L1-MSP v0.0

Lag-1 Minute-Share Persistence is the parameter-free baseline for the Rotation Models family. It forecasts only the next team-game, not a full season.

Target

For player \(i\) in team-game \(g\), define:

\[ y_{i,g} = \frac{m_{i,g}}{\sum_{j \in T_g} m_{j,g}}. \]

The denominator is actual total team minutes. It therefore includes overtime, and each team's player shares sum to one. Players who do not play have a zero share.

Forecast

\[ \widehat y_{i,g+1} = y_{i,g}. \]

There are no player attributes, fitted coefficients, hyperparameters, rolling averages, or NAIL inputs. A player receives a distinct forecast only because the player had a distinct share in the previous team-game.

For evaluation, the support is the union of players in consecutive team-games. A player with a zero prior-game share, whether newly available or previously inactive, has a predicted share of zero. A player absent from the current game retains the prior predicted share and has an actual share of zero. This deliberately exposes the cold-start and rotation-change problem.

Evaluation

The primary metric is team-game allocation error, measured as total variation:

\[ \operatorname{TV}_g = \frac{1}{2}\sum_i |y_{i,g} - \widehat y_{i,g}|. \]

It ranges from zero (identical allocation) to one (disjoint allocations). We also report player-share MAE and RMSE.

The distributional Brier score is:

\[ \operatorname{BS}_g = \sum_i (y_{i,g} - \widehat y_{i,g})^2. \]

It is finite even when L1-MSP misses a newly active player, and unlike the per-player MSE it does not depend on how many players are in the evaluated union support.

Strict cross-entropy

We additionally report strict cross-entropy:

\[ \operatorname{CE}_g = -\sum_{i:y_{i,g}>0} y_{i,g}\log \widehat y_{i,g}. \]

For L1-MSP, this is (+\infty) whenever a player logs positive minutes after receiving a zero prior-game share. That is not a numerical failure; it is the baseline's exact cold-start failure. The aggregate therefore reports the strict cross-entropy, the fraction of team-games with infinite cross-entropy, and the mean cross-entropy among finite team-games. A future model may introduce a pregame candidate roster and a cold-start probability mass; L1-MSP does not.

Initial benchmark

The first run uses the regular-season curated player-game data currently available in the repository. L1-MSP has no fitted parameters, so 2024-25 is a source-season evaluation and 2025-26 is the held-out evaluation season for later rotation models.

Season	Coverage	Evaluated team-games	Mean TV	Brier	Player-share MAE	Strict CE	Infinite CE rate
2024-25	1,139 available games	2,248	0.2038	0.0278	0.0287	\(\infty\)	72.7%
2025-26	1,230 games	2,430	0.2025	0.0265	0.0229	\(\infty\)	74.7%

The 2024-25 source data currently covers 1,139 games rather than a full 1,230 game regular season. The 2025-26 row is complete: one first team-game is excluded for each of the 30 teams because it has no preceding allocation.

A mean TV of 0.2025 means copying the prior game's allocation leaves roughly 20.25% of a team's next-game minute-share mass allocated to the wrong players or in the wrong amounts. That is deliberately a hard, cold-start-sensitive baseline for subsequent rotation models to beat.

Run

uv run nba-evaluate-l1-minute-share-persistence \
  --seasons 2024-25 2025-26

The command writes per-player predictions, per-team-game metrics, aggregate season metrics, and metadata beneath artifacts/rotation/.