Population-adjusted national rankings in the Olympics

Abstract

Ranking countries in the Olympic Games by medal counts clearly favors large-population countries over small ones, while ranking by medals-per-capita produces national rankings with very small population countries on top. We discuss why this happens, and propose a new national ranking system for the Olympics, also based upon medals won, which is inclusive in the sense that countries of widely-varying population can achieve high rankings. This population-adjusted probability ranking ranks countries by how much evidence they show for high capability at Olympic sports. In particular, it ranks countries according to how improbable their medal counts would be in an idealized reference model of the Games which posits that all medal-winning nations have equal propensity per capita for winning medals. The ranking index U is defined using a simple binomial sum. Here we explain the method, and we present population-adjusted national rankings for the last three summer Olympics (London 2012, Rio 2016 and Tokyo 2020, held in 2021). If the advantages of this ranking method come to be understood by sports media covering the Olympics and by the interested public, it could be widely reported alongside raw medal counts, thus adding excitement and interest to the Olympics.