Minimum Violations (MinV)
College Football Ranking
 

 

Final MinV Ranking for the 2007 Season


At right are the rankings of all NCAA Division 1-A college football teams thru the games of January 7, 2008 (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 78 violations out of 718 Division 1-A games, or a minimum violation percentage of 10.86%.  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 625 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 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.  His research with Ken Jennings and Frank McLaughlin on final offer arbitration in professional baseball has been published in Cal-Berkeley's Industrial Relations journal.
 
 

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.
 
 

 

Please forward all comments to jcoleman@unf.edu

Jay Coleman's Home Page

This page last updated on January 9, 2008 at 6:43 p.m.

 

1

West Virginia

2

Oklahoma

3

Missouri

4

Kansas

5

LSU

6t

Ohio State

6t

Virginia Tech

8

Oregon

9

Southern Cal

10

Michigan

11

Florida

12

Clemson

13t

Cincinnati

13t

Illinois

15

Penn State

16

Texas A&M

17

Texas

18

Arizona St

19

Oregon St

20

California

21

Tennessee

22

Arkansas

23

South Carolina

24

Georgia

25

Troy

26

Oklahoma St

27

Texas Tech

28t

Mississippi St

28t

Nebraska

28t

Virginia

31t

Kentucky

31t

Wake Forest

33

Florida St

34t

Connecticut

34t

Maryland

36t

Boston College

36t

Rutgers

36t

Wisconsin

39t

Michigan St

39t

South Florida

41

Auburn

42

Indiana

43

Purdue

44

Central Florida

45

Tulsa

46

Brigham Young

47

Hawai`i

48

Louisiana-Monroe

49

Alabama

50

Vanderbilt

51t

Fresno St

51t

Iowa St

53t

Georgia Tech

53t

Kansas St

55t

Central Michigan

55t

Colorado

55t

Mississippi

58

Miami OH

59

Ball St

60

Navy

61

Air Force

62

Utah

63t

Louisville

63t

TCU

65

New Mexico

66

Arizona

67t

Notre Dame

67t

Washington St

69

UCLA

70

Washington

71

Boise St

72

Pittsburgh

73t

North Carolina St

73t

Southern Miss

75

East Carolina

76

North Carolina

77

Western Michigan

78

Iowa

79

Stanford

80

Florida Atlantic

81t

Houston

81t

Miami FL

83

Bowling Green

84

Syracuse

85

Duke

86

Northwestern

87

Minnesota

88

Western Kentucky

89

Middle Tennessee St

90

Arkansas St

91

Baylor

92

Buffalo

93

Akron

94

Nevada

95

Memphis

96

Marshall

97

San Diego St

98

Colorado St

99t

Toledo

99t

Wyoming

101

Ohio U.

102

Louisiana-Lafayette

103

Louisiana Tech

104

Army

105

Temple

106

Eastern Michigan

107

Northern Illinois

108

Kent St

109t

Alabama-Birmingham

109t

San Josť St

109t

UNLV

112t

Tulane

112t

Utah St

114t

New Mexico St

114t

Rice

116

UTEP

117

SMU

118

Florida Int'l

119

North Texas

120

Idaho