`predict_outcome` asserted `teams.len() == 2` and returned `[p, 1 - p]`,
allocating no probability to a draw even with `p_draw > 0`. For a
draw-enabled model the numbers were simply wrong, at any team count.
It now returns `Result<Prediction, InferenceError>` and supports N teams.
Two algorithms, both deterministic:
- Who finishes first. Performances are independent Gaussians, so this
separates into a one-dimensional integral per team rather than a
multivariate orthant probability. Adaptive Gauss-Kronrod evaluates it
to ~1e-15, matching the exact two-team closed form.
- A specific finishing order. The factor graph only constrains
rank-adjacent teams, so a full order is a chain of local constraints,
not a general orthant integral. That chain collapses into a sequential
recursion over cumulative integrals: O(teams * grid) per order.
Fixed-node Gauss-Hermite is the obvious tool for the first and is a trap:
when a rival's sigma is small the CDF product becomes a step narrower
than the node spacing, and the nodes step over it. Measured 4.4e-4 off
the closed form on a mildly skewed matchup and 1.7e-2 on a small-sigma
one, while still returning something that looks like a probability.
Adaptive refinement is what makes that case safe, and
`win_probabilities_survive_a_rival_with_a_tiny_sigma` pins it down.
The acceptance test is an identity rather than a golden: the outcome
space is exhaustive and disjoint, so the probabilities sum to one. Any
drift is integration error and nothing else. Gauss-Hermite failed it at
4.4e-4; this holds to ~1e-9.
Also from #21: unknown keys are now reported rather than dropped, so a
team of strangers can no longer produce a confident-looking prediction.
`predict_quality` returns `Result` for the same reason.
BREAKING CHANGE: `predict_outcome` returns `Result<Prediction, _>`
instead of `Vec<f64>`; `predict_quality` returns `Result<f64, _>`.
Refs #21, #39
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
`quality()` was two-group-only in three separate ways, and
`History::predict_quality` inherited all of them.
- The contrast-matrix column counter tracked two positions with two
variables that only agree on the first row, so three or more groups wrote
past the end of the row and panicked with an out-of-bounds index. The
negative block always begins immediately after the positive one, so the
second counter is unnecessary.
- `Matrix::inverse` was implemented only for the 1x1 case and otherwise
`panic!("eh, okey")`. It now uses LU decomposition with partial pivoting,
which also replaces the recursive cofactor `determinant` — that was O(n!)
and allocated a `Vec` per minor, so a 10-team match needed 362,880 terms.
- Degenerate inputs (zero groups, one group, empty groups) underflowed or
produced NaN. They now assert with a message naming the requirement.
`Matrix` also gains dimension checks on multiply/add and bounds checks on
indexing, and loses the now-unused `adjugate`/`minor` cofactor path.
The two-group golden is unchanged. N-group behaviour is covered by
invariants — permutation invariance, and quality falling as a skill gap
widens — since no reference values were available to compare against; the
sublee/trueskill cross-check remains open.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DnsaJg74eNSva3PJjK2eej
logaritmiskandClaude Opus 5