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I'm trying to apply statistical methods to some data I've collected from cybersport match outcomes. For each team, I have the number of games they've played as well as their win-rate. This win-rate calculation is straightforward except the fact that draw counts as 0,5 of win so you can see team played 3 matches and has 50% win-rate (win, loss, draw). What I want is to identify teams whose performance is definitely higher than 50%. F.e. if the team played once and won this is not so reliable as a team who played 20 times and won 70%. So I've decided to test the hypothesis that Win-rate is equal to 50% but I'm struggling which test should I use. 2 things I have to notice: 1) Number of games in most cases is less than 10, so I'm not sure if I have to adjust SD somehow 2) I do understand that I can manually calculate probabilities for Bernoulli trials but if you know any Excel formula to calculate p-values without this - it will be highly appreciated.

Many thanks in advance!

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You want to use this binomial testing with:

  1. Null hypothesis: chance of win is 50%
  2. Alternative hypothesis: chance of win is greater than 50% (one-tail greater)

But you have multiple teams where you look for difference which might lead to family-wise errors in a sequential testing (you may read about this from this multiple correction article, but the basic idea is this: in one test probability of having an error is x, but when you have n test, this x error might be in any of the n testing thus, leading to a situation where you might find the difference when there is none).

This might be corrected with a Holm-Bonferroni method or a Holm-Sidak method, but you may require some additional software to not caltulate this by your hand.

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  • $\begingroup$ Thanks Ewynn, you've helped a lot. Actually, I wanted to ask about Bonferroni adjustment as the third point but decided that my initial question is too basic to touch such topics. Thanks once again! $\endgroup$
    – user54060
    Feb 6, 2020 at 16:01

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