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Expected length of longest winning streak in a 162game baseball season 
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#1
Apr2909, 08:17 AM

P: 47

Hi!
The Red Sox just finished an 11game winning streak, which made me wonder. Do most teams experience winning streaks this long over the course of a season? What is the expected value of the length of the longest winning streak for a .500 team over the course of a season? In general: if you flip a coin N times with a probability of getting a head of P, what is the expected length of the longest series of consecutive heads embedded in the results of the N flips? ACG 


#2
Apr2909, 08:51 AM

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P: 3,684

To a good first approximation, there are (n  k + 1) independent chances with probability 1/2^k each to get a winning streak of length k in n games. (Of course they're not independent at all, but it's close enough.)
So the chance of getting an 11game winning streak in 162 games is about 7%. 


#3
Apr2909, 09:06 AM

P: 47

Correct. However, as you know they're far from independent. If game 11 is a loss (50% chance) then there's no way for the set of games ranging from 2 to 11 to be the start of an 11game streak. That dosen't sound like it will work.
ACG 


#4
Apr2909, 11:37 AM

Sci Advisor
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P: 3,684

Expected length of longest winning streak in a 162game baseball season



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