assert_eq!(
+        smoothed.len(),
+        filtered.len(),
+        "both curves must cover the same time points"
+    );
+
+    let (smoothed_time, first_smoothed) = smoothed[0];
+    let (filtered_time, first_filtered) = filtered[0];
+
+    assert_eq!(smoothed_time, filtered_time);
+
+    assert!(
+        first_filtered.sigma() > first_smoothed.sigma(),
+        "filtered sigma {} at the first point is not above smoothed {}; the smoother \
+         collapses uncertainty before the first round is drawn, which is the whole \
+         reason this method exists",
+        first_filtered.sigma(),
+        first_smoothed.sigma()
+    );
+
+    assert!(
+        first_filtered.sigma() < trueskill_tt::SIGMA,
+        "filtered sigma {} at the first point is not below the prior {}; one game was \
+         played, so some uncertainty must have been resolved",
+        first_filtered.sigma(),
+        trueskill_tt::SIGMA
+    );
+
+    for pair in filtered.windows(2) {
+        assert!(
+            pair[1].1.mu() > pair[0].1.mu(),
+            "filtered mu must climb at every step for a competitor who wins every \
+             game: t={} mu={} then t={} mu={}",
+            pair[0].0,
+            pair[0].1.mu(),
+            pair[1].0,
+            pair[1].1.mu()
+        );
+    }
+}
+
+#[test]
+fn filtered_curves_plural_agrees_with_singular() {
+    let mut history = repeated_winner(4);
+
+    history.converge().unwrap();
+
+    let curves = history.filtered_learning_curves();
+
+    assert_eq!(
+        curves["b"],
+        history.filtered_learning_curve("b"),
+        "the plural form must agree with the singular for the same key"
+    );
+}
+
+#[test]
+fn filtered_evidence_is_invariant_to_convergence() {
+    let mut history = repeated_winner_with(6, tight());
+
+    let before = history.filtered_log_evidence();
+
+    let report = history.converge().unwrap();
+    assert!(
+        report.converged,
+        "fixture must converge: {:?}",
+        report.final_step
+    );
+
+    let after = history.filtered_log_evidence();
+
+    assert!(
+        (before - after).abs() < 1e-8,
+        "filtered evidence moved across converge(): {before} -> {after}. The pass must \
+         carry its own forward messages; anything reading skill.forward shows exactly \
+         this drift, because converge() contaminates it with backward information."
+    );
+}
+
+#[test]
+fn single_slice_filtered_matches_smoothed() {
+    let mut history = History::builder().convergence(tight()).build();
+
+    history
+        .add_events([
+            Event {
+                time: 1,
+                teams: smallvec![
+                    Team::with_members([Member::new("a")]),
+                    Team::with_members([Member::new("b")]),
+                ],
+                outcome: Outcome::winner(0, 2),
+            },
+            Event {
+                time: 1,
+                teams: smallvec![
+                    Team::with_members([Member::new("c")]),
+                    Team::with_members([Member::new("d")]),
+                ],
+                outcome: Outcome::winner(0, 2),
+            },
+        ])
+        .unwrap();
+
+    history.converge().unwrap();
+
+    let smoothed = history.learning_curve("a");
+    let filtered = history.filtered_learning_curve("a");
+
+    assert_eq!(smoothed.len(), 1);
+    assert_eq!(filtered.len(), 1);
+
+    assert!(
+        (smoothed[0].1.mu() - filtered[0].1.mu()).abs() < 1e-8
+            && (smoothed[0].1.sigma() - filtered[0].1.sigma()).abs() < 1e-8,
+        "one slice has no future to propagate back, so filtered and smoothed must \
+         agree: smoothed mu={} sigma={}, filtered mu={} sigma={}",
+        smoothed[0].1.mu(),
+        smoothed[0].1.sigma(),
+        filtered[0].1.mu(),
+        filtered[0].1.sigma()
+    );
+}
+
+#[test]
+fn filtered_curves_do_not_depend_on_ingestion_order() {
+    let events = |time: i64, winner: &'static str, loser: &'static str| Event {
+        time,
+        teams: smallvec![
+            Team::with_members([Member::new(winner)]),
+            Team::with_members([Member::new(loser)]),
