We evaluate the sporting effects of the seeding system reform in the major football club tournament -the Champions League -organized by the Union of European Football Associations (UEFA). In the UEFA Champions League, before the 2015-16 season, the teams were seeded in the group stage with respect to their ratings. Starting from the 2015-16 season, national champions of the Top-7 countries are seeded in the first pot, whereas other teams are seeded by their rating as before. We propose a probabilistic model for predicting the score of a single match in UEFA tournaments as well as the whole UEFA season. This model uses clubs' ratings as inputs. Applying Monte-Carlo simulations, we show that the expected rating of the UEFA Champions League winner, as well as the sum of the finalists' ratings, slightly decreased after the reform. At the same time, the difference in the finalists' ratings, which is a measure of competitive balance, increased. The UEFA Europa League became stronger and less balanced. We check the robustness of the results by introducing local fluctuations in the clubs ratings. Also, we study which national associations took advantage of the reform. For seeding rules before and after the reform, we estimate the transition matrix (p ij ), where p ij is the probability of i-th strongest national association moving to j-th position after the season. The effect of reform on a single national association measured by the change in probability to increase or decrease the association's UEFA rank is not more than 3%.
We evaluate the sporting effects of the seeding system reforms in the Champions League, the major football club tournament organized by the Union of European Football Associations (UEFA). Before the 2015–2016 season, the teams were seeded in the group stage by their ratings. Starting from the 2015–2016 season, national champions of the Top-7 associations are seeded in the first pot, whereas other teams are seeded by their rating as before. Taking effect from the season 2018–2019, the team’s rating no longer includes 20% of the rating of the association that the team represents. Using the prediction model, we simulate the whole UEFA season and obtain numerical estimates for competitiveness changes in the UEFA tournaments caused by these seeding reforms. We report only marginal changes in tournament metrics that characterize ability of the tournament to select the best teams and competitive balance. Probability of changes in the UEFA national association ranking does not exceed several percent for any association.
We propose a theoretical model of a round-robin tournament with limited resources motivated by the fact that in a real-world round-robin sport tournament participating teams are sometimes forced to distribute their effort over an extended period. We assume that the participating teams have a limited amount of effort that must be distributed between all matches. We model the outcome of each match as a first-price sealed-bid auction. Results are aggregated after all matches are played with respect to the number of wins. The teams distribute their effort striving to maximize the expected payoff at tournament completion. For a three team tournament, we describe the set of all subgame perfect Nash equilibria in pure strategies. For tournaments with a relatively low first prize, we found two types of equilibria: 'effort-saving' and 'burning out', both leading to unequal payoffs. In contrast, for tournaments with a large first prize a limited budget of effort, in general, does not allow for the first or the last move advantage to be exploited.
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