Space-Time VON CRAMM: Evaluating Decision-Making in Tennis with Variational generatiON of Complete Resolution Arcs via Mixture Modeling
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Sports tracking data are the high-resolution spatiotemporal observations of a competitive event. The growing collection of these data in professional sport allows us to address a fundamental problem of modern sport: how to attribute value to individual actions? Taking advantage of the smoothness of ball and player movement in tennis, we present a functional data framework for estimating expected shot value (ESV) in continuous time. Our approach is a three-step recipe: 1) a generative model for a full-resolution functional representation of ball and player trajectories using an infinite Bayesian Gaussian mixture model (GMM), 2) conditioning of the GMM on observed positional data, and 3) the prediction of shot outcomes given the functional encoding of a shot event. From the ESV we derive three metrics of central interest: value added with shot taking (VAST), Shot IQ, and value added with court coverage (VACC), which respectively attribute value to shot execution, shot selection and movement around the court. We rate player performance at the 2019 US Open on these advanced metrics and show how each adds a novel perspective to performance evaluation in tennis that goes beyond simple counts of outcomes by quantitatively assessing the decisions players make throughout a point.
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