A Bayesian two-stage framework for lineup-independent assessment of individual rebounding ability in the NBA

In basketball, traditional methods of assessing individual rebounding ability are problematic because they depend on all players present on the court rather than just on the player of interest. Although there exist modeling approaches to correct for this dependence, they are generally unsuitable for events with binary outcomes. In this paper, a Bayesian two-stage model is proposed to predict both individual and team rebound allocation. This approach makes it possible to identify players who help their team win the fight for rebounds, regardless of their individual rebounding totals. Although similar in flavor to the popular Adjusted Plus-Minus (APM) framework, the proposed strategy is different in that it does not assume that individual contributions are linearly additive on the response scale. Furthermore, the regularization approach is improved through rebounding-specific heuristics. A simulation study is performed to show the effectiveness of the proposed model, and the parameters are estimated using data from the 2020-21 NBA season. Predictions are then made for rebounding in the 2021-22 season. This study confirms that relying exclusively on individual rebounding rates could lead to the mis-evaluation of players' rebounding abilities.