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

 P: 47 Hi! The Red Sox just finished an 11-game 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
 Sci Advisor HW Helper 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 11-game winning streak in 162 games is about 7%.
 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 11-game streak. That dosen't sound like it will work. ACG