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The outcome of some football matches has benefited both teams at the expense of a third team because head-to-head results were used for breaking ties. Inspired by these examples, our mathematical analysis identifies all possible collusion…
A strong structural regularity of classes is found in soccer teams ranked by the Union of European Football Associations (UEFA) for the time interval 2009-2014. It concerns 424 to 453 teams according to the 5 competition seasons. The…
A paper published in a leading journal of management science has recently analysed the mechanism used for the UEFA Champions League Round of 16 draw. Since the authors have not been familiar with the related sports analytics literature,…
The Elo algorithm, renowned for its simplicity, is widely used for rating in sports tournaments and other applications. However, despite its widespread use, a detailed understanding of the convergence characteristics of the Elo algorithm is…
The integrity of a sport can be seriously undermined if its rules punish winning as this creates incentives for strategic manipulation. Therefore, a sports tournament can be called unfair if the overall win probabilities are not ordered…
This report is devoted to the forecast of the UEFA EURO 2020, Europe's continental football championship, taking place across Europe in June/July 2021. We present the simulation results for this tournament, where the simulations are based…
The play-offs of the UEFA Euro 2020 qualifying tournament determine the last four participants in the UEFA European Championship 2020. 16 teams, which have failed to obtain a slot in the qualifying group stage, will be selected and divided…
This work is concerned with the rating of players/teams in face-to-face games with three possible outcomes: loss, win, and draw. This is one of the fundamental problems in sport analytics, where the very simple and popular, non-trivial…
Competitive balance in a football league is extremely important from the perspective of economic growth of the industry. Many researchers have earlier proposed different measures of competitive balance, which are primarily adapted from the…
In the last round of the FIFA World Cup group stage, games for which the outcome does not affect the selection of the qualified teams are played with little enthusiasm. Furthermore, a team that has already qualified may take into account…
Penalty shootouts play a crucial role in the knockout stage of major football tournaments. Their importance has substantially increased from the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals…
In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is…
In this paper a new heuristic optimization algorithm has been introduced based on the performance of the major football leagues within each season in EU countries. The algorithm starts with an initial population including three different…
This work reconciles two perspectives on the Elo ranking that coexist in the literature: the practitioner's view as a heuristic feedback rule, and the statistician's view as online maximum likelihood estimation via stochastic gradient…
The Elo rating system is a highly successful ranking algorithm for games of skill where, by construction, one team wins and the other loses. A primary limitation of the original Elo algorithm is its inability to predict information beyond a…
The Elo rating system has been used world wide for individual sports and team sports, as exemplified by the European Go Federation (EGF), International Chess Federation (FIDE), International Federation of Association Football (FIFA), and…
Competitive balance is the subject of much interest in the sports analytics literature and beyond. In this paper, we develop a statistical network model based on an extension of the stochastic block model to assess the balance between teams…
FIFA World Cup is one of the most watched sporting event in the world and its popularity continue to increase. While currently 32 teams participate in this event, starting with 2026 the number of participants will increase to 48. As a…
Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the…
Competitive balance is an important concept for professional sports and one of the key issues that European football has to address in order to ensure its long-term prosperity. However, the quantification of competitive balance is not an…