Chasing DiMaggio: Streaks in Simulated Seasons Using Non-Constant At-Bats

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. The simulations in this paper treated at-bats in a game as a random variable. For each player in each season, the number of at-bats for each simulated game was bootstrapped. The number of hits for player i in season j in game k is a binomial random variable with the number of trials being equal to the number of at bats the player gets in game k and the probability of success being equal to that player's batting average for that season. The result of using non-constant at-bats in the simulation was a decrease in the percentage of the baseball histories to see a hitting streak of at least 56 games from 42% (Arbesman and Strogatz) to approximately 2.5%.