Modeling spatial batting ability using a known covariance matrix

Cross Jared and Sylvan Dana ()
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Cross Jared: Hunter College of the City University of New York – Mathematics and Statistics, New York, NY, USA
Sylvan Dana: Hunter College of the City University of New York – Mathematics and Statistics, New York, NY, USA

Journal of Quantitative Analysis in Sports, 2015, vol. 11, issue 3, 155-167

Abstract: In baseball, heat maps, which visualize a batter’s ability across regions in and around the strike zone, play an important role in baseball commentary and scouting reports. We represent the stochastic process underlying these heat maps as a spatial Gaussian field with isotropic covariance. Spatial interpolation (kriging) relies on the assumption of a known covariance function, but in reality the parameters of the covariance are typically estimated from the data. Our simulation study, based on a known covariance function, helps to understand and explain the spatial dependence of the process and allows us to produce improved heat maps.

Keywords: baseball; heat maps; Monte Carlo simulations; random fields; spatial interpolation (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/jqas-2014-0089

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