  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.
