We are the champions. The index for evaluating concentration of championships using a sliding window approach

The concept of competitive balance is considered to be an essential aspect in the field of sport economics. This work describes a novel approach for measuring and evaluating competitive balance through concentration of championships. The concentration of championships was assessed using a sliding window approach with the length of five consecutive competitions (years) and a single competition (year) increment over the whole evaluated period. Because the sliding window was relatively short, the newly developed index, termed 'We Are the Champions' (WAC₅), is sensitive to rapid changes in competitive balance. The WAC₅ index, average WAC₅ (aWAC₅), expected WAC₅ (eWAC₅), and ΔWAC₅ (eWAC₅ - a_WAC ) were applied to data from 68 competitions of several individual and team sports collected for the 1960-2020 period. The significance of indices was tested by resampling (bootstrapping and permutation). The results of the study show a growth in competitive balance of several ice hockey competitions (national and international), but decreasing competitive balance in Formula 1 racing and in several European soccer competitions. In soccer competitions, there was a substantially lower competitive balance in a league than in a domestic cup competition within each country/federation. The difference between the overall competitive balance in the most popular, North American, professional leagues and the top European soccer leagues is growing. A significant grouping of champions was determined for all sports involving individual athletes, but also for several team competitions.