Forward Portable-Matchup Contextual RAPM

Forward Portable-Matchup Contextual RAPM is a rolling contextual RAPM model that preserves a total lineup-context correction while making two parts of it identifiable: a portable unit score and an opponent-specific matchup residual. It uses the same forward exposure-gated player priors, cold starts, player profiles, composition features, spline basis, and Ridge alpha as Forward Contextual RAPM.

For two five-player units \(A\) and \(B\), the completed context state is:

\[ C(A,B) = \underbrace{h(x(A)) - h(x(B))}_{\text{portable composition advantage}} + \underbrace{q(x(A),x(B))}_{\text{specific matchup interaction}}. \]

Here \(x(A)\) is the same side-level feature vector used by the prior contextual models: stabilized prior-season shooting, passing, usage, turnover, rebounding, steal, and block rates plus the published composition summaries.

Total Context State

The total \(C\) is fitted as a relative spline Ridge function using the same contextual feature family as the original model. Each training observation is paired with its reversed orientation, including the negated residual target. At prediction time the model returns:

\[ C(A,B) = \frac{g(x(A)-x(B))-g(x(B)-x(A))}{2}. \]

Consequently, orientation symmetry is exact:

\[ C(A,B)=-C(B,A). \]

This is the critical difference from the pure decomposed ablation. The model does not require every useful contextual pattern to be expressible as a difference of independent side scores. It retains a nonseparable \(q\) term for actual opponent-specific effects.

Identifying h And q

After every completed season \(t\), the model stores a possession-weighted reference distribution \(\mathcal R_t\) of all observed home and away unit feature vectors. For any candidate unit \(A\):

\[ h_t(x(A)) = \mathbb E_{R\sim\mathcal R_t}[C_t(A,R)]. \]

The matchup component is then the exact residual:

\[ q_t(A,B) = C_t(A,B)-h_t(x(A))+h_t(x(B)). \]

Because the same reference distribution is used on both sides and \(C\) is antisymmetric, \(q\) has no average portable effect:

\[ \mathbb E_{R\sim\mathcal R_t}[q_t(A,R)] = 0. \]

Thus \(h\) is a unit's expected context against the completed-season field, not a player rating or an absolute context level. \(q\) reports what changes for this exact opponent after both units' portable context values have been removed.

Rolling Forecast Boundary

For a stint in season \(t\), only the completed prior-season total context is subtracted before fitting the same prior-centered additive RAPM state:

\[ y^{\mathrm{adj}}_{s,t}=y_{s,t}-C_{t-1}(H_s,A_s). \]

The frozen 2025-26 forecast uses the completed 2024-25 \(C\) model and the 2024-25 empirical reference field. The 2025-26 model is fit only after that forecast has been scored, and is retained for the next season's state.

Frozen 2025-26 Result

This model improves the primary regular eligible-game margin metric and both full-game margin metrics while retaining the side/matchup decomposition:

Metric	Forward contextual RAPM	Portable-matchup contextual RAPM
Regular eligible-game margin RMSE	14.6525	14.6349
Regular full-game margin RMSE	15.0190	14.9602
Regular full-game margin MAE	11.8474	11.7780
Regular team NetRtg RMSE	4.1572	4.1864
Regular Pythagorean-win RMSE	9.3153	9.3999
Playoff eligible-game margin RMSE	17.5493	17.5261

It is therefore a competitive contextual candidate rather than an across-the-board replacement. The full metric record is maintained in the Frozen Preseason Leaderboard.

Artifact

The completed through-2025-26 run is forward-portable-matchup-contextual-rapm-2025-26-20260808T165815Z-0d9d87f0 under artifacts/models/forward_portable_matchup_contextual_rapm/2025-26/. Its forecast_reference_units.parquet file exposes the frozen 2024-25 unit distribution that identifies \(h\) and centers \(q\). The model artifact also stores every seasonal context state, player-prior state, and frozen evaluation table.

Before proposing another contextual function family, inspect the saved seasonal total components in the Context Function Audit.