Bibliography on College Football Ranking Systems

Contributions are welcome. Send them by e-mail to: dwilson@engr.wisc.edu Many of these articles are available on-line at JSTOR (Journal Storage) through the member institutions. Some others are available through CiteSeer.IST.psu.edu. Some others are from Project Euclid.
Ali, I., W. Cook, and M. Kress "On the minimum violations ranking of a
   tournament" Management Science 32:6 1986 660-672
                                        Soren P. Sorensen   Nov 12 '99

Amoako-Adu, B., H. Marmer, and J. Yagil "The Effeciency of Certain Speculative
   Markets and Gambler Behavior" Journal of Economics and Business 37 1985
                                        Soren P. Sorensen   Nov 12 '99

Anderson, L.B., "Paired Comparisons," Chapter 17 in Operations Research
   and the Public Sector, Volume 6 of Handbooks in Operations Research and
   Management Science, S. M. Pollock, M. H. Rothkopf, and A. Barnett, eds.,
   Amsterdam, London, New York, Tokyo: North-Holland, 1994, 585-620
                                        Lowell Anderson   Sep 4 '01

Annis, David H. and Bruce A. Craig (2005) "Hybrid Paired Comparison
   Analysis, with Applications to the Ranking of College Football Teams,"
   Journal of Quantitative Analysis in Sports: Vol. 1  : Iss. 1, Article 3.
                                        Christopher M. Rump   Jan 9 '07

Annis, David H. "Dimension Reduction for Hybrid Paired Comparison Models"
   Journal of Quantitative Analysis in Sports 3:2, April 2007
                                        John Trono   May 1, 2007

Annis, David H. and Samuel S. Wu "A Comparison of Potential Playoff
   Systems for NCAA I-A Football"
                                        Jim Ashburn   May 25, 2007

Ashburn, James and Paul Colvert "A Bayesian Mean-Value Approach
   with a Self-Consistently Determined Prior Distribution for the Ranking
   of College Football Teams" Feb. 2006
                                        Jim Ashburn   Mar 24 '06

Bassett, Gilbert W. "Robust Sports Ratings Based on Least Absolute
   Errors." The American Statistician.  May 1997:1-7
                                        Kenneth Massey   Sep 10 '99

Bethel, Roy  "A Solution to the Unequal Strength of Schedule Problem."  2005.
   NFL Results.

Boand, William F.  "Azzi Ratem."  1930.  Booklet. and "Azzi Ratem - Boand 
   Football Ranking System."  1950.  Booklet.

   An explanation of a mathematical rating system.  Ratings of leading
   teams.
                                        Anton Grobani   1975
   
Boand, William F.  "National Football Champions."  1941.  Booklet.

   Facts, ratings since 1924.
                                        Anton Grobani   1975
   
Boginski, Vladimir, Sergiy Butenko and Panos M. Pardalos  "Matrix-based
   Methods for College Football Rankings" 2003
                                        Jim Ashburn   Nov 23 '05

Bradley, R. A. and Terry, M. E.  "Rank analysis of incomplete block designs.
   I.  The method of paired comparisons", Biometrika (volume 39, 1952)
   pages 324-45.

   The idea was first proposed (I've been told) in
   Zermelo, E. (1929).  Die Berechnung der Turnier-Ergebnisse
   als ein Maximumproblem der Wahrscheinlichkeitsrechnung.
   Mathematische Zeitschrift 29, 436-60.
                                        David Rothman    Dec 2 '98

Bühlmann, Hans and Peter J. Huber,  "Pairwise Comparison and Ranking in
   Tournaments," The Annals of Mathematical Statistics, Received Oct. 1962,
   501-510.
                                        Jim Ashborn   Apr 24 '09

Callaghan, Thomas, Mason A. Porter, and Peter J. Mucha  "Random Walker Ranking
   for NCAA Division I-A Football", Georgia Institute of Technology 2003

   Thomas Callaghan (an undergrad), Mason Porter (a postdoc), and I have
   recently studied a relatively simple-to-explain ranking scheme, in 
   terms of individual idealized voters changing their minds according 
   to the win/loss outcomes of games. It may not be mathematically 
   completely novel (in particular, it is a subclass of the "direct 
   methods" described in Keener's SIAM Review article), but we believe 
   the interpretation in terms of these model voters is new.
                                        Peter J. Mucha   Nov 1 '03

Callaghan, Thomas, Peter J. Mucha, and Mason A. Porter  "The Bowl
   Championship Series: A Mathematical Review" Sept. 2004 Notices of the
   AMS 887-893
                                        Jim Ashburn   Nov 23 '05

Cassady CR, Maillart LM, Salman S "Ranking sports teams: A customizable
   quadratic assignment approach" INTERFACES 35 (6): 497-510 NOV-DEC 2005
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Chebotarev PY, Shamis E "Preference fusion when the number of
   alternatives exceeds two: indirect scoring procedures" JOURNAL OF THE
   FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 336 (2):
   205-226 MAR 1999
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Conner, G. R. and C. P. Grant "An Extention of Zemelo's Model for Ranking by
   Paired Comparison" Euro. Jnl of Applied Mathematics, 11:3, June 2000 225-247
                                        Jim Ashburn   Jan 14 '02

Cook, W., I. Golan and M. Kress "Heuristics for ranking players in round robin
   tournaments" Computers and Operations Research 15:2 1988 135-144
                                        Soren P. Sorensen   Nov 12 '99

Dickinson, Frank G. "Dickinson's Football Ratings."  1941.  Booklet.
   An explanation of his rating system, with team ratings from 1924-40.
                                        Anton Grobani   1975

Eaton, Morris L., "Some Optimum Properties of Ranking Procedures,"
   The Annals of Mathematical Statistics, Received July 1966, 124-137.
                                        Jim Ashburn   Apr 24 '09

Elo, Arpad E., The Rating of Chess Players Past and Present 2nd Ed. ,
  New York, Arco Pub., 1986
                                        Kenneth Massey   Feb 9 '00

Fahrmeir, L. and Tutz, G. "Dynamic Stochastic Models for Time-Dependent
   Ordered Pair-Comparison Systems," Journal of the American Statistical
   Association, 89, 1438-49 (1994)
                                        Peter R. Wolfe   Dec 4 '00

Fainmesser, I., Fershtman, C. and Gandal, N. "A Consistent Weighted Ranking
  Scheme with an Application to NCAA College Football Rankings," 2009.
                                        Neil Gandal      May 2 '09

Farmer, Christopher J.  "Probabilistic Modelling in Multi-Competitor
   Games"  Univ. of Edinburgh  2003
                                        Jim Ashburn   Nov 23 '05

Fluek, John A. and James F. Korsh,  "A Generalized Approach to Maximum
   Likelihood Paird Comparison Ranking," The Annals of Statistics, 3(4), 1975
   846-861.
                                        Jim Ashburn   Apr 24 '09

Ford, LR Jr.  "Solution of a Ranking Problem from Binary Comparisons."
   American Mathematical Monthly, 64(8) part 2, 1957, p. 28-33.
                                        Peter R. Wolfe   Sep 16 '01

Gimpel, Kevin "Beating the NFL Football Point Spread"
                                        Jim Ashburn   Dec 19 '07

Glickman, Mark E. "Dynamic Paired Comparison Models with Stochastic Variances"
                                        Jim Ashburn   Jan 14 '02

Glickman, Mark E. "Parameter Estimation in Large Dynamic Paired Comparison
   Experiments"
                                        Jim Ashburn   Jan 14 '02

Glickman, M. E., and H. Stern "A State-Space Model for National Football
   League Scores" Journal of the American Statistical Association 93 1998
                                        Soren P. Sorensen   Nov 12 '99

Goddard, S. "Ranking in tournaments and group decission making" Management
   Science 29:12 1983 1384-1392
                                        Soren P. Sorensen   Nov 12 '99

Grafton, Clive.  "Junior College Football Rating Systems."  Statistics
   Bureau of the National Junior College Athletic Association.  1955.  Booklet.

   The development of the junior college football rating systems and
   a comparison between the Williamson and Gridiron Index Systems.
                                        Anton Grobani   1975

Grobani, Anton.  "Guide to Football Literature", Gale Research Company,
   Detroit, 1975.

   The entries credited here to Anton Grobani are from pages 177-178
   of this book.
                                        Eric M. Kemp   Oct 10 '99

Glickman, M.E. and Stern, H.S. "A State-Space Model for National
   Football League Scores," Journal of the American Statistical
   Association, 93, 25-35 (1998)
                                        Peter R. Wolfe   Dec 4 '00

Gupta, Shanti S. and Milton Sobel.  "On a Statistic which arises in
   Selection and Ranking Problems."  The Annals of Mathematical Statistics,
   pp. 957-967 (1957)
                                        Jim Ashburn   May 19 '10

Harville, David.  "The Use of Linear-Model Methodology to Rate High
   School or College Football Teams."  Journal of the American Statistical
   Association.  June 1977: 278-289.
                                        Kenneth Massey   Sep 10 '99

Harville, David.  "Predictions for NFL Games Via Linear-Model
   Methodology."  Journal of the American Statistical Association.
   Sep. 1980: 516-524.
                                        Kenneth Massey   Sep 10 '99

Harville DA and Smith MH, "The Home-Court Advantage: How Large and Does
   it Vary from Team to Team?". The American Statistician Vol. 48 (1),
   p.22-28  (1994).
                                        Peter R. Wolfe   Sep 14 '99

Harville, David.  "College Football: A Modified Least-Squares Approach to
   Rating and Prediction."  American Statistical Proceedings of the
   Section on Statistics in Sports, 2001.  [Available Spring 2002.]
                                        Peter R. Wolfe   Sep 16 '01

Harville, David.  "The Selection and/or Seeding of College Basketball or
   Football Teams for Postseason Competition: a Statistician's
   Perspective."  American Statistical Proceedings of the Section on
   Statistics in Sports, 2000, p. 1-18.
                                        Peter R. Wolfe   Sep 16 '01

Harville DA "The selection or seeding of college basketball or football
   teams for" postseason competition JOURNAL OF THE AMERICAN STATISTICAL
   ASSOCIATION 98 (461): 17-27 MAR 2003
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Helms Athletic Foundation.  "National Football Champions"  1942.  Booklet.

   The record of each team picked by Helms as the national champion
   from 1883-1941.  Sketches of great coaches.
                                        Anton Grobani   1975

Hochbaum, Dorit S. "Ranking Sports Teams and the Inverse Equal Paths Problem."
    Department of Industrial Engineering and Operations Research and 
    Walter A. Haas School of Business, University of California, Berkeley
                                        Jim Ashburn   May 19, 2010

Houlgate, Deke.  "Ten Thousand and One Scores."  1938.  Paperbound.

   Teams ratings based on scores of major games from 1928-37.
                                        Anton Grobani   1975

Huang, Tzu-Kuo and Ruby C. Weng and Chih-Jen Lin "Generalized
   Bradley-Terry Models and Multi-Class Probability Estimates"
   Journal of Machine Learning Research 7 (2006) 85-115
                                        Jim Ashburn   May 25, 2007

Huber, Peter J., "Pairwise Comparison and Ranking: Optimum Properties of
   the Row Sum Procedure," The Annals of Mathematical Statistics, Received
   Nov. 1962, p. 511-520.
                                        Jim Asburn   April 24 '09

