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Joe DiMaggio's Streak

Journey to Baseball's Alternate Universe
Samual Arbesman and Steven Strogatz
Op-Ed, March 30, 2008

In 1941 Joe DiMaggio had a 56-game hitting streak. The authors used simulation to estimate the probability that in the history of baseball a player has a streak of 56 or more hits. By history of baseball the authors mean since 1871 when the first professional baseball league, the National Association of Professional Base Ball Players, was established. They used baseball data from 1871 to 2005 available, for example, from here

For every player and every season played they simulated the player getting a hit or not using the batting average as the probability of getting a hit each time at bat. Then they recorded the longest streak for each each season the player played. They repeat this 10,000 times and take the average of the longest streaks as an estimate of the longest streak a player would have in a season.