In search of peak human athletic potential: A mathematical investigation

Abstract

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect", where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics, that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatio-temporal trends in group composition.

Numerous new experiments since v1. Equal contribution from first two authors

References in corpus (16)

• Measuring and testing dependence by correlation of distances
• Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies
• Power-law distribution in the number of confirmed COVID-19 cases
• Complexity in economic and social systems: cryptocurrency market at around COVID-19
• COVID-19 second wave mortality in Europe and the United States
• Safe Leads and Lead Changes in Competitive Team Sports
• Competition of noise and collectivity in global cryptocurrency trading: route to a self-contained market
• Collective correlations, dynamics, and behavioural inconsistencies of the cryptocurrency market over time
• Trends in COVID-19 prevalence and mortality: a year in review
• Anomalous Diffusion and Long-range Correlations in the Score Evolution of the Game of Cricket
• Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil
• Decay of distance autocorrelation and Lyapunov exponents
• Efficiency of communities and financial markets during the 2020 pandemic
• A new measure between sets of probability distributions with applications to erratic financial behavior
• Understanding spatial propagation using metric geometry with application to the spread of COVID-19 in the United States
• Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States

Cited by in corpus (11)

• Economic state classification and portfolio optimisation with application to stagflationary environments
• Global and regional changes in carbon dioxide emissions: 1970-2019
• Spatio-temporal trends in the propagation and capacity of low-carbon hydrogen projects
• Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies
• Dual-domain analysis of gun violence incidents in the United States
• Geometric persistence and distributional trends in worldwide terrorism
• Distributional trends in the generation and end-use sector of low-carbon hydrogen plants
• An exploration of the mathematical structure and behavioural biases of 21st century financial crises
• On financial market correlation structures and diversification benefits across and within equity sectors
• Detecting imbalanced financial markets through time-varying optimization and nonlinear functionals
• Nonlinear shifts and dislocations in financial market structure and composition