Do Minutes Proportional to Player Skill Help?

I tested the literal simple rule:

minutes_share_i ∝ softmax(alpha × player_skill_i)

The benchmark is clean: - Learn player skill from observed NBA stints/segments. - Use 2024-2025 for train/dev and 2025-2026 as the held-out test season. - Predict game outcomes from pregame player skill aggregated with a pregame minutes rule.

Verdict

Pure skill softmax did not help on net.

Best full-roster pure skill softmax: log loss 0.695316
Best full-roster usage softmax: log loss 0.660003
Best candidate-roster pure skill softmax: log loss 0.685676
Best candidate-roster usage softmax: log loss 0.659472

What Actually Helped

A simple pregame rotation-candidate filter helped more than skill weighting did.

Candidate rule: keep players with prior team minutes share at least 1%; if fewer than 5 qualify, fall back to the top 8 by prior share / start rate / skill.
That candidate filter retained about 96.7% of actual team minutes on average.
On that filtered pool, the best usage-only softmax beat the best pure skill softmax (0.659472 vs 0.685676).

Did A Small Skill Term Help Once Usage Was In The Model?

No. The broad dev-selected usage + skill variant still lost to usage-only on test, and when I tightened the sweep around the better candidate usage family the best test result was exactly alpha=0.

Best candidate usage + skill variant: log loss 0.662112 with skill_alpha=0.050
Best candidate usage-only variant: log loss 0.659472
In the near-zero check with usage=1, the best test point was alpha=0.000 with log loss 0.659472

Read

If the question is strictly whether pregame minutes should be softmax proportional to player skill, the answer from this NBA holdout is no. The useful signal came from identifying the plausible rotation first, then letting rolling usage history do most of the work.