Spatial performance analysis in basketball with CART, random forest and extremely randomized trees

This paper proposes tools for spatial performance analysis in basketball. In detail, we aim at representing maps of the court visualizing areas with different levels of scoring probability of the analysed player or team. To do that, we propose the adoption of algorithmic modeling techniques. Firstly, following previous studies, we examine CART, highlighting strengths and weaknesses. With respect to what done in the past, here we propose the use of polar coordinates, which are more consistent with the basketball court geometry. In order to overcome CART's drawbacks while maintaining its points of force, we propose to resort to CART-based ensemble learning algorithms, namely to Random Forest and Extremely Randomized Trees, which are shown to be able to give excellent results in terms of interpretation and robustness. Finally, an index is defined in order to measure the map's graphical goodness, which can be used-jointly with measures of the out-of-sample error-to tune the algorithm's parameters. The functioning of the proposed approaches is shown by the analysis of real data of the NBA regular season 2020/2021.