  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.
