Minimum Violations (MinV)
College Football Ranking
 

 

MinV Ranking for the 2008 Season (FINAL)


At right are the rankings of all NCAA Division 1-A college football teams thru the games of January 8, 2009 (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 69 violations out of 717 Division 1-A games, or a minimum violation percentage of 9.62%. Stated otherwise, the ranking at right matches the results of 90.38% 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 573 points.  Finally, the ranking shown at right at least approximately matches a secondary target ranking – in this case the current Sagarin ranking – as closely as 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 secondary target ranking.  However, the ranking shown is likely a reasonably close approximation.

Note on the Texas-Oklahoma-Texas Tech “cyclic triad”: These three teams could obviously not be ranked in any order without incurring a game violation. However, when enforcing the minimum weighted violations secondary objective, the Texas Tech win over Texas is the game result that should be violated. That game’s victory margin was 6 points, whereas the Texas win over Oklahoma was 10 points and the Oklahoma win over Texas Tech was 44 points. With that established, Texas should be ranked ahead of Oklahoma (and Oklahoma over Texas Tech) in order to avoid incurring a second game score violation in that grouping.

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 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.  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, and his research with Allen Lynch and Mike DuMond on voting behavior for the NBA MVP is forthcoming in the Journal of Sports Economics.
 
 

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 10, 2008 at 1:58 p.m.

 

1

Florida

2

Southern Cal

3

Texas

4

Oklahoma

5

Utah

6

Alabama

7

TCU

8

Penn State

9

Texas Tech

10

Boise St

11

Oregon

12

Oregon St

13

Ohio State

14

Florida St

15

Virginia Tech

16

Oklahoma St

17

Missouri

18

Nebraska

19

Arizona

20

Maryland

21

California

22t

Kansas

22t

Cincinnati

24t

Colorado

24t

Pittsburgh

26

West Virginia

27

North Carolina

28

Georgia Tech

29t

Clemson

29t

Georgia

31

Boston College

32

Brigham Young

33

Michigan St

34

Northwestern

35

Iowa

36

South Carolina

37

Notre Dame

38

Hawai`i

39t

Air Force

39t

Nevada

41t

Louisiana Tech

41t

Colorado St

41t

Wisconsin

44

Fresno St

45

Rutgers

46

South Florida

47t

North Carolina St

47t

UNLV

47t

Connecticut

50t

Miami FL

50t

Arizona St

52t

UCLA

52t

Wake Forest

54t

Stanford

54t

Duke

54t

Tennessee

57t

Vanderbilt

57t

Virginia

59t

Kentucky

59t

Mississippi

59t

Rice

62t

Houston

62t

Arkansas

64

LSU

65

Auburn

66

Southern Miss

67

East Carolina

68

Tulsa

69

Ball St

70

Navy

71

Baylor

72

Troy

73

Minnesota

74

Purdue

75

Florida Atlantic

76

Central Michigan

77

Western Michigan

78t

Illinois

78t

Buffalo

80

New Mexico

81

Mississippi St

82

Northern Illinois

83

Bowling Green

84

Temple

85

Wyoming

86

Ohio U.

87

Akron

88

Syracuse

89

Louisville

90

Kansas St

91

San Josť St

92t

San Diego St

92t

Utah St

94

Idaho

95

New Mexico St

96t

Alabama-Birmingham

96t

UTEP

98t

Central Florida

98t

Louisiana-Lafayette

100

Marshall

101t

Memphis

101t

Florida Int'l

103t

Toledo

103t

Arkansas St

105t

Texas A&M

105t

Michigan

107

Middle Tennessee St

108

Iowa St

109

Indiana

110

Army

111

Kent St

112

Washington St

113

Washington

114

Tulane

115

Louisiana-Monroe

116

Eastern Michigan

117

SMU

118

Miami OH

119

North Texas

120

Western Kentucky