# Thread: Confidence level based on number of games and probability

1. ## 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.

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:

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?

3. ## 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.

4. ## Re: Confidence level based on number of games and probability

Thanks I will have a look

5. ## 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.

6. ## Re: Confidence level based on number of games and probability

Originally Posted by stans
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?

7. ## 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.