Minimum Violations (MinV)
College Football Ranking
 

 

MinV Ranking for the 2010 Season (FINAL)


At right are the rankings of all NCAA Division 1-A college football teams thru the games of January 10, 2010 (through the BCS national championship game) 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 67 violations out of 718 Football Bowl Subdivision (Division 1-A) games, or a minimum violation percentage of 9.33%. Stated otherwise, the ranking at right matches the results of 90.67% of the games played this season, which is the highest value possible. In addition to minimizing the total number of violations, the ranking minimizes the deviation from the collective victory margins, without violating any game results. In sum, the ranking at right matches all the game results for the 2010 season as closely as is mathematically possible.

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 2009 college football season can be found here.

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 recent research (with Jeff Steagall, Andres Gallo, and Paul Mason) on voter bias in the Associated Press college football poll, first published in the Journal of Sports Economics, has been featured by the Wall Street Journal and the Florida Times-Union, among others.

 

Dr. Colemanís research with Allen Lynch 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. Recent follow-up research (with Lynch and Mike DuMond) investigating bias in the NCAA Tournament selection and seeding process has been published in Managerial and Decision Economics, and featured by Sports Illustrated. Related research by Coleman and Lynch on predicting NCAA Tournament game results, 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. Colemanís 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 Lynch and 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 11, 2011 at 12:22 p.m.

1

Auburn

2

Oregon

3

Stanford

4

TCU

5

Nevada

6

Boise St

7

Wisconsin

8

Ohio State

9

Virginia Tech

10

Iowa

11

Missouri

12

Arkansas

13

LSU

14

Texas A&M

15

Oklahoma

16

North Carolina St

17

Florida St

18

South Carolina

19

Alabama

20

Nebraska

21

Oklahoma St

22

Mississippi St

23

Florida

24

Oregon St

25

Michigan St

26t

Michigan

26t

Tulsa

28t

Illinois

28t

Notre Dame

30t

Southern Cal

30t

Utah

32t

Brigham Young

32t

Arizona St

34

Connecticut

35t

West Virginia

35t

Miami FL

37

Pittsburgh

38

Arizona

39

North Carolina

40

San Diego St

41

Baylor

42

Air Force

43t

Maryland

43t

Washington

45t

California

45t

Boston College

47t

Colorado

47t

Syracuse

49t

Kansas St

49t

Hawai`i

51

Central Florida

52t

Georgia

52t

Iowa St

54t

Tennessee

54t

Northern Illinois

56

Mississippi

57

Kentucky

58

South Florida

59

Clemson

60

Penn State

61

UCLA

62

Texas

63

Texas Tech

64

Navy

65

Fresno St

66

Cincinnati

67

Louisville

68

Rutgers

69

Miami OH

70

Temple

71

Army

72t

Northwestern

72t

SMU

74

Rice

75

East Carolina

76

Southern Miss

77t

Houston

77t

Kansas

77t

Louisiana Tech

80

Georgia Tech

81

Wake Forest

82

Duke

83

Virginia

84

Washington St

85

Florida Int'l

86

Vanderbilt

87

Colorado St

88

Idaho

89

Indiana

90

Utah St

91

Marshall

92

Alabama-Birmingham

93

Troy

94

Tulane

95

UTEP

96t

UNLV

96t

New Mexico St

98

New Mexico

99

Wyoming

100t

Toledo

100t

Arkansas St

102t

Central Michigan

102t

Purdue

104t

Minnesota

104t

Western Michigan

106

Kent St

107

Ohio U.

108

San Josť St

109

Louisiana-Monroe

110

North Texas

111

Memphis

112

Middle Tennessee St

113

Florida Atlantic

114

Western Kentucky

115

Louisiana-Lafayette

116

Eastern Michigan

117

Ball St

118

Akron

119

Buffalo

120

Bowling Green