## Senior Independent Study Theses

#### Abstract

In baseball, teams are faced with a difficult dilemma every day: given a set of nine players, find the optimal sequence in which they should bat (Sokol 353). An optimal batting order is that which produces the most runs and/or greatest number of wins. In this study, the optimal batting order for the 2008 College of Wooster Fighting Scots softball team for the 2008 season was calculated and analyzed. The optimal order was determined using statistical analysis and computer simulation. Statistical analysis was performed by collecting and analyzing data from the Wooster Softball archive. Using the archives' play-by-plays and box scores, thirty-eight statistics were evaluated for all nine Wooster players. These statistics were then entered into a computer program, designed and executed in MATLAB, which simulated a regulation softball game. Using the computer simulation and a random play generator, the program ran 10,000 simulated games for each hundreds of batting orders. After 10,000 simulations, the top ten batting orders, as well as bottom ten batting orders, were determined based on average runs per game. After analyzing the top ten and bottom ten orders, these twenty batting lineups were run through the program an additional fifty times, totaling 500,000 games per lineup, to ensure consistency. From these 500,000 games, the optimal batting order was determined. This optimal order was then compared to the line-up regularly used during the 2008 season. Significant differences in player positioning within the lineup was exhibited. In addition, this study also analyzed differences in winning percentage between the commonly used and optimal batting order, using a Pythagorean expectation formula. Overall, the optimal batting order increased the 2008 softball teams win total by three games. Lastly, comparisons were made between softball coaches' typical game strategy and the strategy employed using mathematical modeling.

Pasteur, R. Drew

Mathematics

#### Disciplines

Applied Mathematics

2010

Bachelor of Arts

#### Document Type

Senior Independent Study Thesis

COinS