The following is taken mostly from Bassett(1997) and Glickman and Stern (1998)
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 downweighting 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 downweighted 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 Association. 93.
Harville, D. (1977), "The use of Linear-Model Methodolgy to Rate
High School or College Football Teams," Journal of the American
Statistical Association. 72.
------ (1980), "Predictions for National Football League Games with
Linear Model Methodology," Journal of the American
Statistical Association. 75.
------ (2003), "The Selection or Seeding of College Basketball or
Football Teams for Postseason Competition," Journal of the American
Statistical Association, 98.
Harvill, D. and Smith, M. (1994), "The HOme-Court Advantage: Hop Large
Is It, and Does It Vary From Team to Team?," The American Statistician, 48.
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.
------ (1980), "Improved Least Squares Football Basketball, and Soccer
Predictions", IEEE Transactions on Systems, Man, and Cybernetics,
SMC-10(2).
Stern, H. (1992), "On the Probability of Winning a Football Game,"
The American Statistician, 45.
------ . (1992), "Who's Number One?-Rating Football Teams," in
Proceedings of the Section on Statistics in Sport, 1992.
------ (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.
ADDITIONS ADDED 1-17-05, MAY INCLUDE SOME OF THE ABOVE
1. Harville, David (2002), ``College football: a modified least squares approach to rating and prediction'',
ASA Proceedings of the Joint Statistical Meetings, 1383-1390
2. Rothman, David (2002), ``My contribution to the BCS: yes, Virginia, there is a social welfare function in college football'',
ASA Proceedings of the Joint Statistical Meetings, 2990-
3. Berry, Scott M. (2002), ``Turn! Turn! Turn!'', Chance, New Directions for Statistics and Computers, 15 (1) , 41-46
4. Lock, Robin (2002), ``What's the score in the NFL?'', Stats. The Magazine for Students of Statistics, 0 (33) , 25-27
5. Crowder, Martin , Dixon, Mark , Ledford, Anthony , and Robinson, Mike (2002), ``Dynamic modelling and prediction of
English Football League matches for betting'', The Statistician, 51 (2) , 157-168
6. Kopoci\'{n}ski, Boles\l{}aw (2001), ``Components of the game result in a football league'', Applicationes Mathematicae
[Formerly: @J(ZastApMa)], 28 (1) , 55-72
7. Willoughby, Keith A. (2001), ``The return of a missed field goal in Canadian football'', Chance, New Directions for
Statistics and Computers, 14 (3) , 29-33
8. Lebovic, James H. , and Sigelman, Lee (2001), ``The forecasting accuracy and determinants of football rankings'',
International Journal of Forecasting, 17 (1) , 105-120
9. Glickman, Mark E. (2001), ``Dynamic paired comparison models with stochastic variances'',
Journal of Applied Statistics, 28 (6) , 673-689
10. McFarland, H. Richard, III , and Richards, Donald St. P. (2001), ``Exact misclassification probabilities for
plug-in normal quadratic discriminant functions. I. The equal-means case'', Journal of Multivariate Analysis, 77 (1) , 21-53
11. Harville, David A. (2000), ``The selection and/or seeding of college basketball or football teams for
postseason competition: A statistician's perspective'', ASA Proceedings of the Section on Statistics in Sports, 1-18
12. Tufte, David (2000), ``What can we learn from resampling a football game?'',
ASA Proceedings of the Section on Statistics in Sports, 35-44
13. Gill, Paramjit S. (2000), ``Late-game reversals in professional basketball, football, and hockey'',
The American Statistician, 54 (2) , 94-99
14. Sackrowitz, Harold (2000), ``Refining the point(s)-after-touchdown decision'', Chance, New Directions for
Statistics and Computers, 13 (3) , 29-34
15. Forrest, David , and Simmons, Robert (2000), ``Forecasting sport: The behaviour and performance of football tipsters'',
International Journal of Forecasting, 16 (3) , 317-331
16. Cain, Michael , Law, David , and Peel, David A. (2000), ``Testing for statistical and market efficiency when forecast
errors are non-normal: The NFL betting market revisited'', Journal of Forecasting, 19 (7) , 575-586
