Overview of ranking literature from tbeck
Rating teams based on past performance has recieved some attention in
statistical literature dating back to the late 1970's. Stefani (1977) described
the rating problem, reviewed early sports rating systems, and estimated football
ratings using least squares. Stefani showed how the rating problem could be
posed in terms of the linear regression model, and proposed estimating the
ratings by least squares. At about the same time Harville (1977, 1980)
constructed ratings for sports teams based on maximum likelihood estimates in
which ratings were random variables. Stefani (1980) later showed how the
home-field advantage could be incorporated into the ratings model. Following an
approach suggested earlier by Leake (1976), the least squares ratings were
modified by Stern (1992) to account for the fact that blowout games would affect
the least squares estimates. He proposed down weighting large score differences,
and produced estimates of the relative strengths of NFL teams. Stern (1995) and
Wilson (1995) used least squares to statistically rate college football teams
and determine who was number one. Bassett (1997) proposed using least absolute
value regression as an alternative to down weighted least squares regression.
And recently Glickman and Stern (1998) used Markov Chain Monte Carlo methods to
develop a predictive model for NFL game scores. A number of authors have
examined the points spread as a predictor of game outcomes, including Amoako-Adu,
Marmer, and Yagil (1985), Stern (1991) and Zuber, Gander, and Bowers (1985).
Stern showed that modeling the score difference of a game to have a mean equal
to the point spread is empiracally justifiable.
- Amoako-Adu, B. Marmer, H. and Yagil, J. (1985), "The Effeciency of
Certain Speculative Markets and Gambler Behavior," Journal of Economics
and Business, 37.
- Bassett, G. W. (1997) "Robust Sports Ratings Based on Least Absolute
Errors," The American Statistician, 51(2).
- Glickman, M. E. and Stern, H. S. (1998), "A State-Space Model for
National Football League Scores," Journal of the American Statistical
- Harville, D. (1977), "The use of Linear-Model Methodolgy to Rate High
School or College Football Teams," Journal of the American Statistical
- Harville, D. (1980), "Predictions for National Football League Games
with Linear Model Methodology," Journal of the American Statistical
- Leake, R. J. (1976), "A Method for Ranking Teams with an Application
to 1974 College Football," Management Science in Sports, North Holland.
- Stefani, R. T. (1977), "Football and Basketball Predictions
Using Least Squares," IEEE Transactions on Systems, Man, and
Cybernetics, SMC 7.
- Stefani, R. T.(1980), "Improved Least Squares Football Basketball,
and Soccer Predictions", IEEE Transactions on Systems, Man, and
- Stern, H. (1992), "On the Probability of Winning a Football
Game," The American Statistician, 45.
- Stern, H . (1992), "Who's Number One?-Rating Football Teams," in
Proceedings of the Section on Statistics in Sport, 1992.
- Stern, H (1995), "Who's Number 1 in College Football?... and How
Might We Decide?," Chance, 8(3).
- Thompson, M. L. (1975), "On Any Given Sunday: Fair Competitor
Orderings with Maximum Likelihood Methods," Journal of the American
Statistical Association. 70.
- Wilson, R. L. (1995) "The 'Real' Mythical College Football
Champion," OR/MS Today.
- Zuber, R. A., Gander, J. M. and Bowers, B. D. (1985), "Beating the
Spread: Testing the Efficiency of the Gambling Market for National Football
League Games," Journal of Political Economy, 93.
Overview from David Wilson
Annontated Bibliography on Football Ranking Systems
So far this bibliography has 4 entries. Contributions are welcome. Send them
by e-mail to: firstname.lastname@example.org
- 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
- 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
- Keener, James P., "The Perron-Frobenius Theorem and the Rating of
Football Teams", SIAM Review (volume 35, issue 1, March 1993) pages
- 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
- 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
- The author does, by the way, present enough detail for anyone
interested (with enough computing power) to carry out the ratings
- Mark Hopkins Dec 19 '97
- Wilson, RL. Ranking College Football Teams: A Neural Network Approach.
Interfaces 25:4, 1995. p.44-59. Peter R. Wolfe Jun 12 '99