Related papers: How to Choose a Champion
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…
A tournament graph is a complete directed graph, which can be used to model a round-robin tournament between $n$ players. In this paper, we address the problem of finding a champion of the tournament, also known as Copeland winner, which is…
According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
When $n$ teams play in a football league with home and away matches against every opponent there are $M = n \cdot (n-1)$ matches. There are 3 possible match results: a victory is awarded 3 points, a draw 1 point and 0 points for a defeat.…
A tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $\binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…
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…
Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport…
League of Legends (LoL) is the most widely played multiplayer online battle arena (MOBA) game in the world. An important aspect of LoL is competitive ranked play, which utilizes a skill-based matchmaking system to form fair teams. However,…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
The selection of an appropriate competition format is critical for both the success and credibility of any competition, both real and simulated. In this paper, the automated parallelism offered by the RoboCupSoccer 2D simulation league is…
During the last twenty years, a lot of research was conducted on the sport elimination problem: Given a sports league and its remaining matches, we have to decide whether a given team can still possibly win the competition, i.e., place…
We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the…
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 all competitions where results are based upon an individual's performance the question of whether the outcome is a consequence of skill or luck arises. We explore this question through an analysis of a large dataset of approximately one…
We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…