Ranking methods in sports teams

Document Type : Research Paper

Authors

1 Qom, University of Qom, Department of Mathematics

2 Qom, Qom University, Department of Physical Education and Sport Sciences

Abstract

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.

Keywords

References

[1] W. N. Colley, Colley’s Bias Free College Football Ranking Method, 2002.
[2] A. Y. Govan and C. D. Meyer, Ranking National Football League Teams Using Google’s PageRank, AA Markov Anniversary Meeting, 2006.
[3] A. Y. Govan, A. N. Langville and C. D. Meyer, Offense-defense approach to ranking team sports, Journal of Quantitative Analysis in Sports, 5 (2009).
[4] J. P. Keener,The Perron-Frobenius Theorem and the Ranking of Football Teams, SIAM Review, 35 (1993) 80–93.
[5] A. N. Langville and C. D. Meyer, Google’s PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, 2006.
[6] C. D. Meyer, Matrix analysis and applied linear algebra, SIAM, 2000.
[7] A. N. Langville and C. D. Meyer, Deeper inside PageRank, Internet Mathematics. J., 1 (2005) 335–380.
[8] S. Lawrence and C. L. Giles, Searching the world wide web, Science, 280 (1998) 98–100.
[9] K. Massey, Statistical models applied to the rating of sports teams, Bluefield College, 1997.
[10] History google, http://fa.wikipedia.org/wiki/

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History

  • Receive Date: 05 August 2019
  • Revise Date: 06 January 2020
  • Accept Date: 08 January 2020
  • Publish Date: 23 August 2019

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