A Statistical Model of Serve Return Impact Patterns in Professional Tennis

The spread in the use of tracking systems in sport has made fine-grained spatiotemporal analysis a primary focus of an emerging sports analytics industry. Recently publicized tracking data for men's professional tennis allows for the first detailed spatial analysis of return impact. Mixture models are an appealing model-based framework for spatial analysis in sport, where latent variable discovery is often of primary interest. Although finite mixture models have the advantages of interpretability and scalability, most implementations assume standard parametric distributions for outcomes conditioned on latent variables. In this paper, we present a more flexible alternative that allows the latent conditional distribution to be a mixed member of finite Gaussian mixtures. Our model was motivated by our efforts to describe common styles of return impact location of professional tennis players and is the reason we name the approach a 'latent style allocation' model. In a fully Bayesian implementation, we apply the model to 142,803 return points played by 141 top players at Association of Tennis Professional events between 2018 and 2020 and show that the latent style allocation improves predictive performance over a finite Gaussian mixture model and identifies six unique impact styles on the first and second serve return.