Forward Box-Score Interaction HPM

This is the first controlled extension of Forward Box-Score Residual HPM. It retains the additive lagged box-score residual and adds six predeclared, interpretable player-profile interactions. The base HPM player prior, exposure-gated cold-start behavior, recursive portable context, and frozen evaluation boundary are unchanged.

For returning player \(i\) in target season \(t\), the model predicts the completed HPM residual using prior-season box features \(z_{i,t-1}\) and their products:

\[ \mu^{\mathrm{box-int}}_{i,t}= \mu^{\mathrm{HPM}}_{i,t}+\widehat r(z_{i,t-1}, z_{i,t-1}\otimes z_{i,t-1}). \]

Every numeric feature, including each product, is median-imputed and standardized inside the possession-weighted annual ridge pipeline. Ridge regularization therefore decides whether an interaction retains incremental weight beyond its two constituent additive terms.

Interaction Set

Interaction	Construction	Intended player-profile signal
Usage x assists	\((FGA + 0.44 FTA + TOV) \times AST\)	High-volume creation
Usage x turnovers	\((FGA + 0.44 FTA + TOV) \times TOV\)	Burden and ball-security cost
3PA x eFG%	\(3PA \times eFG\%\)	High-volume efficient shooting
FGA x FTA	\(FGA \times FTA\)	Scoring and free-throw pressure
OREB x DREB	\(OREB \times DREB\)	Rebounding profile
STL x BLK	\(STL \times BLK\)	Defensive-event profile

All counts are on-court events per 100 on-court possessions. Shooting uses the same prior-season empirically stabilized rate as the additive residual model. The set is intentionally small: it tests concrete archetype hypotheses without creating a large, unstable all-pairs feature search.

Boundary And Cold Starts

The interaction branch learns each season only from earlier completed HPM transitions, with regularization selected by expanding completed-season folds. It cannot observe target-season box scores, RAPM, lineup outcomes, or playoff outcomes when constructing a target-season prior.

Returning players with a complete prior-season box profile receive the adjustment. Rookies and other cold starts remain on HPM's established exposure-gated replacement/draft branch.

Frozen 2025-26 Result

The complete recursive run is:

artifacts/models/forward_box_score_interaction_hpm/2025-26/
forward-box-score-interaction-hpm-2025-26-20260812T203047Z-e2680654

The interactions did not improve the primary frozen contract. Relative to the additive box-score residual HPM, regular possession RMSE is essentially tied but marginally worse (1.198771 versus 1.198770), eligible game-margin RMSE rises (14.3577 versus 14.3548), and full-game margin RMSE rises (14.6309 versus 14.6268). The playoff game-margin result also rises, from 16.5027 to 16.5138.

There is one narrow aggregate improvement: Pythagorean-win RMSE is 7.9928, slightly better than the additive residual's 7.9943. It is not sufficient to promote this branch over HPM or the additive residual, particularly because the full-game winner accuracy remains 68.05% and team NetRtg RMSE rises from 3.7536 to 3.7595.

For the frozen 2025-26 prior, the selected interaction ridge penalty is 1.0, based on 27 expanding completed-season folds. The final standardized interaction coefficients are modest: FGA x FTA is +0.0196, steals x blocks is +0.0163, OREB x DREB is +0.0075, 3PA x eFG% is -0.0051, usage x assists is +0.0046, and usage x turnovers is +0.0002. The products are therefore available to the model, but do not carry enough stable incremental signal to beat the simpler prior on the primary metrics.