Integration of model-based recursive partitioning with bias reduction estimation: a case study assessing the impact of Oliver's four factors on the probability of winning a basketball game.

In this contribution, we investigate the importance of Oliver's Four Factors, proposed in the literature to identify a basketball team's strengths and weaknesses in terms of shooting, turnovers, rebounding and free throws, as success drivers of a basketball game. In order to investigate the role of each factor in the success of a team in a match, we applied the MOdel-Based recursive partitioning (MOB) algorithm to real data concerning 19,138 matches of 16 National Basketball Association (NBA) regular seasons (from 2004-2005 to 2019-2020). MOB, instead of fitting one global Generalized Linear Model (GLM) to all observations, partitions the observations according to selected partitioning variables and estimates several ad hoc local GLMs for subgroups of observations. The manuscript's aim is twofold: (1) in order to deal with (quasi) separation problems leading to convergence problems in the numerical solution of Maximum Likelihood (ML) estimation in MOB, we propose a methodological extension of GLM-based recursive partitioning from standard ML estimation to bias-reduced (BR) estimation; and (2) we apply the BR-based GLM trees to basketball analytics. The results show models very easy to interpret that can provide useful support to coaching staff's decisions. Supplementary Information: The online version contains supplementary material available at 10.1007/s10182-022-00456-6.

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.