+        ],
+        outcome: Outcome::winner(0, 2),
+    };
+
+    let all = vec![
+        events(1, "a", "b"),
+        events(1, "c", "d"),
+        events(1, "a", "c"),
+        events(1, "b", "d"),
+        events(2, "a", "d"),
+        events(2, "b", "c"),
+        events(2, "a", "b"),
+    ];
+
+    let mut batched = History::builder().convergence(tight()).build();
+    batched.add_events(all.clone()).unwrap();
+    batched.converge().unwrap();
+
+    let mut incremental = History::builder().convergence(tight()).build();
+    for event in all {
+        incremental.add_events([event]).unwrap();
+    }
+    incremental.converge().unwrap();
+
+    let from_batched = batched.filtered_learning_curve("a");
+    let from_incremental = incremental.filtered_learning_curve("a");
+
+    assert_eq!(from_batched.len(), from_incremental.len());
+
+    for ((time_b, gaussian_b), (time_i, gaussian_i)) in
+        from_batched.iter().zip(from_incremental.iter())
+    {
+        assert_eq!(time_b, time_i);
+
+        assert!(
+            (gaussian_b.mu() - gaussian_i.mu()).abs() < 1e-8
+                && (gaussian_b.sigma() - gaussian_i.sigma()).abs() < 1e-8,
+            "at t={time_b}: batched mu={} sigma={}, incremental mu={} sigma={}",
+            gaussian_b.mu(),
+            gaussian_b.sigma(),
+            gaussian_i.mu(),
+            gaussian_i.sigma()
+        );
+    }
+}

tests/ingestion_equivalence.rs

@@ -0,0 +1,147 @@
+//! Ingesting the same events must give the same answer however they were
+//! batched.
+//!
+//! The numerical goldens all ingest in a single call with one slice per
+//! timestamp, so they never exercise the "append to an existing slice" path.
+//! These do.
+
+use smallvec::smallvec;
+use trueskill_tt::{ConvergenceOptions, Event, Gaussian, History, Member, Outcome, Team};
+
+/// Converge tightly: the default cap of 30 iterations leaves a residual around
+/// 1e-6, which would swamp the comparison. Both paths must reach the same
+/// fixed point, so drive both well past it.
+fn tight() -> ConvergenceOptions {
+    ConvergenceOptions {
+        max_iter: 2_000,
+        epsilon: 1e-12,
+        ..ConvergenceOptions::default()
+    }
+}
+
+fn event(a: &str, b: &str, time: i64) -> Event<i64, String> {
+    Event {
+        time,
+        teams: smallvec![
+            Team::with_members([Member::new(a.to_string())]),
+            Team::with_members([Member::new(b.to_string())]),
+        ],
+        outcome: Outcome::winner(0, 2),
+    }
+}
+
+fn converged_skills(events: Vec<Event<i64, String>>, batched: bool) -> Vec<(String, Gaussian)> {
+    let mut h: History<i64, _, _, String> =
+        History::builder_with_key().convergence(tight()).build();
+
+    if batched {
+        h.add_events(events).unwrap();
+    } else {
+        for ev in events {
+            h.add_events(std::iter::once(ev)).unwrap();
+        }
+    }
+
+    let report = h.converge().unwrap();
+    assert!(
+        report.converged,
+        "fixture must converge before results can be compared; final step {:?}",
+        report.final_step
+    );
+
+    let mut skills: Vec<(String, Gaussian)> = h
+        .learning_curves()
+        .into_iter()
+        .map(|(key, curve)| (key, curve.last().unwrap().1))
+        .collect();
+    skills.sort_by(|a, b| a.0.cmp(&b.0));
+    skills
+}
+
+fn assert_same(batched: &[(String, Gaussian)], incremental: &[(String, Gaussian)], what: &str) {
+    assert_eq!(
+        batched.len(),
+        incremental.len(),
+        "{what}: competitor count differs"
+    );
+
+    for ((kb, gb), (ki, gi)) in batched.iter().zip(incremental.iter()) {
+        assert_eq!(kb, ki, "{what}: key order differs");
+        assert!(
+            (gb.mu() - gi.mu()).abs() < 1e-8 && (gb.sigma() - gi.sigma()).abs() < 1e-8,
+            "{what}: {kb} differs — batched mu={} sigma={}, incremental mu={} sigma={}",
+            gb.mu(),
+            gb.sigma(),
+            gi.mu(),
+            gi.sigma()
+        );
+    }
+}
+
+/// All events share one timestamp, so incremental ingestion repeatedly appends
+/// to an existing slice.
