Forward Context-Reattributed HPM

This is the predictive continuation of the Context-Reattributed RAPM audit. A completed season's frozen context term is projected onto players as \(X\gamma_t\), and a constrained fraction is moved into the next-year player prior:

\[ \mu_{i,t+1}=\mu^{\mathrm{aging/cold}}_{i,t+1}+\rho\gamma_{i,t}. \]

To avoid double counting, the same transferred component is removed from the next season's context correction:

\[ C^{\mathrm{residual}}_t(A,B)=C_t(A,B)-\rho X\gamma_t. \]

Thus the model retains a player-facing CR adjustment and residual portable composition/matchup context. It is genuinely forward-looking: \(\gamma_t\) uses only a context function fit on completed season \(t\), and affects only season \(t+1\).

Frozen 2025-26 Results

The first complete recursive candidate uses \(\rho=0.5\):

artifacts/models/forward_context_reattributed_hpm/2025-26/
forward-context-reattributed-hpm-2025-26-20260812T072008Z-f68f69b1

It is a useful negative result. Compared with current Value-Conditioned Aging HPM, the transfer worsens regular eligible-game margin RMSE from 14.3469 to 14.3909, team NetRtg RMSE from 3.7568 to 3.8791, and Pythagorean win RMSE from 8.0346 to 8.3649. It also does not improve the separate playoff evaluation. The model is therefore documented as an experimental ablation, not promoted to the website or gold-standard rating.

The run still produces season_context_reattributions.parquet with annual \(\gamma_t\) coefficients and season_context_reattribution_metadata.parquet with annual projection fit diagnostics. This makes the next question precise: whether a smaller, forward-selected \(\rho\) can retain any player-persistence benefit without diluting the contextual state.

The smaller \(\rho=0.25\) candidate improves upon the half-transfer run:

artifacts/models/forward_context_reattributed_hpm/2025-26/
forward-context-reattributed-hpm-2025-26-20260812T143351Z-991dad66

Its frozen regular-season possession RMSE is 1.198777 and eligible-game margin RMSE is 14.3677, versus 1.198794 and 14.3909 for \(\rho=0.5\). It also improves team NetRtg RMSE from 3.8791 to 3.8211, Pythagorean-win RMSE from 8.3649 to 8.1949, full-game margin RMSE from 14.6861 to 14.6531, and winner accuracy from 68.21% to 68.37%. It remains behind current HPM (\(\rho=0\)) on these primary regular-season measures, and its playoff eligible-game margin RMSE is slightly worse (16.4769 versus 16.4742). The leaderboard therefore represents the more competitive \(\rho=0.25\) candidate while retaining HPM as the leader.

The still smaller \(\rho=0.1\) run is the best transfer weight tested so far:

artifacts/models/forward_context_reattributed_hpm/2025-26/
forward-context-reattributed-hpm-2025-26-20260812T163434Z-c15576de

It reduces regular eligible-game margin RMSE to 14.3543, team NetRtg RMSE to 3.7827, Pythagorean-win RMSE to 8.0940, and full-game margin RMSE to 14.6344. It also improves regular and playoff possession RMSE relative to every larger transfer weight tested. It remains just behind HPM (\(\rho=0\)) on those error measures, so this remains an experimental branch, but the frozen leaderboard and model tree now represent \(\rho=0.1\).

Full-Transfer Endpoint

The other informative endpoint, \(\rho=1.0\), transfers all player-projectable context into the next-year player prior and forwards only the residual context state. Its completed run is:

artifacts/models/forward_context_reattributed_hpm/2025-26/
forward-context-reattributed-hpm-2025-26-20260812T132121Z-917b17eb

It is decisively worse than both HPM (\(\rho=0\)) and the half-transfer candidate. Frozen 2025-26 regular-season possession RMSE is 1.198826, eligible-game margin RMSE is 14.4337, team NetRtg RMSE is 3.9742, and Pythagorean-win RMSE is 8.6687. This rejects complete transfer: some context is player-projectable, but treating all of it as portable player value degrades the next-season forecast.