A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes

Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this paper, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called <i>expected possession value</i> (EPV), derives from a stochastic process model for the evolution of a basketball possession. We model this process at multiple levels of resolution, differentiating between continuous, infinitesimal movements of players, and discrete events such as shot attempts and turnovers. Transition kernels are estimated using hierarchical spatiotemporal models that share information across players while remaining computationally tractable on very large data sets. In addition to estimating EPV, these models reveal novel insights on players’ decision-making tendencies as a function of their spatial strategy. In supplementary material, we provide a data sample and R code for further exploration of our model and its results.

篮球比赛在时空维度中持续演进，球员始终与队友、对手以及篮球进行交互。然而，当前针对篮球比赛结果的分析往往依赖于离散化的比赛摘要，将这类交互简化为得分、助攻等类似事件的统计汇总。本文提出了一种基于光学球员追踪数据的框架，可实时估算进攻回合结束时所能获得的预期得分。该指标被称为预期进攻回合价值（expected possession value, EPV），其源自描述篮球进攻回合演进的随机过程模型。我们从多分辨率维度对该过程进行建模，区分球员连续且微尺度的移动，以及投篮出手、失误等离散事件。我们采用分层时空模型估算转移核函数，该模型可在球员间共享信息，同时在超大规模数据集上仍保持计算可行性。除了估算EPV之外，这些模型还能揭示球员基于空间策略的决策倾向相关的全新见解。在补充材料中，我们提供了数据集样本与R代码，以供读者进一步探究本文所提出的模型及其分析结果。