There are situations in which a monopoly solution cannot be reached. In these cases, which situation represents the maximum concentration (minimum competitive balance)? It is a relevant question, given that in sports economics, measuring the competitive balance of a league is done through normalized indices. These indices require that the maximum level of concentration be known. Until now, the distribution of results that generates the maximum level of concentration has been identified in the literature as Complete cascade distribution. However, if the scoring system used does not fulfil the stability condition, which implies that the total number of points of a championship is constant, it can be demonstrated that the Complete cascade distribution does not generate the maximum level of concentration. This is the case, for example, with major European football leagues. In this article, we constructed a perfectly unbalanced distribution, which we called a Truncated cascade distribution. This distribution generates the maximum concentration level. Therefore, if we do not use Truncated cascade distribution, there is an overestimation of the concentration measured with normalized indices. Then, the calculated competitive balance will be wrong, that is, underestimated. We provided a spreadsheet for identifying this distribution.

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This article examines competitive balance in the group stage of the UEFA Champions League over the last two decades (1999/2000-2017/2018). Competitive balance is considered both before and after a competition. Have the groups been designed in such a way as to ensure similar levels of competitive balance ex ante? Have the demonstrated strengths (ex post competitive balance) of the different groups been similar over each season? What is the relationship between the competitive balance in the designed groups and that achieved in the same groups after the competition? Are the performance achieved in terms of ex post competitive balance similar to ex ante competitive balance levels? We found that, despite expectations, the groups' ex ante competitive balance was not homogeneous. Although ex ante competitive balance serves as a good predictor, on average, of ex post competitive balance, we observed significant differences at the levels of group and seasons. Therefore, it is possible to improve the design mechanism of the groups that make up the group stage of the champions so that they are composed homogeneously in terms of ex ante competitive balance.

Authorities in the economic field (European Commission and US Federal Trade Commission) focus on the level of market concentration and establish limits in order to promote competition. However, sports authorities do not seem to pay the same attention to competitive balance in the national leagues, given the results achieved in the major leagues and limited interventions and regulations in this area. How are the major European football leagues evaluated based on the limits set for market concentration in the United States or the European Union? Following this line, we undertook a comparative analysis using the distance to competitive balance index, whose range is the unit interval, and define it as a function in a metric space. The comparative analysis shows, as in other studies, the high and ever‐growing concentration of the results of these leagues over the past 25 years. With the European Commission and US Federal Trade Commission criteria, about one in three seasons would have been highly concentrated in the period analysed, and half in the last 10 seasons. Thus, it would seem reasonable that mechanisms that encourage competitiveness are considered.