On the role of chance in fencing tournaments: An agent-based approach

It is a widespread belief that success is mainly due to innate qualities rather than external forces. This is particularly true in sports competitions, where individual talent is usually con- sidered the main, if not the only, ingredient to reach success. In this study, we explore the limits of this belief by quantifying the relative weight of talent and chance in fencing, a com- bat sport involving a weapon, with the help of both real data and agent-based simulations. Fencing competitions are structured as direct elimination tournaments, where randomness is explicitly present in some rules. We focused on e ́ pe ́ e, which is one of three disciplines. We collected data on international competition results and annual rankings, in the range 2008–2020, for male and female fencers under 20 years old (Junior category). Then, we built the model calibrated on our dataset and parametrized by just one free variable a, describing the importance of talent—and, consequently, of chance—in competitions (a = 1 indicates the ideal scenario where only talent matters, a = 0 the complete random one). Our agent-based approach can reproduce the main stylized facts observed in data, at the level of both single tournaments and the entire careers of a given community of e ́ pe ́ e fencers. We find that simulations approximate very well the data for both Junior Men and Women when talent weights slightly less than chance, i.e. when a is around 0.45. We conclude that the role of chance in fencing is unusually high and it probably represents an extreme case for individual sports. Our findings shed light on the importance of external factors in both ath- letes’ results in tournaments and throughout their career, making even more unfair the “win- ner-takes-all” disparities that often occur between the winner and the other classified competitors.