+#[test]
+fn same_slice_incremental_matches_batched() {
+    let events = vec![
+        event("a", "b", 1),
+        event("c", "d", 1),
+        event("e", "f", 1),
+        event("a", "c", 1),
+        event("b", "e", 1),
+    ];
+
+    let batched = converged_skills(events.clone(), true);
+    let incremental = converged_skills(events, false);
+    assert_same(&batched, &incremental, "single shared slice");
+}
+
+/// Distinct timestamps, so each append lands in a fresh slice appended after
+/// the existing ones.
+#[test]
+fn distinct_slices_incremental_matches_batched() {
+    let events = vec![
+        event("a", "b", 1),
+        event("b", "c", 2),
+        event("c", "a", 3),
+        event("a", "c", 4),
+    ];
+
+    let batched = converged_skills(events.clone(), true);
+    let incremental = converged_skills(events, false);
+    assert_same(&batched, &incremental, "distinct slices");
+}
+
+/// Several events per timestamp across several timestamps — appends to
+/// existing slices interleaved with new ones.
+#[test]
+fn mixed_slices_incremental_matches_batched() {
+    let events = vec![
+        event("a", "b", 1),
+        event("c", "d", 1),
+        event("a", "c", 2),
+        event("b", "d", 2),
+        event("a", "d", 3),
+        event("b", "c", 3),
+    ];
+
+    let batched = converged_skills(events.clone(), true);
+    let incremental = converged_skills(events, false);
+    assert_same(&batched, &incremental, "mixed slices");
+}
+
+/// Appending an event to a slice that is *not* the most recent one exercises
+/// the forward refresh of every later slice.
+#[test]
+fn back_dated_event_matches_batched() {
+    let events = vec![
+        event("a", "b", 1),
+        event("b", "c", 5),
+        event("c", "a", 9),
+        // arrives last, but belongs to the middle slice
+        event("a", "c", 5),
+    ];
+
+    let batched = converged_skills(events.clone(), true);
+    let incremental = converged_skills(events, false);
+    assert_same(&batched, &incremental, "back-dated event");
+}

tests/properties.rs

@@ -0,0 +1,167 @@
+//! Property-based tests over generated histories.
+//!
+//! The golden suite pins exact values against the Python/Julia reference on a
+//! handful of fixtures. These pin *invariants* over inputs nobody wrote by
+//! hand, which is where the defects this crate has actually shipped were
+//! hiding: a linear evidence product that underflowed only past ~1000 teams,
+//! and a batching path no golden exercised because every golden ingests in one
+//! call.
+
+mod common;
+
+use common::assert_finite;
+use proptest::prelude::*;
+use smallvec::smallvec;
+use trueskill_tt::{ConvergenceOptions, Event, History, Member, Outcome, Team};
+
+/// Distinct competitors, so no event pits someone against themselves.
+fn pairs() -> impl Strategy<Value = Vec<(usize, usize)>> {
+    prop::collection::vec((0usize..8, 0usize..8), 1..24)
+        .prop_map(|v| v.into_iter().filter(|(a, b)| a != b).collect::<Vec<_>>())
+        .prop_filter("needs at least one valid pair", |v| !v.is_empty())
+}
+
+const KEYS: [&str; 8] = ["a", "b", "c", "d", "e", "f", "g", "h"];
+
+fn history_from(games: &[(usize, usize)]) -> History {
+    let mut h = History::builder()
+        .convergence(ConvergenceOptions {
+            max_iter: 200,
+            epsilon: 1e-10,
+            ..ConvergenceOptions::default()
+        })
+        .build();
+
+    let events: Vec<Event<i64, &'static str>> = games
+        .iter()
+        .enumerate()
+        .map(|(i, &(a, b))| Event {
+            time: i as i64 + 1,
+            teams: smallvec![
+                Team::with_members([Member::new(KEYS[a])]),
+                Team::with_members([Member::new(KEYS[b])]),
+            ],
+            outcome: Outcome::winner(0, 2),
+        })
+        .collect();
+
+    h.add_events(events).unwrap();
+
+    h
+}
+
+proptest! {
+    #![proptest_config(ProptestConfig::with_cases(48))]
+
+    /// Whatever the schedule of games, convergence must not produce NaN or an
+    /// improper posterior. `converge` returns `NonFiniteResult` rather than
+    /// silently reporting a NaN step as converged, so a break shows up here as
+    /// either an Err or a non-finite curve point.
