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Mathematical Details

A full discussion of probability ranking is given in the Journal of Sports Analytics, in a paper that was published on July 12, 2024 after careful review by statisticians.   This paper, Population-adjusted national rankings in the Olympics along with a short Addendum containing additional helpful information, can be read below, or downloaded in pdf form here:

We have also written a discussion of the "Olympic Medal Distribution" which contains important validating information.  Anyone who believes that medals-per-capita is the only correct way to do population-adjusted ranking should take a few minutes to read it here:

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