# Thread: Best way to compare game results

1. ## Best way to compare game results

I have an Excel table containing game results (wins & losses). The results have been grouped according to "win streaks". The table has a column for each streak length (0 wins, 1 win, 2 wins, 3 wins, . . .).

Based on the actual tallies and the overall win % (total wins/total games), I have calculated the actual win%,the expected win%, and the expected tallies. Based on that, I have calculated the error in the tallies and the %s.

I would like a way to calculate some measure of the relative error so I can see by how much the actual tallies for each streak length differ from the expected. Intuitively, it seems like a good comparison would be the number of standard deviations from the mean each tally is. In the example below, I calculate mean and std dev for the two errors and use that to calculate the Z scores, which are identical.

Here's a sample table:

The problem is that I am not sure that the means and std devs are valid. While all of the data comes from the same 833 games, I worry that when I calculate separate tallies for each streak length, I have created separate populations, which would make the means meaningless. No?

Can someone tell me if the Z scores are valid measures of the relative magnitudes of the errors? For example, does the Z score for the 0-win streaks (1.83) mean that its tally (76) is almost 8 times farther from the mean (1.83/0.23) than the 1-win streaks?

If this is not valid, can someone point me to a valid measure and show me how to calculate it? Please try to speak slowly and use works of one or two syllables.

2. ## Re: Best way to compare game results

hi,
what is the goal of your work? Do you have any specific hypothesis to test?

By the looks of it, if you want to see whether there could be winning streaks longer then what pure chance would explain, you should use the chi-square test imo.

regards

3. ## Re: Best way to compare game results

Originally Posted by rogojel
hi,

what is the goal of your work? Do you have any specific hypothesis to test?

By the looks of it, if you want to see whether there could be winning streaks longer then what pure chance would explain, you should use the chi-square test imo.
It's just curiosity. I want a way to compare the errors for streaks of different lengths. I don't think I have a true/false hypothesis. I want to be able to rank order the streaks by the absolute magnitude of the error.

As I was looking over the data in writing this response, I noticed that the 4-win and 5-win streaks have exactly the same error (-0.74), at least to 2 decimal places. But since they are based on significantly different expected values (17.64 vs 12.64), I would expect the Z scores to also be quite different. They are not (-0.74).

I think this disqualifies these Z scores for what I want. So I calculated two new sets of Z scores based on the % errors. Row 17 contains the % errors of the tallies. Row 19 contains the % errors of the % errors.

Rows 18 & 20 contain the corresponding Z scores, which look much better. At least the Z scores for the 4-win and 5-win streaks are not identical.

Here's the new sample table:

Are these Z scores better measures of the relative errors?

4. ## Re: Best way to compare game results

It also occurred to me that even if these latest Z scores are good measures, the underlying Normal distributions on which they are based may not be. It is not possible to have negative tallies, so the Normal distribution is not symmetrical. This is probably not significant for the shorter win streaks where the tallies are large relative to the std dev. But for the longer win streaks, the expected tallies are much less than "1". Is there an Excel function that will allow me to specify a limit on one of the tails?

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