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Thread: Comparing tallies of win streaks of different lengths

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    Comparing tallies of win streaks of different lengths




    I'm not sure of the correct terminology for explaining my question, so please bear with me.

    Suppose I have a random event with a binary outcome (win/lose) and I have a set of data showing how many times win streaks of various lengths occurred:
    Code: 
    #Wins   0    1    2    3    4    5   6   7   8   9  10  11  12  13  14
    Tally  59   36   30   18   12    4   7   4   5   6   2   0   3   1   2
    Exp   53.5 38.3 27.5 19.7 14.1 10.1 7.3 5.2 3.7 2.7 1.9 1.4 1.0 0.7 0.5
    
    The third line is the expected number of times each streak should have occurred based on the total number of games played (668) and wins (479) yielding a winning % of 71.7%.

    I would like to calculate a 4th line showing the probability of each tally given the total number of games played and the win%. For example, what are the odds that there would be 59 0-win streaks, 36 1-win streaks, 30 2-win streaks, etc.?

    Can someone help me with the correct formula? I think it has something to do with normal distributions and the distance from the mean, but my statistics skills are not up to the task.

    Thanks...

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    Re: Comparing tallies of win streaks of different lengths

    What are you hoping to learn from the numbers you want to calculate? I think there is probably a better approach to what I think you're trying to get at but it's hard to say without you explaining more what your actual goal is.
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    Re: Comparing tallies of win streaks of different lengths


    Quote Originally Posted by Dason View Post
    What are you hoping to learn from the numbers you want to calculate? I think there is probably a better approach to what I think you're trying to get at but it's hard to say without you explaining more what your actual goal is.
    My immediate goal is just to be able to compare the tallies. I'd like some measure of how "far off" each tally is from the expected value. A secondary goal is to learn a little more about statistics.

    The Error line shows the absolute difference between the actual and expected tallies. I'd like to be able to calculate the relative differences so that I can rank the errors from low to high. For example, how does an error of +2.5 on a tally of 30 for 2-win streaks compare with an error of +5.5 on a tally of 59 for 0-win streaks?

    It occurred to me that I can divide the absolute error by the expected tally.



    Does this provide a reasonable relative measure of the various errors? Is an error of +5.5 on a tally of 59 for 0-win streaks really slightly greater than an error of +2.5 on a tally of 30 for 2-win streaks (+10.3% vs +9.1%)?

    And is the +2.5 error for the 2-win streaks slightly greater on the plus side than the -1.7 error for the 3-win streaks is on the negative side (+9.1% vs -8.6%)?
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