From Markov models to Poisson point processes: Modeling movement in the NBA

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Jacob Mortensen
Luke Bornn


Abstract: With the rise of optical tracking data, the ability to accurately model player movement has become a key competitive advantage in many sports. Analysis of this data presents a substantial challenge, due to both the scale of the data, which can consist of more than 100 million rows for a given season, and to the sophisticated methods required to make sense of it. Current approaches generally fall into two categories, black-box methods and Markov models, but both groups have clear shortcomings. Black-box methods have no clear interpretation while traditional Markov-based methods rely on restrictive assumptions about the nature of movement, limiting their capacity to represent complex movement patterns. In this work, we combine elements of traditional Markov approaches with tools from spatial statistics to develop a flexible nonparametric method which allows for complicated patterns of movement and incorporates the presence of meaningful spatial features (such as the three-point line), while remaining completely interpretable. Our key insight is that Markov transition densities can be estimated using a Poisson point process. In this paper we provide a brief overview of the connection between these two mathematical concepts and demonstrate how this relationship is useful in a variety of NBA applications.