17. Carmichael, F. , Thomas, D. , and Ward, R. (2000), ``Team performance: The case of English Premiership football'', \
Managerial and Decision Economics, 21 , 31-45
18. Hadley, L. , Poitras, M. , Ruggiero, J. , and Knowles, S. (2000), ``Performance evaluation of National Football
League teams'', Managerial and Decision Economics, 21 , 63-70
19. Forrest, David , and Simmons, Robert (2000), ``Making up the results: The work of the Football Pools Panel,
1963-1997'', The Statistician, 49 (2) , 253-260
20. Carlin, Bradley P. , and Stern, Hal S. (1999), ``Designing a college football playoff system'', Chance,
New Directions for Statistics and Computers, 12 (3) , 21-26
21. Snyder, Scott , Subramanian, Neepa , and Sun, Jiayang (1998), ``Discrimination and clustering -- Can we learn
from this college football data set?'', ASA Proceedings of the Section on Statistics in Sports, 40-45
22. Stern, Hal S. (1998), ``Football strategy: Go for it!'', Chance, New Directions for Statistics and Computers, 11 (3) , 20-24
23. Glickman, Mark E. , and Stern, Hal S. (1998), ``A state-space model for National Football League scores'',
Journal of the American Statistical Association, 93 , 25-35
24. Dixon, Mark J. , and Robinson, Michael E. (1998), ``A birth process model for association football matches'',
The Statistician, 47 , 523-538
25. Mosteller, Frederick (1997), ``Lessons from sports statistics'', The American Statistician, 51 , 305-310
26. Dixon, Mark J. , and Coles, Stuart G. (1997), ``Modelling association football scores and inefficiencies in the
football betting market'', Applied Statistics, 46 , 265-280
27. Wright, Daniel B. (1997), ``Football standings and measurement levels'', The Statistician, 46 , 105-110
28. Samuelson, Andy , and Samuelson, Douglas A. (1996), ``Will the new bowl structure settle picking the number
1 college football team?'', ASA Proceedings of the Section on Statistics in Sports, 28-33
29. Samuelson, Andy , and Samuelson, Douglas A. (1995), ``How would a chess coach choose the number 1 college football team?'',
ASA Proceedings of the Section on Statistics in Sports, 45-49
30. Stern, Hal S. (1995), ``Who's number 1 in college football? \dots\ And how might we decide?'', Chance, New Directions
for Statistics and Computers, 8 (3) , 7-14
31. Dobson, S. M. , and Goddard, J. A. (1995), ``The demand for professional league football in England and Wales, 1925-92'',
The Statistician, 44 , 259-277
32. Phillips, Haynes , and Wilburn, Denise Phillips (1994), ``Consistency and predictability of football results'',
Chance, New Directions for Statistics and Computers, 7 (3) , 38-41
33. Craig, Lee A. , and Hall, Alastair R. (1994), ``Trying out for the team: Do exhibitions matter? Evidence from the
National Football League'', Journal of the American Statistical Association, 89 , 1091-1099
34. DeStefano, Joseph , Doyle, Peter , and Snell, J. Laurie (1993), ``The evil twin strategy for a football pool'',
The American Mathematical Monthly, 100 , 341-343
35. Barnett, V. , and Hilditch, S. (1993), ``The effect of an artificial pitch surface on home team performance in football (soccer)'',
Journal of the Royal Statistical Society, Series A, General, 156 , 39-50
36. Kozlov, S. M. , Pitman, J. B. , and Yor, M. (1993), ``Wiener football'', Theory of Probability and its Applications , 550-553
37. Stern, Hal (1992), ``Who's number one? -- Rating football teams'', ASA Proceedings of the Section on Statistics in Sports, 1-6
38. Stefani, Raymond , and Clarke, Stephen (1992), ``Predictions and home advantage for Australian rules football'',
Journal of Applied Statistics, 19 , 251-261
39. Stern, Hal (1991), ``On the probability of winning a football game'', The American Statistician, 45 , 179-183
40. Freeman, G. H. (1989), ``Comments on ``Discriminating between the Poisson and negative binomial distributions:
An application to goal scoring in association football'' (V15 p347-354)'', Journal of Applied Statistics, 16 , 437-438
41. Cooil, Bruce , and Day, Theodore (1988), ``Beating the wagering line for National Football League games'',
ASA Proceedings of the Business and Economic Statistics Section, 314-318
42. Baxter, Mike , and Stevenson, Richard (1988), ``Discriminating between the Poisson and negative binomial
