A causality-inspired plus-minus model for player evaluation in team sports

Abstract

We present a causality-inspired adjusted plus-minus model for evaluating individual players from their performance on a team. We take an explicitly causal approach to this problem, defining the value of a player to be the expected change in the score had we substituted the player for one who has zero value. (This quantity is “causal” in the sense that it is an inference about a hypothetical intervention.) We adapt recent ideas of factor modeling to handle the indirectly measured confounding in estimating player values, considering each player to be a “treatment” who contributes to the outcome of the game. We demonstrate the behavior of the model on data about soccer and basketball.