Related papers: A paradox of tournament seeding
We propose a statistical framework for quantifying the importance of single events that do not provide intermediate rewards but offer implicit incentives through the reward structure at the end of a multi-event contest. Applying the…
Forecast of football outcomes in terms of Home Win, Draw and Away Win relies largely on ex ante probability elicitation of these events and ex post verification of them via computation of probability scoring rules (Brier, Ranked…
Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest…
Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…
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…
The non-scientific event of a soccer match is analysed on a strictly scientific level. The analysis is based on the recently introduced concept of a team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of finite-size scaling. A…
We argue for the application of bibliometric indices to quantify the 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…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
In this paper we show a new technique to analyze families of rankings. In particular we focus on sports rankings and, more precisely, on soccer leagues. We consider that two teams compete when they change their relative positions in…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
With the development of measurement technology, data on the movements of actual games in various sports can be obtained and used for planning and evaluating the tactics and strategy. Defense in team sports is generally difficult to be…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
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,…
In this work we study the ranking algorithm used by F\'ed\'eration Internationale de Football Association (FIFA); we analyze the parameters it currently uses, show the formal probabilistic model from which it can be derived, and optimize…
This paper considers the challenge of designing football group draw mechanisms which have the uniform distribution over all valid draw assignments, but are also entertaining, practical, and transparent. We explain how to simulate the FIFA…
The COVID-19 pandemic has left its marks in the sports world, forcing the full-stop of all sports-related activities in the first half of 2020. Football leagues were suddenly stopped and each country was hesitating between a relaunch of the…
Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner…
We describe a round robin scheduling problem for a competition played in two divisions, motivated by a scheduling problem brought to the second author by a local sports organisation. The first division has teams from 2n clubs, and is played…