Forward Decomposed Contextual RAPM

Forward Decomposed Contextual RAPM is an interpretability ablation of Forward Contextual RAPM. It retains the same forward player-prior, cold-start, profiles, spline basis, Ridge penalty, and season-by-season information boundary. Its only substantive change is the contextual function: every lineup has an identifiable side score, and a matchup context correction is exactly the home score minus the away score.

This is not the predictive default. On the frozen 2025-26 evaluation, the original relative-context model has better regular-season game-margin, team net-rating, and Pythagorean-win errors. The decomposed form remains useful as a clean diagnostic and as a potential building block for an interactive lineup tool because it exposes a per-unit context value.

Same Inputs, Different Constraint

Each five-player unit receives the same leakage-safe context profile used by the original model. It includes stabilized prior-season rates for shooting, assists, turnovers, usage, offensive and defensive rebounds, steals, and blocks, plus the same eleven composition summaries:

• Bottom-two shooting, credible-shooter count, top-two assists, and usage concentration.
• Square-root offensive and defensive rebounding totals.
• Imputed/replacement-profile counts and weights.
• Shooting-by-usage, shooter-by-passing, and rebounding-by-usage interactions.

The original model directly fits a function of the relative lineup feature vector, \(g_t(\phi(H)-\phi(A))\). This model first maps a unit's own profile to a scalar score \(h_t(\phi(U))\), then requires the matchup correction to be

The side model uses the same quadratic spline basis with four knots and the same possession-weighted Ridge alpha of \(10{,}000\). The spline transformer and scaler are fit on the pooled home and away side-feature rows. Ridge is fit without an intercept, so antisymmetry is a structural property rather than an approximation:

Rolling State Transition

For regular-season stint \(s\) in season \(t\), the completed prior-season side function is subtracted before the same prior-centered additive RAPM fit:

The model then fits possession-weighted one-number RAPM with the existing season-specific forward exposure-gated lambda. After the season completes, it fits \(h_t\) to the residual lineup effects. The frozen 2025-26 evaluation uses only \(h_{2024-25}\), player state through 2024-25, and 2025-26 oracle lineups and exposure; \(h_{2025-26}\) is retained only for the next forecast season.

Why The Constraint Matters

The decomposed design makes a unit's context contribution portable across opponents: the difference between two home units is independent of the away unit. That makes side-level displays and feature attribution straightforward. It also removes patterns that can only be expressed as a relative matchup effect. For example, a nonlinear response to a home-minus-away rebounding gap need not equal the difference between two independent side scores. The frozen results indicate that this lost flexibility matters in the current feature set.

The full comparison is maintained in the Frozen Preseason Leaderboard.

Artifact

The completed through-2025-26 run is forward-decomposed-contextual-rapm-2025-26-20260808T133655Z-41f61af6 in artifacts/models/forward_decomposed_contextual_rapm/2025-26/. It stores the per-season player state, profiles, decomposed context models, context metadata, and frozen regular-season/playoff, team, and win evaluation tables.