A rank-size approach to analyse soccer competitions and teams: the case of the Italian football league “Serie A"

In this paper, we present a data-analysis rank-size approach to assess the features of soccer competitions and competitors. We investigate the championships rankings and the teams' final scores in the most relevant Italian league, the "Serie A", between 1930 and 2020. We use the final rankings and the teams' scores to explore the presence of rank-size regimes in the various yearly championships. Besides, we analyse the teams one by one, ranking their performance over the years and using the rank-size law's parameters to compare their performances across the tournaments. We chose to do so via the Discrete Generalised Beta Distribution, a three-parameter rank-size function. We offer a cluster analysis of the rank-size law parameters based on a k -means algorithm to provide additional insights and capture similarities and deviations among championships and teams. Concluding, we propose a measure of competitiveness within championships and per team. The best fit results are statistically outstanding, and the cluster analysis presents two main clusters capturing teams' performances and years in which they have competed in the "Serie A". The competitiveness analysis shows that the teams at the bottom of the championships ranking have obtained decreasing scores in recent years.