Jech, Thomas. "The Ranking of Incomplete Tournaments: A Mathematician's
   Guide to Popular Sports."  American Mathematical Monthly, 90(4), 1983,
   p. 246-66.
                                        Peter R. Wolfe   Sep 16 '01

Karlin, Samuel, Mathematical Methods & Theory in Games, Programming, &
  Economics, Dover Publications, March 1992
                                        Kenneth Massey   Feb 9 '00

Karlis, D. and I. Nizoufras "Statistical Modelling for Soccer Games:
   the Greek League" 1998
                                        Jim Ashburn   Jan 14 '02

Keener, James P., "The Perron-Frobenius Theorem and the Rating of Football
   Teams", SIAM Review (volume 35, issue 1, March 1993) pages 80-93.

   This reviews the author's pet rating systems, one of which includes a
   system formulated on a least likelihood principle using the same formula
   as Rothman does, but with a slightly different grading function.
   
   The use of the least likelihood principle with the form A/(A+B), along
   with iteration methods for calculating the numbers is actually due to
   Zermelo, from 1926.
   
   The author also mentioned the 'retrodiction criterion' (fitting the past
   whereas the 'prediction criterion' fits the future) and assessed his
   rating systems according to it.  All of this was done only for Division I
   games for 1989.
   
   It wouldn't be too hard to write a paper updating the situation,
   particularly assessing the different rating methods out there according to
   how well they do on all 680-plus teams and 3500 games, instead of just
   Division I-A.  The ability to separate out the Division I-A, I-AA, II and
   III teams is a critical test for any rating method.  I suspect that 2 or 3
   of the 4 methods the author describes will fail the test.
   
   One of them can't be used at all since it breaks down when there's more
   than one weakly connected component.  This is a similar problem that
   Rothman's rating method would experience if it were converted to a
   win's-only rating method (which is why he uses point margins to a limited
   extent).

   The author does, by the way, present enough detail for anyone interested
   (with enough computing power) to carry out the ratings computation.
                                        Mark Hopkins   Dec 19 '97

Kuonen, Diego "Statistical Models for Knock-out Soccer Tournaments"
   Winter 1996/97
                                        Jim Ashburn   Jan 14 '02

Knorr-Held, L. "Dynamic Rating of Sports Teams," The Statistician, 49,
   261-76 (2000)
                                        Peter R. Wolfe   Dec 4 '00

Leake, RJ. A Method for Ranking Teams: With an Application to College
   Football. In Management Science in Sports, ed. Machol RE et al.
   Amsterdam: North-Holland Publishing Co., 1976. p. 27-46.
                                        Peter R. Wolfe   Jun 12 '99

Lebovic JH, Sigelman L "The forecasting accuracy and determinants of
   football rankings" INTERNATIONAL JOURNAL OF FORECASTING 17 (1):
   105-120 JAN-MAR 2001
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Martinich, Joseph "College Football Rankings: Do Computers Know Best?"
   Interfaces 32(5) pp. 85-94 SEP-OCT 2002
 
   An analysis of the systems used in the 2001 BCS.
                                        Frank Alder   Aug 7 '03

McFarland, William N.  "An Examination of Football Scores."  Waverly
   Press.  1932.

   A rating system devised for game scores.  Ratings of leading teams.
                                        Anton Grobani   1975

Mease, David  "A Penalized Maximum Likelihood Approach for the Ranking
   of College Football Teams Independent of Victory Margins"
   Department of Statistics, Univerisity of Michigan, Ann Arbor, MI
   The American Statistician, Nov. 2003.

Menke, Joshua and Tony Martinez "A Bradley-Terry Artificial Neural Network
   Model for Individual Ratings in Group Competitions" Computer Science
   Departments, Brigham Young University 2006

Mosteller, Frederick.  "Collegiate Football Scores, U.S.A." Journal of
   the American Statistical Association. 65, pp.35-48 (1970).

