Post-Hoc Kalman Player-State Audit (Invalid Candidate)

Last updated: 2026-08-24

This audit tested whether the player component of NAIL should retain an explicit uncertainty state between seasons. Production NAIL v1.2.1.2 carries a forward aging-adjusted point prior. This branch treated the completed RAPM fit as a noisy annual observation and carried both a posterior mean and variance.

It is not a valid model candidate. The completed RAPM coefficient is already a ridge-regularized estimate centered on that season's player prior. Applying a Kalman gain to that coefficient treats a prior-shrunk posterior as an independent measurement and shrinks the same signal again. The results are retained as a diagnostic, not included in the frozen leaderboard or model tree.

State Update

For player \(i\) in completed season \(t\), \(m^-_{i,t}\) is the exact prior used in that season's RAPM fit and \(y_{i,t}\) is its completed RAPM estimate:

Low-exposure estimates have larger observation variance \(R_{i,t}\), so they move the state less. The next-season mean is the existing forward, value-conditioned aging projection of \(m^+_{i,t}\). The variance transition is

The implementation did not use \(P^-\) to vary the RAPM penalty itself; it used the filtered posterior mean as a conventional player prior. That is the source of the invalid observation model described above.

Information Boundary

The update for season \(t\) is applied only after season \(t\) is complete. The prior for \(t+1\) therefore uses no \(t+1\) possession, box-score, or context outcome. Gap-returner transitions similarly start from the last filtered observed state and use only known biographical inputs during the gap.

Diagnostic Replay

The recursive fit completed through 2025-26 and the strict replay forecasts 2023-24 through 2025-26 from each matching pre-season state. The incumbent is the production B2B-control model; all player, profile, lineup-context, and schedule contracts are identical apart from the filtered player prior.

The diagnostic has been invalidated, rather than merely not promoted. It produces a small playoff improvement and a higher pooled game-winner accuracy, but loses every primary pooled regular-season margin metric and substantially worsens team net-rating RMSE. More importantly, those comparisons are not a valid test of a Kalman state-space RAPM because of double shrinkage.

The correct follow-up is a precision-weighted prior-centered RAPM: retain the filtered state mean as the prior, use the state variance to set each player's ridge precision, and derive the completed posterior directly from that fit. With equal precision for every player, that implementation must reproduce the incumbent exactly before any state-space comparison is admitted to the leaderboard.

State Audit

kalman_player_states.parquet records the prior, observation, posterior, and variance for every player-season state used while constructing a target prior. For the state available before 2025-26, the Kalman gain distribution was:

This confirms the implemented calculation: a low-exposure coefficient receives only a small update, while a high-exposure coefficient can move the next prior substantially. It does not validate the calculation as a correctly specified state-space RAPM observation model.

Artifacts

• Recursive fit: artifacts/models/forward_nail_rapm_v1213_kalman_player_state/2025-26/forward-nail-rapm-v1213-kalman-player-state-2025-26-20260824T211727Z-b02c15b2
• Frozen replay: artifacts/models/nail_v1213_kalman_player_state_frozen_backtest/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260824T214244Z-ae4dd903