Department of Biological Physics, Eötvös Loránd University
Abstract
Ranking athletes by their performance in competitions and tournaments is
common in every popular sport and has significant benefits that contribute to
both the organization and strategic aspects of competitions. Although rankings
are perhaps the most concise and most straightforward representation of the
relative strength among the competitors, beyond this one-dimensional
characterization, it is also possible to capture the relationships between
athletes in greater detail. Following this approach, our study examines the
networks between athletes in individual sports such as tennis and fencing,
where the nodes are associated with the contestants and the edges are directed
from the winner to the loser. We demonstrate that the connections formed
through matches arrange themselves into a time-evolving hierarchy, with the top
players positioned at its apex. The structure of the resulting networks
exhibits detectable differences depending on whether they are constructed
purely from round-robin data or from purely elimination-style tournaments. We
find that elimination tournaments lead to networks with a smaller level of
hierarchy and thus, importantly, to an increased probability of circular
win-loss situations (cycles). The position within the hierarchy, along with
other network metrics, can be used to predict match outcomes. In the systems
studied, these methods provide predictions with an accuracy comparable to that
of forecasts based on official sports ranking points or the Elo rating system.
A deeper understanding of the delicate aspects of the networks of pairwise
contests enhances our ability to model, predict, and optimize the behaviour of
many complex systems, whether in sports tournaments, social interactions, or
other competitive environments.