Minimum Violations (MinV)
College Football Ranking
 
Final MinV Ranking for the 2005 Season

At right are the rankings of all NCAA Division 1-A college football teams thru the games of January 4, 2006 (i.e., through the end of the 2005 season and 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 64 violations out of 664 Division 1-A games, or a minimum violation percentage of 9.64%.

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 119 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 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 5, 2006 at 11:10 p.m.

 

1 Texas
2 Southern Cal
3 Penn State
4 Ohio State
5 UCLA
6 LSU
7 Notre Dame
8 TCU
9 Wisconsin
10 Auburn
11 Alabama
12 Florida
13 Texas Tech
14 Florida St
15 Miami FL
16 Virginia Tech
17 West Virginia
18 Oklahoma
19 Nebraska
20 Michigan
21 Iowa St
22 Boston College
23 Georgia
24 Oregon
25 California
26 Stanford
27 Arizona St
28 Northwestern
29 Iowa
30 Clemson
31 North Carolina St
32 South Florida
33 Louisville
34 Northern Illinois
35 Maryland
36 North Carolina
37 Virginia
38 Minnesota
39 Purdue
40 Michigan St
41 Oregon St
42 Boise St
43 Washington St
44 Colorado
45 Texas A&M
46 Indiana
47 Illinois
48 Rutgers
49 Navy
50 Kansas St
51 Colorado St
52 Kansas
53 Nevada
54 New Mexico
55 Tulsa
56 Missouri
57 Louisiana Tech
58 South Carolina
59 Fresno St
60 Toledo
61 Vanderbilt
62 Hawai`i
63 Arkansas
64 San Diego St
65 Utah
66 Georgia Tech
67 Tennessee
68 Brigham Young
69 Wake Forest
70 Baylor
71 Western Michigan
72 Central Michigan
73 Bowling Green
74 Miami OH
75 Wyoming
76 Ohio U.
77 Pittsburgh
78 Cincinnati
79 Connecticut
80 Army
81 Air Force
82 Washington
83 Arizona
84 Southern Miss
85 Central Florida
86 Mississippi
87 Memphis
88 East Carolina
89 Marshall
90 SMU
91 Alabama-Birmingham
92 Ball St
93 UTEP
94 Eastern Michigan
95 Houston
96 Syracuse
97 Kentucky
98 Mississippi St
99 Oklahoma St
100 Akron
101 Utah St
102 San Josť St
103 UNLV
104 Rice
105 Buffalo
106 Kent St
107 Duke
108 Tulane
109 Idaho
110 New Mexico St
111 Louisiana-Lafayette
112 Louisiana-Monroe
113 Middle Tennessee St
114 Arkansas St
115 Temple
116 Troy
117 Florida Int'l
118 Florida Atlantic
119 North Texas