That's the Second-Biggest Hitting Streak I've Ever Seen! Verifying Simulated Historical Extremes in Baseball

There is considerable interest in two consecutive game streak records in baseball, namely, the celebrated 56-game hitting streak of Joe DiMaggio and the less famous 84-games-reaching-base streak of Ted Williams, and how likely these records would be predicted to occur if the history of Major League Baseball were repeated. I strive to answer this question through simulated replication using a series of Bernoulli-type models. I assume that the number of games played by each player in each season is held constant while the batting and on-base averages are estimated from and shrunk towards the career trends of each player to smooth over outlying seasons. These simulation models are then verified against streaks that might be expected to occur, such as all-time streaks ranked 6 through 30, and are allowed to vary over time to reflect the changing distribution of opposing pitching. I find that a validated model for predicting hitting streaks contains no hot hand effect and suggests that the variability of opposing pitching has decreased markedly in the past 140 years. I also find that under this model, the DiMaggio streak can be considered exceptional while validated models for on-base streaks require considerably more complexity, including but not limited to a term that dampens on-base streaks.