IMPACT

Impact is a box-priored regularized adjusted plus-minus. The game is divided into stints, the intervals during which the ten players on the floor do not change.

Each stint is one row, recording which five players were on each side and the scoring margin over the possessions counted in it. Possessions are counted from the play-by-play as FGA + 0.44·FTA + TOV − OREB; a stint whose possessions cannot be counted is dropped rather than estimated from the clock. The solver then finds the coefficients that best explain every stint at once, and a player separates from his context because he appears alongside many teammates and against many opponents. Rows are weighted by possessions, and in multi-season windows by a decay of 0.5^(n/1.3).

Ridge regularization at α = 3000 pulls every coefficient toward its prior in proportion to how few possessions support it, which stops a small sample from producing an extreme rating.

That prior is not zero. The target is the stint margin less 0.25 times the on-court OBPM/DBPM difference, and the same quarter of a player’s own box rating is added back to his coefficient afterwards, so a player with few possessions is drawn toward what his box production predicts rather than toward average. The prior does not dominate: its term carries a standard deviation of 0.73 against Impact’s 2.02, and shipped Impact correlates 0.96 with the same solve run without it. Defence additionally carries a team-season fixed effect at a looser penalty, so scheme is absorbed by the team column before it is charged to whoever was on the floor.