Home Modeling spatial batting ability using a known covariance matrix
Article
Licensed
Unlicensed Requires Authentication

Modeling spatial batting ability using a known covariance matrix

  • Jared Cross and Dana Sylvan EMAIL logo
Published/Copyright: May 12, 2015

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.


Corresponding author: Dana Sylvan, Hunter College of the City University of New York – Mathematics and Statistics, New York, NY, USA, e-mail:

Acknowledgments

We wish to thank the Editor-in-Chief, Associate Editor and two anonymous reviewers for their constructive suggestions that helped improve the presentation of this paper.

References

Albert, J. 2014. “Beyond Run Expectancy.” Technical Report, Bowling Green State University.Search in Google Scholar

Baumer, B. and D. Draghicescu. 2010. “Mapping Batter Ability in Baseball by Using Spatial Statistics Techniques.” JSM, American Statistical Association 3811–3822.Search in Google Scholar

Birnbaum, P. 2011. “The Tango Method of Regression to the Mean.” URL: http://blog.philbirnbaum.com/2011/08/tango-method-of-regression-to-mean-kind.html (accessed April, 2015).Search in Google Scholar

Buchan, G. 2014. “Expanded 2013 wOBA Projections Comparison.” URL: http://blog.rotovalue.com/expanded-2013-woba-projections-comparison/ (accessed April, 2015).Search in Google Scholar

Chilès, J. and P. Delfiner. 1999. Geostatistics. Modeling Spatial Uncertainty. Hoboken, New Jersey: John Wiley & Sons, Inc.Search in Google Scholar

Fast, M. 2010. “What the Heck is PITCHf/x?” The Hardball Times Baseball Annual 2010. URL: http://baseball.physics.illinois.edu/FastPFXGuide.pdf (accessed April, 2015).Search in Google Scholar

Fast, M. 2011. “Can We Predict Hot and Cold Zones for Hitters?” Baseball Prospectus. URL: http://www.baseballprospectus.com/article.php?articleid=15363 (accessed April, 2015).Search in Google Scholar

Furrer, R., D. Nychka, and S. Sain. 2012. “Fields: Tools for Spatial Data.” URL: http://CRAN.R-project.org/package=fields, r package version 6.7 (accessed April, 2015).Search in Google Scholar

Gelman, A. 2014. “A World without Statistics.” Signficance 11:47.Search in Google Scholar

James, B. 1987. Bill James Presents The Great American Baseball Stat Book. New York, New York: Ballantine Books.Search in Google Scholar

Kaat, J. 2004. “Technology in the Dugout.” Popular Mechanics 181:122–125.Search in Google Scholar

Lindsey, G. R. 1963. “An Investigation of Strategies in Baseball.” Operations Research 11:477–501.10.1287/opre.11.4.477Search in Google Scholar

Marchi, M. and J. Albert. 2014. Analyzing Baseball Data with R. Boca Raton, Florida: CRC Press.Search in Google Scholar

Mills, B. 2011. “Maximizing Sabermetric Visual Content: Smooth Comparisons and Leveraging Color.” Prince of Slides. URL: http://princeofslides.blogspot.com/2011/10/maximizing-sabermetric-visual-content.html (accessed April, 2015).Search in Google Scholar

MLBAM. 2014. “MLBAM Gameday.” URL: http://gd2.mlb.com/components/game/mlb (accessed April, 2015).Search in Google Scholar

Pankin, M. D. 1987. “Baseball as a Markov Chain.” Technical Report.Search in Google Scholar

Petti, B. 2015. “How Teams can Get the Most out of Analytics.” The Hardball Times. URL: http://www.hardballtimes.com/how-teams-can-get-the-most-out-of-analytics/ (accessed April, 2015).Search in Google Scholar

R Core Team. 2013. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. URL: http://www.R-project.org/ (accessed April, 2015).Search in Google Scholar

Reich, B. J., J. S. Hodges, B. P. Carlin, and A. M. Reich. 2006. “A Spatial Analysis of Basketball Shot Chart Data.” The American Statistician 60:3–12.10.1198/000313006X90305Search in Google Scholar

Roegele, J. 2013a. “The Living Strike Zone.” Baseball Prospectus. URL: http://www.baseballprospectus.com/article.php?articleid=21262 (accessed April, 2015).Search in Google Scholar

Roegele, J. 2013b. “A Simple Strike Zone Formula and Calculating Plate Discipline Stats.” Beyond the Box Score. URL: http://www.beyondtheboxscore.com/2013/8/5/4576622/simple-strike-zone-formula-calculating-plate-discipline-stats-pitchfx-sabermetrics (accessed April, 2015).Search in Google Scholar

Sheehan, J. 2008. “More Run Values.” URL: http://baseballanalysts.com/archives/2008/02/ (accessed April, 2015).Search in Google Scholar

Shortridge, A., K. Goldsberry, and M. Adams. 2014. “Creating Space to Shoot: Quantifying Spatial Relative Field Goal Efficiency in Basketball.” Journal of Quantitative Analysis in Sports 10:303–313.10.1515/jqas-2013-0094Search in Google Scholar

Superak, H. M. 2011. “Analyzing Batting Patterns of Major League Baseball Players For Advance Scouting Reports: Using R to Generate High-Level Spatial Plots of PITCHf/x Data.” Master’s Thesis, Rollins School of Public Health.Search in Google Scholar

Thorn, J. and P. Palmer. 1985. The Hidden Game of Baseball. New York, New York: Doubleday.Search in Google Scholar

Wilcox, A. and E. Mannshardt. 2013. “Baseball Scouting Reports Via a Marked Point Process for Pitch Types.” New England Symposium on Statistics.Search in Google Scholar

Published Online: 2015-5-12
Published in Print: 2015-9-1

©2015 by De Gruyter

Downloaded on 29.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/jqas-2014-0089/html
Scroll to top button