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 Josť 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