Analysis of Professional Basketball Field Goal Attempts via a Bayesian Matrix Clustering Approach

We propose a Bayesian nonparametric matrix clustering approach to analyze the latent heterogeneity structure in the shot selection data collected from professional basketball players in the National Basketball Association (NBA). The proposed method adopts a mixture of finite mixtures framework and fully uses the spatial information via a mixture of matrix normal distribution representation. We propose an efficient Markov chain Monte Carlo algorithm for posterior sampling that allows simultaneous inference on both the number of clusters and the cluster configurations. We also establish large-sample convergence properties for the posterior distribution. The compelling empirical performance of the proposed method is demonstrated via simulation studies and an application to shot chart data from selected players in the NBAs 2017–2018 regular season. Supplementary materials for this article are available online.

我们提出一种贝叶斯非参数（Bayesian nonparametric）矩阵聚类方法，用于分析从美国职业篮球联赛（National Basketball Association, NBA）职业篮球运动员处采集的投篮选择数据中的潜在异质性结构。所提方法采用有限混合的混合框架，并通过矩阵正态分布混合表示充分利用空间信息。我们提出一种高效的马尔可夫链蒙特卡洛（Markov chain Monte Carlo）算法用于后验采样，该算法可同时完成聚类数目与聚类配置的推断。此外，我们还建立了后验分布的大样本收敛性质。所提方法的优异实证性能通过模拟研究，以及对NBA 2017-2018赛季常规赛入选球员的投篮热图（shot chart）数据的应用得到验证。本文补充材料可在线获取。