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Context-Reattributed RAPM (CR-RAPM)

HPM deliberately reserves some predictive signal for a frozen lineup-context term. That improves forecasting when a lineup's profile and matchup matter, but a conventional player table can understate players who repeatedly create favorable context. CR-RAPM is an accounting audit that asks how much of that frozen context signal can be represented as a player term on the usual RAPM design, and how much remains genuinely lineup-specific.

It is not a replacement predictive model and is not eligible for the frozen leaderboard. It observes the realized target-season lineup exposures only after the HPM forecast state was frozen.

Ledger

For a target-season stint, the completed-season HPM ledger has the form

\[ \hat y = X\beta + b + C(A,B), \]

where \(X\) is the signed home-minus-away player matrix, \(\beta\) is the completed-season HPM player rating vector, \(b\) is its home-court intercept, and \(C(A,B)\) is the portable composition-plus-matchup context prediction from the prior-season frozen state.

CR-RAPM makes a separate possession-weighted ridge projection on those same stints:

\[ C(A,B) \approx X\gamma + a + r(A,B). \]

\(\gamma\) is the context-reattribution vector, \(a\) is its intercept, and \(r\) is residual synergy. The projection uses HPM's selected target-year player regularization, so \(\gamma\) is constrained on the same sparse-design scale as the player fit. It is not tuned against game outcomes.

Substitution gives an exact accounting identity:

\[ \hat y = X(\beta + \gamma) + (b+a) + r(A,B). \]

The player-facing CR-RAPM value is therefore

\[ \operatorname{CRRAPM}_i = \beta_i + \gamma_i. \]

A positive \(\gamma_i\) says that, across the realized target-season units in this audit, player \(i\)'s presence helps reconstruct HPM's context term after the other players in a lineup are considered. It is not a causal estimate and does not say that the player owns every nonlinear lineup effect.

Reading Residual Synergy

The residual \(r(A,B)\) is the portion of HPM context that the additive player projection cannot express. A residual near zero means that the frozen context signal for that stint is effectively portable to its players under this design. A large positive or negative residual means the model still needs a configuration-specific interaction after all reattributed player terms are included.

This distinction addresses the central attribution question directly:

  • a player can gain CR-RAPM credit for recurring profile-based context;
  • a unit can retain residual synergy without forcing that interaction onto any one teammate;
  • the original HPM forecast is unchanged in every case.

Initial 2025-26 Audit

The initial audit evaluates the frozen 2024-25 HPM context state on all 39,918 realized 2025-26 regular-season stints (122,886 estimated possessions). It uses the HPM target-season regularization, \(\lambda=0.03\), for the player projection.

Diagnostic Result
Context variance represented by player reattribution (weighted \(R^2\)) 68.76%
Residual-synergy RMSE 2.352
Residual-synergy MAE 1.864
5th / 50th / 95th residual percentile -3.99 / -0.00 / +3.94
Correlation: frozen context vs. player projection 0.859

This is strong agreement, but it is not an argument that residual synergy is zero. Roughly one-third of the context variance remains outside the additive player projection, and individual stints can still retain several net-rating points per 100 of configuration-specific signal. The fixed 2024-25 context state is forward-looking; the 2025-26 player reattribution is retrospective and therefore not a new forecast evaluation.

The reattribution moves several high-context players upward. The examples below are descriptive, not a second predictive leaderboard.

Player HPM player rating Context reattribution CR-RAPM
Shai Gilgeous-Alexander +6.78 +1.94 +8.72
Nikola Jokić +5.24 +2.02 +7.26
Stephen Curry +1.01 +1.25 +2.26
Draymond Green -2.87 +1.00 -1.88
James Harden -1.34 +1.69 +0.35

Curry is the useful motivating example: CR-RAPM finds a meaningful recurring player-associated share of the frozen HPM context term, but does not make the entire context effect his. That is the intended separation between portable player reattribution and residual lineup-specific interaction.

Audit Outputs

Run the build guide to create an immutable audit artifact. It contains:

  • player_context_reattribution.parquet: HPM rating, context reattribution, CR-RAPM, and target-season on-court possessions for every identified player.
  • stint_context_ledger.parquet: frozen HPM context, player-projected context, and residual synergy for each realized stint.
  • lineup_residual_synergy.parquet: possession-weighted exact lineup-pair residuals above the configured exposure threshold.
  • audit_metrics.parquet: projection \(R^2\), RMSE, residual quantiles, and coverage.

Published artifact:

artifacts/models/context_reattributed_rapm_audit/2025-26/
context-reattributed-rapm-audit-2025-26-20260812T053955Z-a045caca