Probability ranking is a new, more meaningful way to rank countries in the Olympic Games while adjusting for population.  It promises to make the Olympic competition more exciting and interesting at the national level.  Unlike simple medal-counts, which are always topped by the largest-population countries, or Olympic medals-per-capita rankings, which are invariably topped by the smallest-population medal-winners, probability ranking highlights the best performers across the wide range of national populations.  It does this by ranking according to the Probability Index U, which has a simple meaning: 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 medal-winning capabilities.

The method was originally published in the Journal of Sports Analytics at Population-adjusted National Rankings in the Olympics. For more information about the underlying statistics see Math Details.

 

During the Paris Games, probability ranking was reported in The New York Times and  The Guardian UK/US/Australia, and in many other news media worldwide , with especially high interest in Australia and New Zealand. 

Listed below are the Final / Day 16 Olympic rankings through 6:00 PM Paris time (CET) August 11.  Note that the column labeled "Medals Behind Leader" does not increase in a simple additive way with higher ranks because these numbers depend upon national populations, not just upon differences in medal counts. Details about how these rankings were calculated are given on the Math Details page which also explains the meaning of U_T .  Also shown below is the Top 30 probability ranking progression for the Paris Olympics.