University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 Ranking methods in sports teams Ranking methods in sports teams 67 81 24363 10.22108/msci.2020.118609.1334 FA Efat Golpar Raboky Qom, University of Qom, Department of Mathematics Maryam Nedaee Qom, Qom University, Department of Physical Education and Sport Sciences Journal Article 2019 08 05 Ranking is a general order relation, a relationship between elements of a set in which one element has a higher rank than another. Ranking establishes an ordering of scores in such a way that the first element has the highest score and the last element has the lowest score. A sports scoring system is a system that analyzes the results of sports competitions to assign scores to each team or player. Various ranking methods have been proposed, their performance based on the points teams earn in different games. Some of these methods rank teams based solely on the number of wins and losses, while in some ranking methods, the situation of the rival team is also considered in scoring. In these methods, wins and losses against weak and strong teams are not valued equally. If a team's victories are only against weak teams, it cannot be confidently said that this team is strong, and necessarily, the number of wins cannot demonstrate a team's superiority. There are various methods for ranking teams, using statistics, graph theory, and linear algebra. In this article, we discuss some ranking methods that mostly utilize linear algebra concepts. In this regard, we examine methods such as percentage of wins, ranking percentage index, Massey method, Colley method, Keener method, defense-offense method, and the page-rank method. We illustrate the results of ranking with these methods through an example. Ranking is a general order relation, a relationship between elements of a set in which one element has a higher rank than another. Ranking establishes an ordering of scores in such a way that the first element has the highest score and the last element has the lowest score. A sports scoring system is a system that analyzes the results of sports competitions to assign scores to each team or player. Various ranking methods have been proposed, their performance based on the points teams earn in different games. Some of these methods rank teams based solely on the number of wins and losses, while in some ranking methods, the situation of the rival team is also considered in scoring. In these methods, wins and losses against weak and strong teams are not valued equally. If a team's victories are only against weak teams, it cannot be confidently said that this team is strong, and necessarily, the number of wins cannot demonstrate a team's superiority. There are various methods for ranking teams, using statistics, graph theory, and linear algebra. In this article, we discuss some ranking methods that mostly utilize linear algebra concepts. In this regard, we examine methods such as percentage of wins, ranking percentage index, Massey method, Colley method, Keener method, defense-offense method, and the page-rank method. We illustrate the results of ranking with these methods through an example. https://math-sci.ui.ac.ir/article_24363_813293d9194c2ac94a0d2f93a9268169.pdf