Mathematical Details

The new rankings are based upon the Population- Adjusted Probability Index U, a number that quantifies the degree to which a country's Olympic performance gives evidence for medal-winning capability.  Specifically, U measures the improbability that a country of a given population would win as many medals as it has, or more medals, if all people in competitive countries worldwide had equal sports capabilities.

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: