Student-t Forward RAPM

This model is the first robust-likelihood version of the recursive, one-number Forward Exposure-Gated RAPM state. It retains the same strictly forward player priors, replacement-token cold starts, regular-season training set, and frozen 2025-26 evaluation as the Gaussian model. Only the observation model for stints changes.

Model

For stint (i), with observed home net rating (y_i), signed player design row (x_i), lineup coefficients \(\beta\), and intercept \(\alpha\), the Gaussian RAPM fit assumes residuals are normally distributed. Here they follow a Student-t distribution:

The player prior remains the same prior-centered Gaussian ridge penalty, \(\beta_j \sim \mathcal{N}(m_j, \tau^2)\), where \(m_j\) is the frozen returning-player or exposure-gated cold-start prior. The first exemplar fixes \(\nu=5\), which gives large-residual stints less influence than a Gaussian likelihood while retaining finite variance.

It is fitted by iteratively reweighted ridge regression. At each IRLS update, the usual possession weight \(p_i\) is multiplied by

Thus an ordinary residual has weight near one, while a highly unusual stint is downweighted. The model does not yet use a Student-t distribution for player talent or for the prior; this experiment isolates robust observation errors first.

Comparison Contract

Each season uses the per-season lambda selected by the completed Gaussian forward exposure-gated run. Keeping that schedule fixed means the comparison answers a narrow question: does a Student-t error model improve the frozen preseason forecast, holding the recursive prior system and coefficient regularization policy constant?

The prior entering 2025-26 is frozen after 2024-25. Evaluation then uses the realized 2025-26 regular-season and playoff lineup exposures without refitting players. The published artifact contains possession, game-margin, team NetRtg, and Pythagorean-win outputs so it can enter the Frozen Preseason Leaderboard.

Run the model with Train Student-t Forward RAPM.

Current Result

The completed five-degree-of-freedom run is artifacts/models/student_t_forward_rapm/2025-26/student-t-forward-rapm-2025-26-20260806T131834Z-b1cc6592/. All 30 seasonal IRLS fits converged, with 14 to 15 updates per season.

Against the otherwise identical Gaussian recursive model, Student-t is worse on regular-season possession RMSE (1.198993) and game-margin RMSE (14.8225), as well as the regular team metrics. It improves playoff game-margin RMSE from 17.4188 to 17.1300, but the frozen aging prior remains the current playoff leader at 16.4946. This first robust-likelihood specification is therefore a useful negative result, not a promoted predictive state.

Published Outputs