Probability of Winning

[IniquiTrance]

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?

 

[mathman]

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?

 

[IniquiTrance]

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?

 

[mathman]

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?

 

[IniquiTrance]

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??

 

[mathman]

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.