Optimizing defensive alignments in baseball through integer programming and simulation

Abstract

Baseball is an incredibly complex game where the managers of the baseball teams have numerous decisions to make. The managers are in control of the offense and defense of a team. Some managers have ruined their teams’ chances of a victory by removing their star pitcher too soon in a game or leaving them in too long; managers also choose to pinch hit for batters or pinch run for base runners in order to set up a “favorable match-up” such as a left handed pitcher versus a right handed batter. This research’s goal is to aid managers by providing an optimal positioning of defensive players on the field for a particular batter. In baseball, every ball that is hit onto the field of play can be an out if the fielders are positioned correctly. By positioning the fielders in an optimal manner a team will directly reduce the number of runs that it gives up, which increases the chances of a win. This research describes an integer program that can determine the optimal location of defensive players. This integer program is based off of a random set of hits that the player has produced in the past. The integer program attempts to minimize the expected costs associated with each hit where the cost is defined by a penalty (single, double or triple) or benefit (out) of the person’s hit. By solving this integer program in Opl Studio 4.2, a commercial integer programming software, an optimal defensive positioning is derived for use against this batter. To test this defense against other standard defenses that teams in the MLB currently use, a simulation was created. This simulation uses Derek Jeter’s actual statistics; including his 2009 regular season hit chart. The simulation selects a hit at random according to his hit chart and determines the outcome of the hit (single, double, out, double play, etc.). Once this simulation is complete a printout shows the batter’s statistics; including his average and slugging percentage. VI By comparing the optimized defensive alignment with some commonly used major league alignments, it can be shown that this optimal alignment would decrease Jeter’s average by nearly 13% and decrease his slugging by 35%. It is my opinion that managers should use this tool to help them win more games. These defenses can be seamlessly implemented by any coach or team.