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Thread: Confidence level based on number of games and probability

  1. #1
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    Confidence level based on number of games and probability

    hi,

    I'm trying to find a way to calculate confidence level for my ELO rating based on number of games team has played.
    In the simplified table below you have a list of games between different teams with result, probability and number of games.


    Confidence level based on number of games and probability-conf12.jpg

    I grouped teams by number of games played.
    In this example I wanted to check confidence level for teams with exactly 30 games. Then I tried to find error based on simple calculation of Result - Probability.
    Then I calculated standard deviation and looked up confidence level from Z table:

    Confidence level based on number of games and probability-conf11.jpg



    Is this a correct way of finding confidence level based on number of games played? If not could somebody walk me through it step by step please?

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    Re: Confidence level based on number of games and probability

    any ideas please?
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    Re: Confidence level based on number of games and probability

    I posted a response to you several days ago but, for some reason, I am not seeing my response here. In short: the assumptions of the z-test or t-test are not satisfied in your data set. So you should calculate confidence intervals based on bootstrap. You can read a short description of bootstrap here: Bootstrap Sampling. For more detailed overview and properties, check the references therein.
    Last edited by stans; Nov 11th 2017 at 04:08 AM.
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    Re: Confidence level based on number of games and probability

    Thanks I will have a look
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    Re: Confidence level based on number of games and probability

    One more note: when working with binary variables (0 or 1), you have to be careful. Usually, they require special treatment and different types of tests.
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    Re: Confidence level based on number of games and probability

    Quote Originally Posted by stans View Post
    I posted a response to you several days ago but, for some reason, I am not seeing my response here. In short: the assumptions of the z-test or t-test are not satisfied in your data set. So you should calculate confidence intervals based on bootstrap. You can read a short description of bootstrap here: Bootstrap Sampling. For more detailed overview and properties, check the references therein.
    One more thing, what if my list was longer let's say 100 rows - would this method be correct?
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    Re: Confidence level based on number of games and probability

    No, unfortunately. 100 observations is enough to make slightly non-Gaussian variables into Gaussian averages (exploiting the Central Limit Theorem) but for binary variables many more observations is necessary... Also, your data are correlated over teams - one more violation of the z-test. Bootstrap would be better if properly implemented. It would take care of several issues automatically.

    The most user-friendly implementation of bootstrap is in SPSS. R and Matlab would be best tools if you were to customize the calculation.
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