The Role of Chance in Individual Sports: an Agent-Based Approach for Fencing Tournaments

Abstract

It is a widespread belief that success is mainly due to innate qualities, rather than to external forces. This is particularly true in sport competitions, where individual talent is considered the only ingredient in order to reach success. In this study, we propose to explore the relative weight of talent and luck in individual sports through agent-based models. In particular, we chose fencing as case study, that is a combat sport involving a weapon. Fencing competitions are structured as direct elimination tournaments, where randomness is explicitly present in some rules. Our dataset covers the last decade of international events and consists of both single competition results and annual rankings for male and female fencers under 20 years old (Junior category). We show that our agent-based approach, calibrated on the dataset and parametrized by just one free variable a describing the importance of talent in competitions (a = 1 indicates the ideal scenario where only talent matters, a = 0 the complete random one) is able to reproduce the main stylized facts observed in real data, both at the level of single fencing tournaments and of entire careers of a given community of fencers. We find that simulations approximate very well the real data when talent weights slightly more than luck, i.e. when a is around 0.55 for Junior Men, or even slightly less than luck, i.e. when a = 0.45 for Junior Women. We conclude that the role of chance in fencing is highly underestimated even if probably it represents an extreme case for individual sports. Our results shed light on the importance of external factors in both athletes’ results in single tournaments and in their entire career, making even more unfair the “winner-takes-all” disparities in remuneration.