+    #[test]
+    fn converged_posteriors_are_always_finite(games in pairs()) {
+        let mut h = history_from(&games);
+
+        h.converge().unwrap();
+
+        for key in KEYS {
+            for (time, g) in h.learning_curve(key) {
+                assert_finite(g, &format!("{key} at t={time}"));
+            }
+        }
+    }
+
+    /// Log-evidence is a log probability: finite, and never above zero.
+    ///
+    /// The linear-product implementation this replaced underflowed to zero on
+    /// long chains, making `ln(0)` = -inf — finite-ness is the property that
+    /// would have caught it.
+    #[test]
+    fn log_evidence_is_a_finite_log_probability(games in pairs()) {
+        let mut h = history_from(&games);
+
+        h.converge().unwrap();
+
+        let batch = h.log_evidence();
+        let filtered = h.filtered_log_evidence();
+
+        prop_assert!(batch.is_finite(), "batch log-evidence {batch} is not finite");
+        prop_assert!(batch <= 0.0, "batch log-evidence {batch} exceeds zero");
+        prop_assert!(filtered.is_finite(), "filtered log-evidence {filtered} is not finite");
+        prop_assert!(filtered <= 0.0, "filtered log-evidence {filtered} exceeds zero");
+    }
+
+    /// Filtered estimates must not depend on whether `converge` has run — the
+    /// property the whole forward-only design rests on.
+    #[test]
+    fn filtered_evidence_is_invariant_to_convergence(games in pairs()) {
+        let mut h = history_from(&games);
+
+        let before = h.filtered_log_evidence();
+
+        h.converge().unwrap();
+
+        let after = h.filtered_log_evidence();
+
+        prop_assert!(
+            (before - after).abs() < 1e-8,
+            "filtered evidence moved across converge(): {before} -> {after}"
+        );
+    }
+
+    /// Ingesting the same games one at a time must reach the same fixed point
+    /// as ingesting them in one call.
+    #[test]
+    fn ingestion_order_does_not_change_the_answer(games in pairs()) {
+        let batched = {
+            let mut h = history_from(&games);
+            h.converge().unwrap();
+            h
+        };
+
+        let incremental = {
+            let mut h = History::builder()
+                .convergence(ConvergenceOptions {
+                    max_iter: 200,
+                    epsilon: 1e-10,
+                    ..ConvergenceOptions::default()
+                })
+                .build();
+
+            for (i, &(a, b)) in games.iter().enumerate() {
+                h.add_events([Event {
+                    time: i as i64 + 1,
+                    teams: smallvec![
+                        Team::with_members([Member::new(KEYS[a])]),
+                        Team::with_members([Member::new(KEYS[b])]),
+                    ],
+                    outcome: Outcome::winner(0, 2),
+                }])
+                .unwrap();
+            }
+
+            h.converge().unwrap();
+            h
+        };
+
+        for key in KEYS {
+            let one = batched.current_skill(key);
+            let other = incremental.current_skill(key);
+
+            match (one, other) {
+                (Some(one), Some(other)) => {
+                    prop_assert!(
+                        (one.mu() - other.mu()).abs() < 1e-6
+                            && (one.sigma() - other.sigma()).abs() < 1e-6,
+                        "{key}: batched mu={} sigma={}, incremental mu={} sigma={}",
+                        one.mu(),
+                        one.sigma(),
+                        other.mu(),
+                        other.sigma()
+                    );
+                }
+                (None, None) => {}
+                _ => prop_assert!(false, "{key} present in only one history"),
+            }
+        }
+    }
+}

tests/quality.rs

@@ -0,0 +1,119 @@
+//! `quality()` beyond two rating groups.
+//!
+//! The historical golden (two equal singletons) is asserted in
+//! `src/lib.rs::tests::test_quality`. These cover the N-group generalisation,
+//! which previously panicked with an out-of-bounds index at 3+ groups.
