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Student-t Talent-Prior Contextual RAPM

This controlled ablation combines the current Forward Contextual RAPM state with the Student-t talent prior. It keeps Gaussian stint errors, the recursive exposure-gated cold-start policy, the published per-season lambda schedule, and the lagged contextual spline function unchanged.

Seasonal Transition

For season \(t\), the completed context function \(g_{t-1}\) is subtracted from the raw stint target before fitting player coefficients:

\[ y^{\mathrm{adj}}_{s,t}=y_{s,t}-g_{t-1}(z_{s,t}). \]

The player adjustment around the forward prior \(\mu_{i,t}\) receives a Student-t penalty instead of the Gaussian ridge penalty used by the base contextual model:

\[ \beta_{i,t}-\mu_{i,t} \sim \operatorname{StudentT}(\nu=3,0,s=3). \]

IRLS turns that into a player-specific local shrinkage multiplier. The fitted additive state then defines the raw residual used to fit \(g_t\), which is carried into season \(t+1\). Thus the model changes only the player-prior departure distribution; it does not alter cold starts, context features, or the information boundary.

Frozen 2025-26 Result

The run artifacts/models/student_t_talent_contextual_rapm/2025-26/student-t-talent-contextual-rapm-2025-26-20260808T012017Z-7bbeadf3/ fits 1996-97 through 2025-26. Its frozen 2025-26 forecast uses the completed 2024-25 player state and \(g_{2024-25}\), then scores realized target-season lineup exposure without a player refit.

Cohort Possession RMSE Possession MAE Eligible-game RMSE Team NetRtg RMSE Pythagorean win RMSE
Regular season 1.199026 1.141556 14.6770 4.1771 9.3594
Playoffs 1.192959 1.135643 17.6146 - -

It narrowly improves the base contextual model's regular-season possession MAE (1.141571 to 1.141556), but is worse on its primary full-game margin metric (15.0190 to 15.0487), team NetRtg RMSE, and Pythagorean win RMSE. It is therefore retained as a transparent combination test, not promoted over Forward Contextual RAPM.

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

Outputs

The immutable artifact includes the standard frozen possession, eligible-game, full regular-game, team NetRtg, and Pythagorean-win outputs. It also retains the per-season player priors, exposure-gated replacement tokens, cold-start metadata, contextual models, and contextual fit metadata needed to reproduce the state transition.