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from I - Baseball
Introduction
In baseball, a player can gain instant fame by duplicating or exceeding one of the fabled types of batting streaks. The most well known is Joe DiMaggio's (1941) streak of hitting in 56 consecutive games. There are also other batting streaks such as Ted Williams' (1949) 84-game consecutive on-base streak, Joe Sewell's (1929) 115-game streak of not striking out in a game, and the 8-game streak of hitting at least one home run in each game, held by three players. Other streaks include most consecutive plate appearances with a hit (the record is 12 held by Walt Dropo (1952)), most consecutive plate appearances getting on-base (the record is 16 held by Ted Williams (1957)), and the most consecutive plate appearances with a walk (the record is seven held by five players).
In this paper, we present two functions to calculate the probability of a player duplicating a hitting streak. One is recursive; the other is a new piecewise function that calculates the probability directly.
We use them to compare the difficulty of duplicating different streaks, in particular, the 56-game consecutive hitting streak and the 84-game consecutive on-base streak.
Our results can be applied to streaks outside of baseball.
A recursive function to calculate the probability of a player having a 56-game hitting streak at some point in a season
Michael Freiman [1] gives a recursive function, R(n), to calculate the probability of a player having a 56-game hitting streak at some point in the season.
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