Universality, Limits and Predictability of Gold-Medal Performances at the Olympic Games

Filippo Radicchi

doi:10.1371/journal.pone.0040335

Abstract

Inspired by the Games held in ancient Greece, modern Olympics represent the world’s largest pageant of athletic skill and competitive spirit. Performances of athletes at the Olympic Games mirror, since 1896, human potentialities in sports, and thus provide an optimal source of information for studying the evolution of sport achievements and predicting the limits that athletes can reach. Unfortunately, the models introduced so far for the description of athlete performances at the Olympics are either sophisticated or unrealistic, and more importantly, do not provide a unified theory for sport performances. Here, we address this issue by showing that relative performance improvements of medal winners at the Olympics are normally distributed, implying that the evolution of performance values can be described in good approximation as an exponential approach to an a priori unknown limiting performance value. This law holds for all specialties in athletics–including running, jumping, and throwing–and swimming. We present a self-consistent method, based on normality hypothesis testing, able to predict limiting performance values in all specialties. We further quantify the most likely years in which athletes will breach challenging performance walls in running, jumping, throwing, and swimming events, as well as the probability that new world records will be established at the next edition of the Olympic Games.

Highlights

Modern Olympics are inspired by the ancient version of the Games, but based on a wider idea of globality
While former statistical studies have mainly analyzed the progression of absolute performance values along the various editions of the Games, here we change point of view and focus our attention on relative improvements in performances between two consecutive editions of the Olympics
We report from left to right: the name of the specialty, the best estimates of the asymptotic performance value ^p?, the best estimate of the mean value m^, the best estimate of the standard deviation s^, the statistical significance or p-value of the test of normality, the number E of Olympic Games that included the specialty, the probability P that the actual world record will be beaten in London 2012, and the most likely performance value ^p2012 that gold-medal winners will obtain at the edition of the Olympic Games

Summary

Introduction

Modern Olympics are inspired by the ancient version of the Games, but based on a wider idea of globality. While ancient Games were opened only to Greek speaking athletes [1], modern Olympics were, since their beginning, considered a world event involving people from every part of the globe [2]. The same symbol of the Olympics, composed of five interlocking rings standing for the five continents, was designed by the Baron Pierre de Coubertin, the founder of the modern Olympic Games, with the aim of reinforcing the idea that the Games are an international event and welcome all countries of the world [3]. The Olympics generally play a fundamental and positive role for the economic and urban development of the city that hosts the event [7,8]

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Results

Conclusion