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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Steve Rigdon, PhD

CiteScore 2018: 1.67

SCImago Journal Rank (SJR) 2018: 0.587
Source Normalized Impact per Paper (SNIP) 2018: 1.970

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Volume 10, Issue 2


Volume 1 (2005)

An Oracle method to predict NFL games

Eduardo Cabral Balreira / Brian K. Miceli / Thomas Tegtmeyer
Published Online: 2014-03-27 | DOI: https://doi.org/10.1515/jqas-2013-0063


Multiple models are discussed for ranking teams in a league and introduce a new model called the Oracle method. This is a Markovovian method that can be customized to incorporate multiple team traits into its ranking. Using a foresight prediction of NFL game outcomes for the 2002–2013 seasons, it is shown that the Oracle method correctly picked 64.1% of the games under consideration, which is higher than any of the methods compared, including ESPN Power Rankings, Massey, Colley, and PageRank.

Keywords: foresight predictions; NFL; oracle; PageRank; rankings


  • Agresti, A. 2002. Categorical Data Analysis, Wiley Series in Probability and Statistics. Hoboken, New Jersey: Wiley-Interscience, 2nd edition.Google Scholar

  • Agresti, A. and D. B. Hitchcock. 2005. “Bayesian Inference for Categorical Data Analysis.” Statistical Methods and Applications 14:297–330.CrossrefGoogle Scholar

  • Bradley, R. A. and M. E. Terry. 1952. “Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons.” Biometrika 39:324–345.Google Scholar

  • Brin, S. and L. Page. 1998. “The Anatomy of a Large-Scale Hypertextual Web Search Engine.” Computer Networks ISDN Systems 30:107–117.Google Scholar

  • Callaghan, T., P. J. Mucha, and M. A. Porter. 2007. “Random Walker Ranking for NCAA Division I-A Football.” American Mathematical Monthly 114:761–777.Google Scholar

  • Colley, W. 2002. “Colley’s Bias Free College Football Ranking Method: The Colley Matrix Explained.” Retrieved January 10, 2014 from http://www.colleyrankings.com/matrate.pdf.

  • Constantine, P. G. and D. F. Gleich. 2010. “Random Alpha PageRank.” Internet Mathematics 6:189–236.Google Scholar

  • David, H. A. 1963. The Method of Paired Comparisons. New York: Hafner Publishing Company.Google Scholar

  • Easterbrook, G. 2008. “Time to Look Back on Some Horrible Predictions.” Retrieved January 10, 2014 from sports.espn.go.com/espn/page2/story?page=easterbrook/090210.Google Scholar

  • ESPN 2014. “NFL Power Rankings.” Retrieved January 10, 2014 from http://espn.go.com/nfl/powerrankings.

  • Ford, J. L. R. 1957. “Solution of a Ranking Problem from Binary Comparisons.” American Mathematical Monthly 64:28–33.CrossrefGoogle Scholar

  • Gleich, D. F. 2011. “Review of: Numerical algorithms for personalized search in self-organizing information networks by Sep Kamvar, Princeton University Press, 2010.” Linear Algebra and its Applications 435:908–909.Google Scholar

  • Horn, R. A. and C. R. Johnson. 1990. Matrix Analysis. New York, NY: Cambridge University Press.Google Scholar

  • Hunter, D. R. 2004. “MM Algorithms for Generalized Bradley-Terry Models.” The Annals of Statistics 32:384–406.Google Scholar

  • Keener, J. P. 1993. “The Perron-Frobenius Theorem and the Ranking of Football Teams.” SIAM Review 35:80–93.CrossrefGoogle Scholar

  • Langville, A. N. and C. D. Meyer. 2003. “Deeper Inside PageRank.” Internet Mathematics 1:257–380.Google Scholar

  • Langville, A. N. and C. D. Meyer. 2006. Google’s PageRank and Beyond: The Science of Search Engine Rankings. Princeton, NJ, USA: Princeton University Press.Google Scholar

  • Langville, A. N. and C. D. Meyer. 2012. Who’s #1?: The Science of Rating and Ranking. Princeton, NJ, USA: Princeton University Press.Google Scholar

  • Massey, K. 1997. “Statistical Models Applied to the Rating of Sports Teams.” Bachelor’s honors thesis, Bluefield College.Google Scholar

  • Page, L., S. Brin, R. Motwani, and T. Winograd. 1999. “The Pagerank Citation Ranking: Bringing Order to the Web.” Technical Report 1999–66, Stanford InfoLab.Google Scholar

  • Sports Reference, LLC. 2014. “Pro-Football-Reference.” Retrieved January 10, 2014 from http://www.pro-football-reference.com/.

  • Thurstone, L. L. 1927. “A Law of Comparative Judgment.” Psychological Review 34:273–286.CrossrefGoogle Scholar

  • Zermelo, E. 1929. “Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung.” Mathematische Zeitschrift 29:436–460.CrossrefGoogle Scholar

About the article

Corresponding author: Eduardo Cabral Balreira, Mathematics, Trinity University, One Trinity Place, San Antonio, TX 78212, USA, Tel.: +2109998243, e-mail:

Published Online: 2014-03-27

Published in Print: 2014-06-01

The method of Massey used for the BCS Rankings in college football is proprietary, and thus not publicly available. The method we discuss is the original idea of Massey (1997), which he developed for an honors thesis as an undergraduate at Bluefield College.

For this data, we compute the rating vector based on the algorithm and Matlab routine given in Hunter (2004).

In Langville and Meyer (2003), it is given that Google originally used α=0.85.

In Callaghan et al. (2007), the authors named their method as Random Walker Ranking. As that description may also fit other Markov methods, we refer to it as Biased Random Walker.

All the variations of PageRank we have tested, always promote T6 to the 2nd highest ranking.

All computations were performed using Matlab R2013a.

One could certainly argue that this addition of the Oracle node opens the possibility for a distortion of the rankings in some way, especially by artificially forcing connectedness early in season. However, the data supports that, at least for standard choices of the statistics—score differential, wins, etc.—incorporated into the up and down vectors, this does not happen.

Teams with identical ranks for all methods other than WH meet, on average, less than once per year in the weeks considered. In the WH method, teams with the same record meet, on average, 24 times per season in the weeks considered.

Citation Information: Journal of Quantitative Analysis in Sports, Volume 10, Issue 2, Pages 183–196, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2013-0063.

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