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

  • Context: Graduate 
  • Thread starter Thread starter ACG
  • Start date Start date
  • Tags Tags
    Baseball Length
Click For Summary

Discussion Overview

The discussion revolves around the expected length of the longest winning streak in a 162-game baseball season, particularly for a team with a .500 win-loss record. Participants explore the mathematical modeling of winning streaks in relation to independent probabilities, drawing parallels to coin flips.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant questions the frequency of long winning streaks, specifically asking about the expected value of the longest winning streak for a .500 team over a season.
  • Another participant proposes a method for estimating the probability of achieving a winning streak of length k in n games, suggesting that there are approximately (n - k + 1) independent chances with a probability of 1/2^k.
  • A later reply challenges the assumption of independence in the proposed model, noting that the outcome of one game affects the potential for previous games to contribute to a winning streak.
  • Further clarification is provided on how the probabilities should be adjusted based on the outcomes of specific games, indicating a nuanced understanding of the dependencies involved.

Areas of Agreement / Disagreement

Participants express differing views on the independence of game outcomes and the implications for calculating probabilities, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion highlights limitations in the assumptions made about independence and the mathematical modeling of winning streaks, which may affect the accuracy of the proposed estimates.

ACG
Messages
46
Reaction score
0
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
 
Physics news on Phys.org
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%.
 
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 doesn't sound like it will work.

ACG
 
ACG said:
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 doesn't sound like it will work.

So in that case you overstate the probability of #2 to #11 by 1/2^11 (1/2^11 rather than 0). But if you know that the 11th game is a win, then you're understating the probability of #2 to #11 by 1/2^11 (1/2^11 rather than 1/2^10). So I don't think it's actually a problem!
 

Similar threads

High School Creating a Board game and finding the Prob. of Winning
  • · Replies 2 ·
Replies
2
Views
6K
Expectation Value- Mean Time to Failure
  • · Replies 8 ·
Replies
8
Views
2K
Which Strategy Maximizes Expected Reward in a Paper-Picking Game?
  • · Replies 5 ·
Replies
5
Views
3K
Physicist's block ? Is it too late for me to pursue physics?
  • · Replies 8 ·
Replies
8
Views
5K