distributions: An application to goal scoring in association football (Com: V16 p437-438)'', Journal of Applied Statistics, 15 , 347-354
43. Stefani, Raymond T. (1987), ``Applications of statistical methods to American football'',
Journal of Applied Statistics, 14 , 61-73
44. Berry, Donald A. , and Berry, Timothy D. (1985), ``The probability of a field goal: Rating kickers (Corr: 85V39 p327)'',
The American Statistician, 39 , 152-155
45. Croucher, John S. (1984), ``The effect of changing competition points in the English football league'',
Teaching Statistics, 6 , 39-42
46. Stephenson, H. W. (1983), ``Using football to teach probability'', Mathematics Teacher, 76 , 585-587
47. Stefani, Raymond T. (1983), ``Observed betting tendencies and suggested betting strategies for European football pools'',
The Statistician, 32 , 319-329
48. Kenkel, James L. , and Kitchen, John H. (1982), ``Can profits be earned by betting on pro football games'',
ASA Proceedings of the Section on Statistical Education, 128-130
49. Maher, M. J. (1982), ``Modelling association football scores'', Statistica Neerlandica, 36 , 109-118
50. Pendlebury, Chris (1982), ``An unusual weekend for second division football'', Teaching Statistics, 4 , 26-27
51. Gallian, Joseph A. (1981), ``An optimal football strategy'', Two Year College Mathematics Journal, 12 , 330-331
52. Stefani, Raymond T. (1980), ``Improved least squares football, basketball, and soccer predictions'',
IEEE Transactions on Systems, Man, Cybernetics, 10 , 116-123
53. Harville, David (1980), ``Predictions for National Football League games via linear-model methodology'',
Journal of the American Statistical Association, 75 , 516-524
54. Tsai, Yung-mei , and Sigelman, Lee (1980), ``Stratification and mobility in big-time college football:
A vacancy chain analysis'', Sociological Methods & Research, 8 , 487-497
55. Canavos, George C. , and Koutrouvelis, Ioannis A. (1979), ``Scoring in the National Football League: A comparison
of the past and present'', ASA Proceedings of the Business and Economic Statistics Section, 407-410
56. Shiffler, Ronald E. , and Lackritz, James R. (1979), ``A teacher's aid for the binomial probability distribution:
A college football contest'', ASA Proceedings of the Section on Statistical Education, 59-60
57. Croucher, J. S. (1979), ``A statistical analysis of rugby league football scores'', Interactive Statistics, 137-145
58. Harville, David A. (1978), ``Football ratings and predictions via linear models (Com: p87-88)'',
ASA Proceedings of the Social Statistics Section, 74-82
59. Goode, Bud (1978), ``Relevant variables in professional football'',
ASA Proceedings of the Social Statistics Section, 83-86
60. Morris, Carl (1978), ``Comments on ``Football ratings and predictions'''',
ASA Proceedings of the Social Statistics Section, 87-88
61. Stefani, R. T. (1977), ``Football and basketball predictions using least squares'',
IEEE Transactions on Systems, Man, Cybernetics, 7 , 117-120
62. Harville, David (1977), ``The use of linear-model methodology to rate high school or college football teams'',
Journal of the American Statistical Association, 72 , 278-289
63. Revo, Larry T. (1976), ``Predicting the outcome of football games or can you make a living working one day a week'',
ASA Proceedings of the Social Statistics Section, 709-710
64. Hart, R. A. , Hutton, J. , and Sharot, T. (1975), ``A statistical analysis of association football attendances
(Corr: 75V24 p308)'', Applied Statistics, 24 , 17-27
65. Hill, I. D. (1974), ``Association football and statistical inference'', Applied Statistics, 23 , 203-208
66. Pollard, R. (1973), ``Collegiate football scores and the negative binomial distribution'',
Journal of the American Statistical Association, 68 , 351-352
67. Mosteller, Frederick (1970), ``Collegiate football scores, U.S.A.'',
Journal of the American Statistical Association, 65 , 35-48
68. Reep, C. , and Benjamin, B. (1968), ``Skill and chance in association football'',
Journal of the Royal Statistical Society, Series A, General, 131 , 581-585
69. Porter, Richard C. (1967), ``Extra-point strategy in football'', The American Statistician, 21 (5) , 14-15