by David Rockoff and Philip Yates
On March 30, 2008, Samuel Arbesman and Steven Strogatz had their article "A Journey to Baseball's Alternate Universe" published in The New York Times. They simulated baseball's entire history 10,000 times to ask how likely it was for anyone in baseball history to achieve a streak that is at least as long as Joe DiMaggio's hitting streak of 56 in 1941. Arbesman and Strogatz treated a player's at bats per game as a constant across all games in a season, which greatly overestimates the probability of long streaks. Our simulation will treat at-bats in a game as a random variable. For each player in each season, we will bootstrap the number of at-bats for each simulated game. Each at bat will be treated as a Bernoulli random variable, with the probability of success being equal to that player's batting average for that season.
David Rockoff is currently pursuing a Ph.D. in Statistics at Iowa State University. He received his Masters in Statistics from the University of Vermont. His statistical research interests include sports, genetics, and survey research. David is a member of SABR as well as the ASA's Section on Statistics in Sports.
Philip Yates is an assistant professor in the department of Mathematics and Statistics at California State Polytechnic University, Pomona. He received his Ph.D. in Statistics from the University of South Carolina, his M.S. in Biostatistics from the University of Vermont, and his B.S. in Mathematical Sciences from DePaul University. His current research includes statistical applications in environmental science, hydrology, political science, and sports.