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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Steve Rigdon, PhD

4 Issues per year


CiteScore 2016: 0.44

SCImago Journal Rank (SJR) 2015: 0.288
Source Normalized Impact per Paper (SNIP) 2015: 0.358

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1559-0410
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A proposed general rating system for which the Colley Matrix Rating System is a special case

Mark J. Stewart
  • Corresponding author
  • Assistant Professor of Physics, East Stroudsburg University, 200 Prospect Street East Stroudsburg, PA 18301, USA
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Published Online: 2013-06-01 | DOI: https://doi.org/10.1515/jqas-2012-0039

Abstract

The Colley Matrix Rating System (CMRS) has been a component of the Bowl Championship Series (BCS) rankings. As such it is important that the assumptions that lead to and differentiate it from other rating systems be well understood. This work investigates an approach to justifying the CMRS based on an approach taken by Massey. This approach leads to both the CMRS and a version of a Massey Matrix Rating System. When approached in the manner proposed here these rating systems can be presented as special cases of one more general rating system.

Keywords: Colley matrix; Massey matrix; rating system

References

  • Bowl Championship Series Web Site. http://www.bcsfootball.org/. Accessed June 25, 2012.

  • Chartier, Timothy P., Erich Kreutzer., Amy N. Langville, and Kathryn E. Pedings. 2011. “Sports Ranking with Non-Uniform Weighting.” The Journal of Quantitative Analysis of Sports 7(3): article 6.Google Scholar

  • Colley, Wesley N. 2002. “Colley’s Bias Free College Football Ranking Method: The Colley Matrix Explained.” www.colleyrankings.com. Accessed May 25, 2013.

  • Elo, Arpad. 1978. The Ratings of Chess Players Past and Present. New York: Arco Publishing.Google Scholar

  • Massey, Ken. 1997. Statistical Models Applied to the rating of sports teams, Honors Thesis, Bluefield College.Google Scholar

  • Ray Stefani. 2011. “The Methodology of Internationally Recognized International Sports Rating Systems.” The Journal of Quantitative Analysis of Sports 7(4):10.Google Scholar

  • Ray Stefani and Richard Pollard. 2007. “Football Rating Systems for Top-Level Competition: A Critical Survey.” The Journal of Quantitative Analysis of Sports 3(3):3.Google Scholar

  • Zenor, Michael. 1995. “Zenor’s College Football Power Ratings.” http://wilson.engr.wisc.edu/rsfc/oth_sites/rate/zenor.html. Accessed May 25, 2013.

About the article

Corresponding author: Mark J. Stewart, Assistant Professor of Physics, East Stroudsburg University, 200 Prospect Street East Stroudsburg, PA 18301, USA


Published Online: 2013-06-01

Published in Print: 2013-06-01


Citation Information: Journal of Quantitative Analysis in Sports, Volume 9, Issue 2, Pages 179–185, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2012-0039.

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