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

Abstract

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 considered 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 combat 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 épée, 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 épée 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 athletes’ results in tournaments and throughout their career, making even more unfair the “winner-takes-all” disparities that often occur between the winner and the other classified competitors.

A study of Tennis Tournaments by Means of an Agent-Based Model Calibrated with a Genetic Algorithm

“…We can see that the model is able to reproduce the same kind of trend for the FWHM shown for the real data. This trend, which has also been shown in other works [11][12][13], is due to the fact that the most talented players are selected to participate in the later stages of the tournaments.…”

“…We can compare our results with previous work to understand which of the two interpretations of the data is an artefact of the model and which reflects the real situation. For both model calibrations carried out in the previous sections, the region on the surface of maximum fitness with low values of σ c , have many parameters, (for example in Table 4 we get σ t = 0.09 for the parameter with maximum verisimilitude) that give a talent distribution with amplitude similar to that used in other works [11,12], a normal distribution with σ t = 0.1 and mean µ = 0.6, derived from the population IQ distribution and thus obtained from real data. We can use this talent distribution in our model, and also fix σ c , taking into account the green values in the tables 4,1 and considering the average of the averages of the σ c values, obtaining σ c = 0.12 as the best representative value, for the region of low values of σ c , on the surface of maximum fitness.…”

“…In order to better understand competitions, we want to focus on sports, which gives us access to a large amount of data. For this type of competitions, previous studies, [11][12][13][14][15], although using different approaches, have again shown that the talent or preparation of the athletes is not the only factor determining the outcome of competitions and that the action of chance is an important component of competitions.…”

“…This mechanism must depend on the sportive performance of the agent-player in such a way to emulate a real situation. Previous work [9,11,12] have used an equation to obtain a numerical value of the sportive performance of an agent-player. We have adapted this equation to the case of a direct competition of two agent-player, and obtained a system of equations:…”

“…To study the phenomenon of competition, previous works [11][12][13] have developed multiparametric models capable of reproducing the data of real competitions, the calibration of these models has been obtained by fixing some parameters with reasonable values extrapolated be antecedent works, with these constraints, the models have been able to provide information regarding the role of chance in contraposition to that of talent in determining the outcome of competitions.…”