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L5-MMP v0.1

Last-5 Median Minutes Persistence is the second parameter-free Rotation Models baseline. It tests whether a small robust history improves materially on copying the prior team-game allocation.

Forecast contract

For a target team-game \(g+1\), use exactly the five preceding completed team-games for that team. Let \(m_{i,k}\) be a player's raw minutes in history game \(k\), with zero assigned when the player was absent or did not play.

\[ \widetilde m_{i,g+1} = \operatorname{median}(m_{i,g-4}, m_{i,g-3}, m_{i,g-2}, m_{i,g-1}, m_{i,g}). \]

The raw median totals are normalized into a valid allocation:

\[ \widehat y_{i,g+1} = \frac{\widetilde m_{i,g+1}}{\sum_j \widetilde m_{j,g+1}}. \]

This is deliberately not a trailing average, not conditional on games played, and not a NAIL-informed model. The median allows a stable rotation player to survive a one-game rest or DNP, while repeated absences push the forecast toward zero.

Evaluation

Evaluation begins with a team's sixth completed game. L5-MMP reports the same metrics as L1-MSP: allocation total variation, distributional Brier score, player-share MAE/RMSE, and strict cross-entropy.

Strict cross-entropy remains \(+\infty\) when a player receives positive target minutes after a zero five-game median. The artifact separately reports:

  • zero_history_actual_share: target share from a player absent from all five historical team-games;
  • zero_median_actual_share: target share from a player assigned zero by the median rule, including players who were present but repeatedly inactive.

Initial benchmark

L5-MMP is a control, not a promoted rotation baseline. It evaluates 120 fewer team-games than L1-MSP in each season because five historical games are required instead of one.

Model Season Evaluated team-games Mean TV Brier Player-share MAE Player-share RMSE Infinite CE rate
L1-MSP 2024-25 2,248 0.2038 0.0278 0.0287 0.0441 72.7%
L5-MMP 2024-25 2,128 0.2174 0.0309 0.0276 0.0442 78.2%
L1-MSP 2025-26 2,430 0.2025 0.0265 0.0229 0.0387 74.7%
L5-MMP 2025-26 2,310 0.2139 0.0291 0.0237 0.0401 75.7%

The median reduces sensitivity to one-game rests for established rotation players, but it is too slow to adapt to real allocation changes. It loses to L1-MSP on the two support-invariant allocation metrics, total variation and Brier score, in both evaluated seasons.

This is not caused by L5-MMP's longer five-game warmup. On the identical 2,310 L5-eligible team-games in 2025-26, L1-MSP has Brier \(0.0271\) and TV \(0.2046\), versus L5-MMP's Brier \(0.0291\) and TV \(0.2139\). L5-MMP wins on Brier in 46.5% of those team-games, including rest-return cases, but it loses slightly more often and by enough to lose on the average.

Run

uv run nba-evaluate-l5-median-minutes-persistence \
  --seasons 2024-25 2025-26

The evaluator writes immutable artifacts beneath artifacts/rotation/l5_median_minutes_persistence/.