Student-t Talent-Prior RAPM

This experiment restores the canonical Gaussian error model for lineup stints and changes only the player-talent prior. It uses the same recursive, regular-season-only exposure-gated state and frozen 2025-26 evaluation as the Gaussian Forward Exposure-Gated RAPM model.

Model

For each stint, the observed home net rating remains Gaussian:

Each player coefficient is centered on their strictly forward prior \(m_j\), but its adjustment follows a Student-t distribution:

The three-point scale is the tail threshold in RAPM points per 100 possessions: near zero adjustment, the local penalty is exactly the completed Gaussian model's ridge penalty; farther from the prior, shrinkage relaxes as

The fit alternates between updating \(q_j\) and solving a sparse, prior-centered ridge problem with a player-specific penalty multiplier. This is the normal-scale-mixture/IRLS representation of a Student-t coefficient prior. It allows a strongly identified outlier to depart from its prior while keeping weakly identified player effects near their forward value.

Comparison Contract

The first run fixes \(\nu=3\), \(s=3\), and the per-season lambda schedule from the completed Gaussian recursive run. It neither tunes those parameters on 2025-26 nor combines this change with the earlier Student-t observation experiment. The 2025-26 prior is frozen after 2024-25, then scored against realized regular-season and playoff lineup exposures without a player refit.

Run it with Train Student-t Talent-Prior RAPM.

Current Result

The completed \(\nu=3\), \(s=3\) run is artifacts/models/student_t_talent_forward_rapm/2025-26/student-t-talent-forward-rapm-2025-26-20260806T203508Z-8e8a2698/. All 30 seasonal fits converged, requiring 9 to 81 IRLS updates (mean 24.4).

Relative to the otherwise identical Gaussian recursive state, it improves all regular-season point estimates: possession RMSE (1.198993 to 1.198989), game-margin RMSE (14.8225 to 14.7993), team NetRtg RMSE (4.6680 to 4.6069), and Pythagorean win RMSE (10.2778 to 10.1176). The playoff metrics worsen, so this is a promising regular-season result rather than a universal replacement. The published 2026-27 rankings use the selected 2025-26 final-season \(\lambda=0.03\).[^lambda-sensitivity]

The completed-state 2026-27 Student-t Talent-Prior Rankings page publishes the sortable top 100 returning players. The lambda sensitivity report holds the 2025-26 entering state fixed and measures the effect of a 0.10 final-season refit against the selected 0.03 value.

[^lambda-sensitivity]: Lambda sensitivity. Holding all 2025-26 entering priors and Student-t settings fixed, the \(\lambda=0.10\) refit has a 0.926 Pearson rating correlation with the \(\lambda=0.03\) fit, but a 0.740 mean absolute RAPM difference and 44.5 mean absolute rank movement across 582 players. Victor Wembanyama moves from +13.84 (rank 1) to +7.33 (rank 5). See the full lambda sensitivity report.

Published Outputs