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Some calculations

Posted By: Timothy Chow
Date: Friday, 28 August 2015, at 1:04 a.m.

In Response To: Just Wondering... (Timothy Chow)

I decided to model the PR of a top player as a gamma distribution with k = 7. So a player with an average PR of 3 will have a standard deviation of about 1.13 and a player with an average PR of 3.3 will have a standard deviation of about 1.25. I'm not sure what match length is needed to keep the variation in PR from match to match this low, but maybe a 5 point match is enough?

Anyway, if we make the simplifying assumption that the overall PR of a bunch of matches is just the average of the PRs of the individual matches, then with the above assumptions, the 3 PR player will have over a 70% chance of racking up a lower average PR than the 3.3 PR player after just 10 matches.

Further driving down the probability that the 3.3 PR player will "upset" the 3 PR player requires more matches of course. To make the better player an 80-20 favorite requires around 20 to 25 matches. To make the better player a 90-10 favorite requires around 50 matches.

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