Understanding Probability of Winning in Sports: 8 Wins, 6 Losses, and 7 Streaks

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Discussion Overview

The discussion revolves around the probability of winning in sports, specifically analyzing a team's record of 8 wins and 6 losses, and how this relates to the occurrence of winning streaks. Participants explore the implications of a specific sequence of wins and losses on the perceived probability of winning over time.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the probability of wins occurring over 7 winning streaks is 1/429, questioning the implications of this on the team's changing probability of winning over time.
  • Others argue that it does not necessarily follow that the probability of winning changes based on the sequence of wins and losses, challenging the assumption that the outcome indicates a changing probability.
  • A participant calculates the number of ways to achieve 7 winning streaks given the team's record, suggesting that the probability of winning does change based on the sequence of games played.
  • Some participants seek to clarify whether the question pertains to the probability of future outcomes based on known past results, and how this relates to the constancy of winning probabilities throughout the season.
  • One participant emphasizes that without additional information, such as injuries or other influencing factors, there is no reason to assume that probabilities should change over the course of the season.

Areas of Agreement / Disagreement

Participants express differing views on whether the probability of winning changes over time based on the sequence of wins and losses. There is no consensus on this matter, as some argue for changing probabilities while others maintain that probabilities remain constant without external influences.

Contextual Notes

The discussion includes assumptions about the nature of probability in sports outcomes and the implications of specific sequences of wins and losses. There is an unresolved debate regarding the conditions under which probabilities may be considered constant or variable.

IniquiTrance
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If a team has a season record of 8 wins, and 6 losses, then the probability of those wins having occurred over 7 winning streaks is:

1/429

Why does it follow then, that if the outcome was:

WLWLWLWLWWLWLW

then we can conclude automatically that the team's probability of winning was changing over time?
 
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IniquiTrance said:
If a team has a season record of 8 wins, and 6 losses, then the probability of those wins having occurred over 7 winning streaks is:

1/429

Why does it follow then, that if the outcome was:

WLWLWLWLWWLWLW

then we can conclude automatically that the team's probability of winning was changing over time?

As far as I'm concerned, it doesn't follow. Where did you get the idea that it does?
 
mathman said:
As far as I'm concerned, it doesn't follow. Where did you get the idea that it does?

Given 7 winning runs, there are:

(7C7)(7C6) = 7 possible ways of having 7 winning streaks, given 8 wins and 6 losses.

I can see that the probability is changing, since say if this happened:

WLWLWLWLWWLWLW

Then game 1 must be a Win, so probability 1.

Game 2 is a win in 1/7 of the possible ways of having a 7 run winning streak, given the above.

game 3 is a win in 6/7 of the outcomes... and so on.

So it seems that the probability is changing.

In what arrangement would the probability be changing less over time, or more over time?
 
Can your question be described as follows. You know in advance the team's final won loss record. Then you are asking what the probability of future outcome would be if you also know what happened partway through?
 
mathman said:
Can your question be described as follows. You know in advance the team's final won loss record. Then you are asking what the probability of future outcome would be if you also know what happened partway through?

Hmm, I'm asking whether during any particular game in the past season, the team's probability of winning was different than during a previous one. i.e., if the probability was changing throughout the season..

Also, in what situation (how many win runs) could we conclude the probability remained constant given m wins, n losses? Such as if we flipped a fair coin (m+n) times, and m = heads, and n = tails??
 
I think you should clarify the problem for yourself. The result of a season's play is a specific realization of probable outcomes. Unless you have other information, like a player broke his leg, there is no reason for probabilities to change.
 

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