Baseball probability calculator
Hitting Streaks
Given a batter’s success rate, number of games in the season, and desired streak length, compute the probability that the batter achieves such a hitting streak at some point during the season.
Success rate is the probability that the player will get a hit in any given game.
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The results assume that the player’s chance of getting a hit is the same in every game and is independent of what happens in other games. See About the Calculation below for details.
Each row gives the probability that a streak of at least the specified length has occurred by that point in the season.
About the calculation
The model assumes that the probability the player gets a hit in any given game is constant and that the results of different games are independent. A longer streak also counts: a 57-game streak, for example, includes a streak of at least 56 games.
The table shows the cumulative probability that a streak of the specified length has occurred within the first n games, for each relevant value of n through the end of the season.
Let p be the success rate, s the specified streak length, and z(n) the probability that such a streak has occurred within the first n games. If n is big enough (i.e. more than s), then upon the completion of game n, the event that a streak of sufficient length has occurred could happen in two ways:
- it had happened in the first n-1 games;
- it happens for the first time in the nth game; in other words the streak has just reached length s.
Thus:
- when n < s, z(n) = 0;
- when n = s, z(n) = ps;
- when n > s, z(n) = z(n − 1) + (1 − z(n − s − 1)) (1 − p) ps.
The final term represents a streak that reaches the specified length for the first time in game n: no earlier qualifying streak, followed by a hitless game and then s consecutive games with a hit.
This recurrence is equivalent to the method described in Michael Freiman's article “56-game hitting streaks revisited.” The Baseball Research Journal 31 (2002): 11-16.