+
+use trueskill_tt::{Gaussian, quality};
+
+const BETA: f64 = 25.0 / 3.0 / 2.0;
+
+fn rating(mu: f64, sigma: f64) -> Gaussian {
+    Gaussian::from_ms(mu, sigma)
+}
+
+#[test]
+fn three_equal_groups_is_finite_and_in_range() {
+    let r = rating(25.0, 3.0);
+    let q = quality(&[&[r], &[r], &[r]], BETA);
+
+    assert!(q.is_finite(), "quality must be finite, got {q}");
+    assert!((0.0..=1.0).contains(&q), "quality out of range: {q}");
+}
+
+#[test]
+fn quality_supports_many_groups() {
+    let r = rating(25.0, 3.0);
+    for n in 2..=8 {
+        let holders: Vec<[Gaussian; 1]> = (0..n).map(|_| [r]).collect();
+        let groups: Vec<&[Gaussian]> = holders.iter().map(|g| g.as_slice()).collect();
+        let q = quality(&groups, BETA);
+        assert!(q.is_finite(), "n={n}: quality must be finite, got {q}");
+        assert!((0.0..=1.0).contains(&q), "n={n}: out of range: {q}");
+    }
+}
+
+/// Equal-strength groups are the best-matched case: introducing a skill gap
+/// must lower quality.
+#[test]
+fn imbalance_lowers_quality() {
+    let strong = rating(40.0, 3.0);
+    let average = rating(25.0, 3.0);
+
+    let balanced = quality(&[&[average], &[average], &[average]], BETA);
+    let lopsided = quality(&[&[strong], &[average], &[average]], BETA);
+
+    assert!(
+        lopsided < balanced,
+        "expected imbalanced quality {lopsided} < balanced {balanced}"
+    );
+}
+
+/// Quality is a property of the multiset of groups, not their order.
+#[test]
+fn quality_is_permutation_invariant() {
+    let a = rating(30.0, 2.0);
+    let b = rating(25.0, 3.0);
+    let c = rating(20.0, 4.0);
+
+    let forward = quality(&[&[a], &[b], &[c]], BETA);
+    let reversed = quality(&[&[c], &[b], &[a]], BETA);
+
+    assert!(
+        (forward - reversed).abs() < 1e-9,
+        "permutation changed quality: {forward} vs {reversed}"
+    );
+}
+
+#[test]
+fn multi_player_groups_work() {
+    let r = rating(25.0, 3.0);
+    let q = quality(&[&[r, r], &[r, r], &[r, r]], BETA);
+    assert!(q.is_finite());
+    assert!((0.0..=1.0).contains(&q));
+}
+
+#[test]
+fn uneven_group_sizes_work() {
+    let r = rating(25.0, 3.0);
+    let q = quality(&[&[r, r], &[r], &[r, r, r]], BETA);
+    assert!(q.is_finite(), "got {q}");
+    assert!((0.0..=1.0).contains(&q), "got {q}");
+}
+
+#[test]
+#[should_panic(expected = "at least 2 rating groups")]
+fn single_group_panics_with_clear_message() {
+    let r = rating(25.0, 3.0);
+    let _ = quality(&[&[r]], BETA);
+}
+
+#[test]
+#[should_panic(expected = "at least 2 rating groups")]
+fn zero_groups_panics_with_clear_message() {
+    let _ = quality(&[], BETA);
+}
+
+#[test]
+#[should_panic(expected = "non-empty")]
+fn empty_group_panics_with_clear_message() {
+    let r = rating(25.0, 3.0);
+    let _ = quality(&[&[r], &[]], BETA);
+}
+
+#[test]
+fn history_predict_quality_supports_three_teams() {
+    use trueskill_tt::History;
+
+    let mut h = History::default();
+    h.record_winner(&"a", &"b", 1).unwrap();
+    h.record_winner(&"b", &"c", 2).unwrap();
+    h.converge().unwrap();
+
+    let q = h.predict_quality(&[&[&"a"], &[&"b"], &[&"c"]]);
+    assert!(
+        q.is_finite(),
+        "3-team predict_quality must be finite, got {q}"
+    );
+    assert!((0.0..=1.0).contains(&q), "out of range: {q}");
+}