   This paper is not completely on topic, but it is a very interesting
   analysis of the data contained in college football scores, written by
   the grand old man of the Department of Statistics at Harvard College.
                                        Peter R. Wolfe   Sep 19 '99

Mundfrom DJ, Heiny RL, Hoff S "Power ratings for NCAA division II
   football" COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
   34 (3): 811-826 2005
                (from Science Citation) Christopher M. Rump   Jan 9 '07

NCAA. NCAA Football Statistics including links to the Football Record Books.

Nutting, Andrew "The Marginal Accuracy of Weekly College Football
  Rankings: Are There Diminishing Returns?" September 2006
                                        Andrew Nutting   Apr 25 '07

Palomino, F., L. Rigotti and A. Rustichini "Skill, Strategy and Passion:
   an Empirical Analysis of Soccer" 1998
                                        Jim Ashburn   Jan 14 '02

Park, Juyong and M. E. J. Newman "Network-based ranking system for U.S.
   college football" Journal of Statistical Physics, P10014 (2005)
   and the talk at NetSci 06
                                        Juyong Park   Aug 24 '06

Qin, Dennis "Predictions and Rankings in College Football." 2009
                                        Jim Ashburn   May 19 '10

Reid, Michael B. "Least Squares Model for Predicting College Football
   Scores" Univ. of Utah 2003
                                        Jim Ashburn   Nov 23 '05

Rue, H. "A Fast and Exact Simulation Algorithm for General Gaussian Markov
   Random Fields" 1999
                                        Jim Ashburn   Jan 14 '02

Rue, H. and 0. Salversen "Prediction and Retrospective Analysis of Soccer
   Matches in a League" 1999
                                        Jim Ashburn   Jan 14 '02

Singh, Jagbir and Thompson WA Jr.  "A Treatment of Ties in Paired
   Comparisons." The Annals of Mathematical Statistics, 39(6), 1988,
   p. 2002-15.
                                        Peter R. Wolfe   Sep 16 '01

Sinuany-Stern Z "Ranking of Sports Teams via the AHP" JOURNAL OF THE
   OPERATIONAL RESEARCH SOCIETY 39 (7): 661-667 JUL 1988
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Smith, Warren D. "Rating Systems for GamePlayers, and Learning"
   NEC July 1994.
                                        Jim Ashburn   Jan 14 '02

Srivastava, M.S. and J. Ogilvie.  "The Performance of some Sequential
   Procedures for a Ranking Problem."  The Annals of Mathematical Statistics
   39:3 pp. 1040-1047 (1968)
                                        Jim Ashburn   May 19 '10

Stefani, Raymond T.  "Football and Basketball Predictions Using Least
   Squares" IEEE Transactions on Systems, Man, and Cybernetics 7 1977
                                        Soren P. Sorensen   Nov 12 '99

Stefani, Raymond T.  "Improved Least Squares Football, Basketball, and
   Soccer Predictions."  IEEE Transactions on Systems, Man, an
   Cybernetics.  Feb 1980: 116-123
                                        Kenneth Massey   Sep 10 '99

Stern, Hal.  "A Continuum of paired comparisons models."  Biometrika.
   77(2), pp.265-73 (1990).
                                        Peter R. Wolfe   Sep 19 '99

Stern, Hal.  "On the Probability of Winning a Football Game."  The
   American Statistician.  August 1991:179-183.
                                        Kenneth Massey   Sep 10 '99

Stern, Hal.  "Who's Number one? - Rating Football Teams" in Proceedings
   of the Section on Statistics in Sports, 1992, p. 1-6
                                        Peter R. Wolfe   Sep 17 '99

Stern, Hal.  "Who's Number 1 in College Football?.. And How Might We
   Decide?"  Chance, Summer, 1995:7-14.
                                        Kenneth Massey   Sep 10 '99

Stern, Hal.  "Statistics in Sports"  1997 Chance Lecture Series
   Go to http://www.dartmouth.edu/~chance/ChanceLecture/contents.msri.html
   and click on "Statistics in Sports" (requires RealPlayer).

