Bayesian Inference of Stochastic Pursuit Models from Basketball Tracking Data

In 2010, the National Basketball Association (NBA) began to install a camera system to track the positions of the players and the ball as a function of time. For the ball and for each of the 10 players on the court, the system records an (x,y) position 25 times per second. Ultimately, this wealth of data should enable us to answer a number of questions regarding basketball strategy that would have seemed intractable just a few years ago. To bring this vision to reality, we must develop new algorithms that can efficiently use the data for inference of appropriate models. In this work, we focus on so-called “fast break” situations where an offensive player races towards the basket in an attempt to score before the defensive team has time to set up their defense. In many such situations, it is relatively easy to identify from the data a runner and a chaser. This motivates the following question that is central to the present paper: using the NBA’s spatial tracking data, how can we infer a stochastic model for the chaser’s pursuit of the runner? To answer this question, we first formulate a stochastic version of the classical pursuit model. Our model consists of a set of coupled, nonlinear stochastic differential equations with time-dependent coefficients. To perform Bayesian inference for this stochastic model, we develop a Markov Chain Monte Carlo (MCMC) algorithm. The MCMC algorithm is derived using a Metropolis scheme; our innovation is to evaluate the log likelihood efficiently using a novel, deterministic method