The paradox of talent: How chance affects success in tennis tournaments

Individual sports competitions provide a natural setting for examining the relative importance of talent and luck/chance in achieving success. The belief that success is primarily due to individual abilities and hard work rather than external factors is particularly strong in this context. Thus, individual talent is regarded as the most important - if not the only - component in ensuring a successful career for athletes. In this study, we test this belief using tennis as a case study, due to its popularity and competition structure in direct-elimination tournaments. Our dataset covers the last decade before Covid-19 pandemics (2010-2019) of main international events in the ATP circuit and consists of tourney results and annual rankings for professional male players. After a preliminary data analysis, we introduce an agent-based model able to accurately simulate the tennis players' dynamics along several seasons. We show that, once calibrated on the dataset, the model is able to reproduce the main stylized facts observed in real data, including the results of single tournaments and the development of players' careers in the ATP community. The strength of our approach lies in its simplicity: it requires only one free parameter a to determine the importance of talent in scoring every single point: a = 1 indicates the ideal scenario in which only talent matters, whereas a = 0 represents the opposite limit case, in which the outcome of each point is entirely due to chance. We find the best agreement between real data and simulation results when talent weights substantially less than luck, i.e. when a is between 0.20 and 0.30. A further comparison between data and simulations, based on the analysis of the direct networks of all the matches, confirms the previous finding. A posteriori, we notice that this surprisingly important role of chance in tennis tournaments is not an exception. On the contrary, it can be explained by a more general paradoxical effect that characterizes highly competitive environments, particularly in individual sports. In other words, when the difference in talent between top players is minimal, chance becomes determinant. Our findings highlight the impact of the - too often underestimated - external factors on athletes' performance in individual tournaments and their careers. Our results point out the unfairness of the ''winner-takes-all"reward system that enhances the disparities between the first classified players and the others in major competitions.