feat!: N-team outcome prediction with draw mass, replacing the 2-team panic

`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
This commit is contained in:
2026-09-07 14:55:11 +02:00
co-authored by Claude Opus 5
parent 87fca8dcca
commit bb2a845882
8 changed files with 1513 additions and 50 deletions
+1 -1
View File
@@ -110,7 +110,7 @@ fn history_predict_quality_supports_three_teams() {
h.record_winner(&"b", &"c", 2).unwrap();
h.converge().unwrap();
let q = h.predict_quality(&[&[&"a"], &[&"b"], &[&"c"]]);
let q = h.predict_quality(&[&[&"a"], &[&"b"], &[&"c"]]).unwrap();
assert!(
q.is_finite(),
"3-team predict_quality must be finite, got {q}"