Minimum Violations (MinV)
College Football Ranking

MinV Ranking for the 2009 Season

At right are the rankings of all NCAA Division 1-A college football teams thru the games of November 14, 2009 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 37 violations out of 560 Division 1-A games, or a minimum violation percentage of 6.61%. Stated otherwise, the ranking at right matches the results of 93.39% 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 301 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 November 15, 2009 at 6:48 p.m.

1	TCU
2	Boise St
3	Texas
4	Alabama
5	Oregon
6	Georgia Tech
7	Clemson
8	Pittsburgh
9	Florida
10	Southern Cal
11t	Ohio State
11t	Cincinnati
13	Oregon St
14	California
15	Houston
16	Oklahoma St
17	Texas Tech
18	Iowa
19	North Carolina
20t	Arizona
20t	Virginia Tech
22t	Nebraska
22t	Miami FL
24	Penn State
25	LSU
26	Rutgers
27	Temple
28	Navy
29	Notre Dame
30t	Boston College
30t	South Florida
32	Florida St
33t	Auburn
33t	Brigham Young
35t	Oklahoma
35t	West Virginia
37	Connecticut
38	Mississippi
39	Baylor
40	Wake Forest
41	Stanford
42	UCLA
43t	Mississippi St
43t	Tennessee
45	Georgia
46	Arkansas
47	Utah
48	Wisconsin
49	Missouri
50	Nevada
51	Fresno St
52t	Arizona St
52t	Central Michigan
54	South Carolina
55	Kentucky
56	Minnesota
57t	Air Force
57t	Michigan St
59	Washington
60	Kansas St
61	Colorado
62t	Texas A&M
62t	Kansas
62t	Louisville
65t	Southern Miss
65t	Iowa St
65t	Duke
68t	Virginia
68t	North Carolina St
70t	Idaho
70t	Syracuse
72t	Northwestern
72t	Northern Illinois
74t	Purdue
74t	Indiana
76	Louisiana Tech
77t	Illinois
77t	Wyoming
79	Michigan
80	Army
81	Vanderbilt
82	UNLV
83	Hawai`i
84	Washington St
85	SMU
86t	East Carolina
86t	Tulsa
88t	Central Florida
88t	Kent St
90t	Marshall
90t	Ohio U.
92	Bowling Green
93	Troy
94	Middle Tennessee St
95	Western Michigan
96	Maryland
97	San Diego St
98	Colorado St
99	Buffalo
100	Alabama-Birmingham
101	Louisiana-Monroe
102	Florida Atlantic
103t	Louisiana-Lafayette
103t	Miami OH
105t	Toledo
105t	Arkansas St
107	Florida Int'l
108	Akron
109	North Texas
110	Ball St
111	Rice
112t	Memphis
112t	Tulane
114	UTEP
115	New Mexico St
116	Utah St
117	San José St
118	New Mexico
119	Western Kentucky
120	Eastern Michigan