   I've found a neat audio/video recording of a 1997 lecture by
   Hal Stern on "Probability and Statistics in Sports," complete with slides.
   The ~50 min lecture covers several sports but includes a discussion on
   ranking college football teams using least-squares.  Stern includes a
   brief discussion of the 1997 Sagarin rankings, which he shows to be highly
   correlated with least-squares.  At the conclusion of the talk, Stern
   presents several references for useful publications on sports statistics.
      Ladany and Machol, 1977:  Optimal Strategies in Sports.
      Machol, Ladany, and Morrison, 1976:  Management Science in Sports.
      Bennett:  Statistics in Sport.
      Chance Magazine (column beginning in Vol. 10)
                                        Eric M. Kemp   May 18 '02

Stern, Hal S.  "American Football" Iowa State University, Dec. 24, 1997
                                        Jim Ashburn   Dec 19, '07

Stern, H.S., and Mock, B. "College Basketball Upsets: Will a 16-seed
   Ever Beat a 1-seed?"  Chance, 11, 26-31 (1998)
                                        Peter R. Wolfe   Dec 4 '00

Stern HS "Statistics and the college football championship" AMERICAN
   STATISTICIAN 58 (3): 179-185 AUG 2004 (with several discussion papers
   and a followup reply)
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Stern, H.S. (2006) "In Favor of A Quantitative Boycott of the Bowl
   Championship Series," Journal of Quantitative Analysis in Sports:
   Vol. 2 : Iss. 1, Article 4.
                                        Christopher M. Rump   Jan 9 '07

Stone, Daniel F. "Testing Bayesian Updating with the AP Top 25"
   John Hopkins University, Oct. 2007
                                        Jim Ashburn   Dec 19, '07

Thomas, I.B.  "Method of Ranking College Football Teams."  Allen, Lane
   and Scott.  1922.  Booklet.

   A point system, using won and loss records.  Results for 1921.
                                        Anton Grobani   1975

Thompson, Mark.  "On Any Given Sunday: Fair Competitor Orderings with
   Maximum Likelihood Methods."  Journal of the American Statistical
   Association. 70, pp. 536-41 (1975).
                                        Peter R. Wolfe   Sep 19 '99

Tong, Y. L.  "An Adaptive Solution to Ranking and Selection Problems."
   The Annals of Statistics 6:3 pp.658-672 (1978)
                                        Jim Ashburn   May 19, 2010

Trono, John A.  "Applying the Overtake and Feedback Algorithm."
   Dr. Dobb's Journal 357, pp. 36-41 (Feb. 2004).
   The Overtake and Feedback (OAF) algorithm "home page"
                                        John A. Trono   Oct 27, '04

Trono, John A.  "An Effective Nonlinear Rewards-Based Ranking System"
   Journal of Quantitative Analysis in Sports 3:2, April 2007
                                        John A. Trono   May 1, '07

West, Brady T. and Madhur Lamsal. "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
                                        Jim Ashburn   May 19, 2010

Wilkins R "Electrical Networks and Sports Competition" ELECTRONICS AND
   POWER 29 (5): 414-418 1983
                (from Science Citation) Christopher M. Rump   Jan 9 '07

Wilson, R. L.  Ranking College Football Teams: A Neural Network Approach.
   Interfaces 25:4, 1995. p.44-59.
                                        Peter R. Wolfe   Jun 12 '99

Wilson, R. L. "The 'Real' Mythical College Football Champion" Operation
   Research / Management Science Today 1995 24-29
                                        Soren P. Sorensen   Nov 12 '99

Zuber, R. A., J. M. Gander, and B. D. Bowers. "Beating the Spread: Testing
   the Efficiency of the Gambling Market for National Football League Games"
   Journal of Political Economy 93 1985
                                        Soren P. Sorensen   Nov 12 '99