E-compare of Soccer Tournament Structures

This paper develops a system integrating the knowledge of statistical modeling and Monte Carlo simulation to evaluate various types of soccer tournament structures. A system called as “E-compare of Soccer Tournament Structures” aims to assist decision makers to choose the competitive soccer design.The system reports various tournaments metrics such as the expected number of goals scored and conceded, the expected number of wins, draws, and losses, and the expected final ranking at the end of the tournament.Based on a large number of simulations using teams participated in the Malaysian soccer super league, our analysis showed that different designs gave different impacts on the final ranking of the teams.Round robin is found to be the best structure in terms of identifying the strongest team to win the league compared to a knockout structure

Bibliometric indices as a measure of long-term competitive balance in knockout tournaments

We argue for the application of bibliometric indices to quantify long-term uncertainty of outcome in sports. The Euclidean index is proposed to reward quality over quantity, while the rectangle index can be an appropriate measure of core performance. Their differences are highlighted through an axiomatic analysis and several examples. Our approach also requires a weighting scheme to compare different achievements. The methodology is illustrated by studying the knockout stage of the UEFA Champions League in the 16 seasons played between 2003 and 2019: club and country performances as well as three types of competitive balance are considered. Measuring competition at the level of national associations is a novelty. All results are remarkably robust concerning the bibliometric index and the assigned weights. Inequality has not increased among the elite clubs and between the national associations, however, it has changed within some countries. Since the performances of national associations are more stable than the results of individual clubs, it would be better to build the seeding in the UEFA Champions League group stage upon association coefficients adjusted for league finishing positions rather than club coefficients.Comment: 23 pages, 9 figures, 7 table

Modelling The Effect of Changing Point Systems to Teams’ Competition Standing in A Malaysian Soccer Super League

In a sports league such as in a soccer league, the teams’ competition standing is based on a cumulative point system.Typically, the standard point system is given to every single match for win, draw and lose teams is the 3-1-0 point system. In this paper, we explore the effect of changing point systems to teams’ competition standing by changing the weight age values for win, draw and lose teams.Three types of point systems are explored in our soccer simulation model; firstly the 3-1-0, secondly the 2-1-0 and thirdly the 4-1-0 point system.Based on the teams participating in a Malaysian soccer Super League, our simulation result shows that there are small changes in term of teams’ competition standing when we compared the actual rank and the simulation rank position.However, the 4-1-0 point system recorded the highest Pearson correlation value which is 0.97, followed by the 2-1-0 point system (0.95) and thirdly the 3-1-0 point system (0.94)

League competitions and fairness

We formulate two fairness principles and characterize the league competition systems that satisfy them. The first principle requires that all players should have the same chance of being the final winner if all players are equally strong, while the second states that the league competition should not favor weaker players. We apply these requirements to a class of systems which includes round-robin tournaments as a particular case.Financial support from the Spanish Ministry of Science and Technology (Project ECO2015-65031-R MINECO/FEDER, UE) is acknowledged. Open Access funding enabled and organized by Projekt DEAL

League competitions and fairness

We formulate two fairness principles and characterize the league competition systems that satisfy them. The first principle requires that all players should have the same chance of being the final winner if all players are equally strong, while the second states that the league competition should not favor weaker players. We apply these requirements to a class of systems which includes round-robin tournaments as a particular case

A paradox of tournament seeding

A mathematical model of seeding is analysed for sports tournaments where the qualification is based on round-robin contests. The conditions of strategyproofness are found to be quite restrictive: if each team takes its own coefficient (a measure of its past performance), only one or all of them should qualify from every round-robin contest. Thus the standard draw system creates incentives for tanking in order to be assigned to a stronger pot as each team prefers to qualify with teams having a lower coefficient. Major soccer competitions are shown to suffer from this weakness. Strategyproofness can be guaranteed by giving to each team the highest coefficient of all teams that are ranked lower in its round-robin contest. The proposal is illustrated by the 2020/21 UEFA Champions League.Comment: 23 pages, 3 table

Stochastic analysis of the Elo rating algorithm in round-robin tournaments

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 still lacking. Aiming to fill this gap, this paper presents a comprehensive (stochastic) analysis of the Elo algorithm, considering round-robin tournaments. Specifically, analytical expressions are derived describing the evolution of the skills and performance metrics. Then, taking into account the relationship between the behavior of the algorithm and the step-size value, which is a hyperparameter that can be controlled, design guidelines and discussions about the performance of the algorithm are provided. Experimental results are shown confirming the accuracy of the analysis and illustrating the applicability of the theoretical findings using real-world data obtained from SuperLega, the Italian volleyball league