Minimum Violations (MinV)
College Football Ranking

MinV Ranking for the 2009 Season (FINAL)

At right are the rankings of all NCAA Division 1-A college football teams thru the games of January 7, 2010 (i.e., all bowl games) using MinV, a model developed by Jay Coleman of the University of North Florida. MinV generates a ranking that minimizes the number of game score violations -- that is, the number of times a game's winner is ranked behind the team it defeated.  In other words, MinV guarantees the ranking with the best retrodictive accuracy.

The ranking at right results in only 58 violations out of 714 Division 1-A games, or a minimum violation percentage of 8.12%. Stated otherwise, the ranking at right matches the results of 91.88% of the games played this season, which is the highest value possible. In addition to minimizing the total number of violations, the ranking this week minimizes the total weighted violations, where each violation is weighted by the victory margin. (In other words, the ranking shown violates the games in which the scores were as close as possible, as opposed to violating games in which the victory margins were larger.) The total weight (i.e., victory margins) of the violated games this week is 536 points. Finally, the ranking shown at right at least approximately matches the game score differences (the victory margins) as closely as mathematically possible, while exceeding neither the minimum number of violations nor the minimum weighted violations.  Due to the size of the problem (the number of games played thus far), MinV was not able to guarantee that the ranking shown is the one that optimally matches the victory margins.  However, the ranking shown is likely a reasonably close approximation.

A minimum violations ranking has never before been presented for college football (due in part to the extreme computational difficulty involved for a problem with 120 teams).  However, there are literally trillions of different rankings at any given point in time that would yield the same minimum number of violations; the ranking shown is only one of those.

"Minimizing Game Score Violations in College Football Rankings," an article describing MinV and its application to the 1994 through 2004 college football seasons, appears in the November-December 2005 issue of Interfaces, a journal of the Institute for Operations Research and the Management Sciences (INFORMS).

The final MinV ranking for the 2008 college football season can be found here.
The final MinV ranking for the 2007 college football season can be found here.
The final MinV ranking for the 2006 college football season can be found here.
The final MinV ranking for the 2005 college football season can be found here.
The final MinV ranking for the 2004 college football season can be found here.

The final MinV pre-NCAA Tournament ranking for college basketball in 2005 can be found here.

About the Author

Jay Coleman is the Richard deRaismes Kip Professor of Operations Management & Quantitative Methods in the Coggin College of Business at the University of North Florida.  His research with Allen Lynch (of Mercer University) on modeling the decisions of the NCAA Tournament Selection Committee, first published in Interfaces, has been featured by the Wall Street Journal, Forbes, Investor's Business Daily, the New York Times, the Associated Press, UPI, and USA Today, as well as over 50 other major media outlets, including CNN Headline News, the Sporting News, and CBS SportsLine.  More information about the NCAA Tournament model can be found at DanceCard.unf.edu. Related research by Coleman and Lynch on predicting NCAA Tournament game results, recently published in the Journal of Quantitative Analysis in Sports, has been featured by CNBC, CNN, ESPN The Magazine, the Associated Press, and Dow Jones Newswires, among others.

Dr. Coleman’s research with Ken Jennings and Frank McLaughlin on final offer arbitration in professional baseball has been published in Cal-Berkeley's Industrial Relations journal, and his research with Allen Lynch and Mike DuMond on voting behavior for the NBA MVP has been published in the Journal of Sports Economics. More information on the NBA MVP model can be found here.

Acknowledgements

The author is very grateful to Peter Wolfe for his invaluable service of providing the game scores used in developing the current ranking.  Special thanks also go to Kenneth Massey and James Howell for providing the game scores from past seasons that were used to develop and test the MinV model.  Kenneth Massey deserves tremendous thanks for compiling and comparing the many different college football ranking systems on the web, and for including the MinV ranking on his site.  Thanks also to Eugene Potemkin for including the MinV ranking in his rank of rating systems for college football, in which the MinV ranking consistently places very highly according to his fairness assessment. Appreciation is also extended to Ray Waits, David Wilson, and Stewart Huckaby, who include MinV on their Superlist of nine leading college football ranking systems.

Please forward all comments to jcoleman@unf.edu

Jay Coleman's Home Page

This page last updated on January 8, 2010 at 6:28 p.m.

1	Boise St
2	Alabama
3	Texas
4	Florida
5	Ohio State
6	TCU
7	Iowa
8	Penn State
9	Oregon
10	Cincinnati
11	LSU
12	Georgia
13t	Georgia Tech
13t	Arkansas
15	Auburn
16	West Virginia
17	Pittsburgh
18	North Carolina
19	Virginia Tech
20	Rutgers
21	Connecticut
22	South Carolina
23	Clemson
24	Wisconsin
25t	East Carolina
25t	Miami FL
27	Central Florida
28	Houston
29	Texas Tech
30	Nebraska
31	Arizona
32	Southern Cal
33t	South Florida
33t	Boston College
35t	Central Michigan
35t	Florida St
37	Brigham Young
38	Oklahoma
39t	Utah
39t	Oregon St
41	California
42t	Stanford
42t	Mississippi St
44t	Mississippi
44t	UCLA
46	Tennessee
47t	Arizona St
47t	Oklahoma St
49	Marshall
50	Ohio U.
51	Temple
52t	Navy
52t	Kentucky
54t	Notre Dame
54t	Missouri
56	Washington
57	Kansas St
58	Colorado
59t	Texas A&M
59t	Kansas
61	Iowa St
62	Minnesota
63t	Michigan St
63t	Air Force
65	Baylor
66	Wake Forest
67	Duke
68	SMU
69	Nevada
70	Louisville
71	Wyoming
72	Fresno St
73	Utah St
74t	Syracuse
74t	Idaho
76t	Northern Illinois
76t	Northwestern
76t	Bowling Green
79t	Troy
79t	Purdue
81t	Middle Tennessee St
81t	Alabama-Birmingham
83	Southern Miss
84	Virginia
85	Indiana
86	Illinois
87	Michigan
88	Louisiana Tech
89	North Carolina St
90	Army
91	Vanderbilt
92	Maryland
93	UNLV
94	San Diego St
95t	Buffalo
95t	Tulsa
97	Hawai`i
98	Memphis
99	Akron
100t	Kent St
100t	Florida Atlantic
102	Western Michigan
103	Louisiana-Lafayette
104	Miami OH
105	Toledo
106	San José St
107	Louisiana-Monroe
108	Arkansas St
109	Florida Int'l
110	North Texas
111	Ball St
112	Rice
113	Tulane
114	UTEP
115	New Mexico St
116t	New Mexico
116t	Eastern Michigan
118	Colorado St
119	Washington St
120	Western Kentucky