Swing Shift: A Mathematical Approach to Defensive Positioning in Baseball

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Abstract

John M. Harris, Professor of Mathematics, Furman University
Elizabeth L. Bouzarth, Associate Professor of Mathematics, Furman University
Benjamin C. Grannan, Assistant Professor of Business and Accounting, Furman University
Andrew J. Hartley, Senior Mathematics Major, Furman University
Kevin R. Hutson, Professor of Mathematics, Furman University
Ella M. Morton, Senior Mathematics Major, Furman University

Abstract

Defensive repositioning strategies (shifts) have become more prevalent in Major League Baseball in recent years. In 2018, batters faced some form of the shift in 34% of their plate appearances. Most teams employ a shift that overloads one side of the infield and adjusts the positioning of the outfield. In this work we describe an integer-programming approach to the positioning of players over the entire field of play. The model uses historical data for individual batters, and it leaves open the possibility of fewer than four infielders. The model also incorporates risk penalties for positioning players too far from areas of the field in which extra-base hits are more likely. Our simulations show that an optimal positioning with three infielders lowered predicted batting average on balls in play (BABIP) by 5.9% for right-handers and by 10.3% for left-handers on average when compared to a standard four-infielder placement of players.

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