Forward Box-Score Residual HPM

This branch adds a true individual box-score prior inside the existing HPM state, instead of replacing HPM with a standalone box-score estimate.

For target season \(t\), HPM supplies the strictly forward prior \(\mu^{\mathrm{HPM}}_{i,t}\). A possession-weighted ridge model learns the completed historical residual

\[ r_{i,t}=\operatorname{HPM}_{i,t}-\mu^{\mathrm{HPM}}_{i,t} \]

from the player's immediately prior-season possession-normalized box profile. The next prior becomes

\[ \mu^{\mathrm{box}}_{i,t}=\mu^{\mathrm{HPM}}_{i,t}+\widehat r_{i,t}. \]

The residual excludes prior RAPM, age, experience, draft, physical dimensions, and position because HPM already contains those signals. It uses lagged on-court possession exposure, scoring volume, assists, turnovers, offensive and defensive rebounds, steals, blocks, fouls, and stabilized shooting rates.

Boundary And Cold Starts

Each annual ridge fit uses only earlier completed HPM seasons. Its penalty is chosen by expanding completed-season folds. No target-season box score, RAPM, or lineup outcome enters the target prior.

Only returning players with a complete prior NBA box profile receive the residual adjustment. Cold starts remain on HPM's exposure-gated replacement/draft branch. The adjusted prior is then possession-centered using the preceding season's exposure.

Rebuilt Frozen 2025-26 Result

The recovered-history rerun is:

artifacts/models/forward_box_score_residual_hpm/2025-26/
forward-box-score-residual-hpm-2025-26-20260813T043212Z-7f53370b

Compared with the matched rebuilt Value-Conditioned Aging HPM run, the box-score residual is effectively tied but slightly worse on the primary lineup-prediction contract: regular possession RMSE is 1.198739 versus 1.198736, eligible game-margin RMSE is 14.3256 versus 14.3214, and playoff game-margin RMSE is 16.4632 versus 16.4069.

It modestly improves aggregate team estimates: regular-season team NetRtg RMSE is 3.5825 versus 3.5858, and Pythagorean-win RMSE is 7.6174 versus 7.6300. The differences are too small to promote it over the parent HPM, but they retain evidence that a strictly lagged box profile supplies some team-level signal.

For 2025-26, the residual moves Stephen Curry's frozen prior from +0.97 to +1.32, and his retrospective rating from +0.93 (111th) to +1.18 (98th). This is a learned box-score residual, not a direct reattribution of contextual value.