Minimum Violations (MinV)
College Football Ranking
 
Final MinV Ranking for the 2006 Season

At right are the rankings of all NCAA Division 1-A college football teams thru the games of January 8, 2007 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 62 violations out of 714 Division 1-A games, or a minimum violation percentage of 8.68%.  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 62 games in which the scores were as close as possible, as opposed to violating 62 games in which the victory margins were larger.)  The total weight (i.e., victory margins) of the 62 violated games this week is 520 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 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 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, 2006 at 10:40 p.m.

 

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