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Frozen Lineup Residual Archetypes

Last updated: 2026-09-08

This audit looks backward from the three frozen production replays to identify which observed five-man units most consistently beat or missed their frozen NAIL prediction. It is a hypothesis generator for future non-additive context features, not a model-selection result and not causal attribution to the five players.

Contract

For each target-season stint, the prediction is the production NAIL state that was available before that season began. The oriented residual for a unit is

\[ r_s = y_s - \widehat{y}^{\mathrm{frozen}}_s, \]

where the sign is reversed for the away unit. Positive values therefore mean that the unit outperformed its frozen prediction against the opponents it actually faced.

Stints are then grouped by target season, team, and the unordered set of five player IDs. Only realized regular-season units with at least 250 possessions are eligible. This deliberately makes the audit retrospective: realized lineup deployment determines which units can be studied. It does not make the residual itself non-frozen.

Lineup means are noisy, so the observed possession-weighted mean \(\bar r_u\) is shrunk toward the pooled stint residual mean \(\bar r\):

\[ \widetilde r_u = \bar r + w_u(\bar r_u - \bar r), \qquad w_u = \frac{n_u}{n_u + \sigma^2 / \tau^2}. \]

Here \(n_u\) is unit possessions, \(\sigma^2\) is the weighted stint-residual variance, and \(\tau^2\) is the estimated between-unit variance after removing average sampling noise. This is an empirical-Bayes shrinkage heuristic, not a new NAIL parameter. Units are assigned to deciles within each season using \(\widetilde r_u\).

Player-profile inputs remain predictive: each target season uses the same strictly lagged, padded profile contract as production NAIL. Target-season box scores are never used to define a unit's profile.

Coverage

Target season Eligible five-man units Eligible possessions Mean shrinkage weight
2023-24 69 38,348 0.745
2024-25 60 28,857 0.736
2025-26 58 26,093 0.718
Pooled 187 93,297 0.734

The top and bottom deciles contain only about six units per season. Results must therefore repeat across seasons before becoming a candidate feature.

Profile Contrasts

The chart compares the profile means of the highest and lowest shrunk-residual deciles. Values are expressed in the pooled standard deviation of the stated lineup summary; positive means the high-residual group is larger.

Exposure-shrunk frozen residual lineup archetypes

Profile summary 2023-24 2024-25 2025-26 Pooled
Maximum conventional USG% -0.31 -0.73 -0.31 -0.43
Top-two usage share -0.22 -0.46 -0.55 -0.40
Top-one minus top-two USG% +1.33 +0.66 -0.60 +0.36
Maximum blocks per 100 +0.02 +0.22 +0.75 +0.28
Mean top-two 3PM per 100 +0.44 -0.52 +0.65 +0.25
Top-two assists per 100 -0.85 +0.90 -0.57 -0.25
Mean bottom-two 3PM per 100 +0.32 -0.75 +0.36 +0.00

The two usage-concentration summaries have the same sign in every season: high-residual units are less dominated by their top usage players. That is a useful descriptive pattern, but it overlaps the production usage-concentration term and cannot by itself establish incremental signal. The other contrasts are not stable: for example, top-two shooting and assists reverse direction across the three seasons. They should not advance to a full frozen refit without a separate, declared feature contract and screen.

Decision Rule

Use this audit to propose a small number of basketball-coherent candidates. Each candidate must then follow the existing sequence:

  1. Define the strictly lagged feature and its sign expectation.
  2. Run the frozen residual screen, including all three target seasons.
  3. Require a coherent decile pattern and a stable directional result before a recursive refit.
  4. Put every full candidate on the three-season frozen leaderboard, regardless of whether it is promoted.

The audit is not evidence that a discovered profile should be added to NAIL; it is evidence about where to look next.

Reproduce

uv run python -m nba_lineup_model.modeling.lineup_residual_archetype_audit \
  --minimum-possessions 250

Artifact: artifacts/models/analysis/lineup_residual_archetypes/lineup-residual-archetypes-20260908T170331Z-989239a0.