Universal temporal features of rankings in competitive sports and games

TL;DR

This study uncovers universal statistical regularities in the dynamics of rankings across various sports and games, suggesting common underlying mechanisms of hierarchy formation that could improve predictions of rank stability.

Contribution

It demonstrates that rank diversity follows a universal functional form across different competitive systems, linking sports rankings to linguistic structures and revealing shared stratification mechanisms.

Findings

Rank diversity exhibits a universal functional form across sports and language systems.

Statistical regularities in rank dynamics suggest common underlying stratification mechanisms.

Results enable potential prediction of rank occupancy lifetimes.

Abstract

Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which may eventually lead to stratified structures such as the wealth distribution worldwide. However, it is still unclear whether the road to hierarchical complexity is determined by the particularities of each phenomena, or if there are universal mechanisms of stratification common to many systems. Human sports and games, with their (varied but simplified) rules of competition and measures of performance, serve as an ideal test bed to look for universal features of hierarchy formation. With this goal in mind, we analyse here the behaviour of players and team rankings over time for several sports and games. Even though, for a given time, the distribution of performance ranks varies across activities, we find statistical regularities in the dynamics of ranks. Specifically the rank diversity, a measure of the number of elements occupying a given rank over a length of time, has the same functional form in sports and games as in languages, another system where competition is determined by the use or disuse of grammatical structures. Our results support the notion that hierarchical phenomena may be driven by the same underlying mechanisms of rank formation, regardless of the nature of their components. Moreover, such regularities can in principle be used to predict lifetimes of rank occupancy, thus increasing our ability to forecast stratification in the presence of competition.