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Robust Rankings for College Football

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  • Burer Samuel

    (University of Iowa)

Abstract

We investigate the sensitivity of the Colley Matrix (CM) rankings---one of six computer rankings used by the Bowl Championship Series---to (hypothetical) changes in the outcomes of (actual) games. Specifically, we measure the shift in the rankings of the top 25 teams when the win-loss outcome of, say, a single game between two teams, each with winning percentages below 30%, is hypothetically switched. Using data from 2006--2011, we discover that the CM rankings are quite sensitive to such changes. To alleviate this sensitivity, we propose a robust variant of the rankings based on solving a mixed-integer nonlinear program, which requires about a minute of computation time. We then confirm empirically that our rankings are considerably more robust than the basic CM rankings. As far as we are aware, our study is the first explicit attempt to make football rankings robust. Furthermore, our methodology can be applied in other sports settings and can accommodate different concepts of robustness besides the specific one introduced here.

Suggested Citation

  • Burer Samuel, 2012. "Robust Rankings for College Football," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(2), pages 1-22, June.
    • Handle: RePEc:bpj:jqsprt:v:8:y:2012:i:2:n:6
    DOI: 10.1515/1559-0410.1405
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    References listed on IDEAS

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    1. Govan Anjela Y & Langville Amy N & Meyer Carl D, 2009. "Offense-Defense Approach to Ranking Team Sports," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(1), pages 1-19, January.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. B. Jay Coleman, 2005. "Minimizing Game Score Violations in College Football Rankings," Interfaces, INFORMS, vol. 35(6), pages 483-496, December.
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    1. Jianzhe Zhen & Dick Hertog, 2017. "Centered solutions for uncertain linear equations," Computational Management Science, Springer, vol. 14(4), pages 585-610, October.
    2. Clive B Beggs & Alexander J Bond & Stacey Emmonds & Ben Jones, 2019. "Hidden dynamics of soccer leagues: The predictive ‘power’ of partial standings," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-28, December.
    3. S. S. Dabadghao & B. Vaziri, 2022. "The predictive power of popular sports ranking methods in the NFL, NBA, and NHL," Operational Research, Springer, vol. 22(3), pages 2767-2783, July.
    4. Zhen, Jianzhe & den Hertog, Dick, 2016. "Centered Solutions for Uncertain Linear Equations (revision of CentER DP 2015-044)," Other publications TiSEM 297fa3b1-5290-48b5-bbc0-0, Tilburg University, School of Economics and Management.
    5. Zhen, Jianzhe & den Hertog, Dick, 2015. "Robust Solutions for Systems of Uncertain Linear Equations," Discussion Paper 2015-044, Tilburg University, Center for Economic Research.
    6. Zhen, Jianzhe & den Hertog, Dick, 2015. "Robust Solutions for Systems of Uncertain Linear Equations," Other publications TiSEM d072bdb9-4168-4522-90d8-1, Tilburg University, School of Economics and Management.
    7. Zhen, Jianzhe & den Hertog, Dick, 2016. "Centered Solutions for Uncertain Linear Equations (revision of CentER DP 2015-044)," Discussion Paper 2016-048, Tilburg University, Center for Economic Research.
    8. Barrow Daniel & Drayer Ian & Elliott Peter & Gaut Garren & Osting Braxton, 2013. "Ranking rankings: an empirical comparison of the predictive power of sports ranking methods," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 9(2), pages 187-202, June.

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