The Optimal Positioning of Infielders in Baseball (UMAP)

When asked in the late 19th century to explain his success at the plate, baseball Hall-of-Famer "Wee Willie" Keeler responded quite simply, " . . . I hit 'em where they ain't." While we will always associate this famous quote with Keeler, it is the objective of all batters in the game of baseball to "hit 'em where they ain't." But who exactly are "they"? Evidently, "they" are the nine fielders on the opposing team. In each trip to the plate, a batter attempts to put the ball into play so that it will not be caught or otherwise intercepted by one of the opposing fielders. Conversely, it is the goal of the nine fielders to do just that-to catch or at least get their gloves on a batted ball. The fielders seek to position themselves so that their collective likelihood of reaching a batted ball is maximized. When facing a right-handed batter known to pull the ball down the third-base line, for instance, the fielders tend to shift to the left. Similarly, when a left-handed pull hitter steps to the plate, the fielders most likely shift to the right. We develop a mathematical model that uses elementary probability and calculus to determine the optimal positioning of each of the four infielders-the third baseman, the shortstop, the second baseman, and the first baseman-as a function of the distribution of the batter's hits.

Table of Contents:

INTRODUCTION

THE MODEL

OPTIMAL POSITIONING

ESTIMATING k

FURTHER ANALYSES

ABOUT THE AUTHORS