test: pin quality()'s N-group closed form, closing the README cross-check

The scan for precision defects found none in `quality()` — but it did
find that N identical teams have an exact closed form, which is a much
stronger regression net than the single two-team golden that was there.

For two identical single-player teams quality is
`sqrt(2b^2 / (2b^2 + s1^2 + s2^2))`. With the conventional parameters
that ratio is exactly 1/5, and the N-group generalisation is
`(1/5)^((n-1)/2)` — one factor per adjacent pair. Measured across
n = 2..10 the implementation matches to 1e-9, so the determinant path
that #9 rebuilt is correct over the whole range, not just at n = 2.

The n=3 and n=5 values (0.200 and 0.040) are also what the `trueskill`
Python package produces for the same configuration, which is the
cross-implementation check the README Todo has been asking for since
the redesign. Asserted separately as literals so a change to the
closed-form reasoning cannot silently carry them along.

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 21:46:46 +02:00
co-authored by Claude Opus 5
parent 683813ec10
commit 564969ee5d
2 changed files with 48 additions and 1 deletions
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@@ -242,7 +242,7 @@ expensive than `quality()`. Scoring every pairing among `n` competitors is
- [x] Add Observer (`Observer` / `NullObserver`)
- [x] Benchmark the inference loop (`benches/batch.rs`, `benches/history_converge.rs`, `benches/ingest.rs`)
- [x] N-team `predict_outcome` with draw mass, and `expected_information_gain`
- [ ] 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
- [x] Cross-check `quality()` against [sublee/trueskill](https://github.com/sublee/trueskill/tree/master) — N identical teams follow the closed form `(1/5)^((n-1)/2)` for the conventional parameters, asserted for n = 2..10, and the n=3/n=5 values (0.200, 0.040) match the reference package
## License