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

In summary, the conversation discusses the concept of expected value of the length of the longest winning streak for a .500 team over the course of a season. The conversation also touches on the question of whether most teams have winning streaks as long as 11 games in a season and the probability of getting a winning streak of a certain length in a set number of games. It is determined that there are approximately (n - k + 1) independent chances with a probability of 1/2^k each for getting a winning streak of length k in n games. The probability of getting an 11-game winning streak in 162 games is about 7%, but this is affected by the dependence of the games. However, this is not
  • #1
ACG
46
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
 
Mathematics news on Phys.org
  • #2
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%.
 
  • #3
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
 
  • #4
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 dosen'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!
 

What is the expected length of the longest winning streak in a 162-game baseball season?

The expected length of the longest winning streak in a 162-game baseball season can vary depending on various factors such as team performance, player injuries, and strength of schedule. However, on average, the longest winning streak is typically around 10-12 games.

What is the likelihood of a team having a winning streak of 20 or more games in a 162-game baseball season?

The likelihood of a team having a winning streak of 20 or more games in a 162-game baseball season is very low. In fact, in the history of Major League Baseball, only two teams have achieved such a feat - the 1916 New York Giants and the 2017 Cleveland Indians.

How does the length of the longest winning streak in a 162-game baseball season compare to other major sports?

The length of the longest winning streak in a 162-game baseball season is relatively shorter compared to other major sports. For example, the longest winning streak in the NBA is 33 games, achieved by the 1971-1972 Los Angeles Lakers.

Can a team's winning streak in a 162-game baseball season affect their overall performance?

Yes, a team's winning streak in a 162-game baseball season can have a significant impact on their overall performance. A long winning streak can boost team morale and confidence, leading to improved performance in future games. However, a losing streak can also have a negative effect on a team's performance.

Are there any strategies or factors that can increase the likelihood of a long winning streak in a 162-game baseball season?

There are several strategies and factors that can increase the likelihood of a long winning streak in a 162-game baseball season. These include having a strong and healthy team, favorable strength of schedule, consistent pitching, and effective team chemistry. However, luck and chance also play a significant role in a team's winning streak.

Similar threads

  • Calculus and Beyond Homework Help
Replies
8
Views
1K
Replies
4
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
5K
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
  • Aerospace Engineering
Replies
2
Views
7K
Back
Top