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Hybrid Paired Comparison Analysis, with Applications to the Ranking of College Football Teams

Author

Listed:
  • Annis David H.

    (Naval Postgraduate School)

  • Craig Bruce A.

    (Purdue University)

Abstract

Existing paired comparison models used for ranking football teams primarily focus on either wins and losses or points scored (either via each team's total or a margin of victory). While reasonable, each approach fails to produce satisfactory rankings in frequently arising situations due to its ignorance of additional data. We propose a new, hybrid model incorporating both wins and constituent scores and show that it outperforms its competitors and is robust against model mis-specification based on a series of simulation studies. We conclude by illustrating the method using the 2003-04 and 2004-05 college football seasons.

Suggested Citation

  • Annis David H. & Craig Bruce A., 2005. "Hybrid Paired Comparison Analysis, with Applications to the Ranking of College Football Teams," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 1(1), pages 1-33, October.
    • Handle: RePEc:bpj:jqsprt:v:1:y:2005:i:1:n:3
    DOI: 10.2202/1559-0410.1000
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    References listed on IDEAS

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    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. Mease D., 2003. "A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins," The American Statistician, American Statistical Association, vol. 57, pages 241-248, November.
    3. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations," Psychometrika, Springer;The Psychometric Society, vol. 16(1), pages 3-9, March.
    4. Stern, Hal S., 2004. "Statistics and the College Football Championship," The American Statistician, American Statistical Association, vol. 58, pages 179-185, August.
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    Cited by:

    1. Karl Andrew T., 2012. "The Sensitivity of College Football Rankings to Several Modeling Choices," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(3), pages 1-44, October.
    2. Lundh Torbjörn, 2006. "Which Ball is the Roundest? - A Suggested Tournament Stability Index," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 2(3), pages 1-23, July.
    3. Ermis Chelmis & Dimitrios Niklis & George Baourakis & Constantin Zopounidis, 2019. "Multiciteria evaluation of football clubs: the Greek Superleague," Operational Research, Springer, vol. 19(2), pages 585-614, June.
    4. West Brady T & Lamsal Madhur, 2008. "A New Application of Linear Modeling in the Prediction of College Football Bowl Outcomes and the Development of Team Ratings," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(3), pages 1-21, July.
    5. Murray Thomas A., 2017. "Ranking ultimate teams using a Bayesian score-augmented win-loss model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 13(2), pages 63-78, June.
    6. Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2014. "Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 146-162.
    7. Annis David H. & Davis J. Wade, 2008. "Linear Inference for Paired Comparisons," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(4), pages 1-14, October.

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