Estimation of NBA players' offense/defense ratings through shrinkage estimation

The standard plus/minus model for rating NBA players combines the offensive and defensive capabilities of each player into a single metric. While this is convenient for the sake of summary, it makes it difficult to isolate the particular contributions that a player makes to either effort. Although adjusted plus/minus and other methods are proposed to address this, given a relatively large number of players against the number of events observed in one season, estimates are subjected to high variance. To correct for this, we construct a penalized regression model that identifies the specific offensive and defensive contributions of each player on each possession, and tune the model using L2-regularization method to optimize its predictive power. It overcomes the limitations of simple and adjusted plus/minus by incorporating offensive and defensive effects separately, and the shrinkage term controls for high variance of the estimates. Furthermore, our model captures net home court advantage on offense, and estimate players’ contributions in offense and defense. Finally, we demonstrate application of our method by simulating unseen matches to correctly predict their outcomes.