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.
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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.
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Acknowledgements
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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.
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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.
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Texas |
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2 |
Southern Cal |
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3 |
Penn State |
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4 |
Ohio State |
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5 |
UCLA |
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6 |
LSU |
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7 |
Notre Dame |
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8 |
TCU |
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Wisconsin |
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10 |
Auburn |
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11 |
Alabama |
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12 |
Florida |
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Texas Tech |
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14 |
Florida St |
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15 |
Miami FL |
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Virginia Tech |
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17 |
West Virginia |
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18 |
Oklahoma |
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19 |
Nebraska |
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20 |
Michigan |
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21 |
Iowa St |
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22 |
Boston College |
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23 |
Georgia |
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24 |
Oregon |
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25 |
California |
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26 |
Stanford |
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27 |
Arizona St |
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28 |
Northwestern |
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29 |
Iowa |
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30 |
Clemson |
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North Carolina St |
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South Florida |
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Louisville |
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Northern Illinois |
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35 |
Maryland |
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North Carolina |
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Virginia |
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Minnesota |
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Purdue |
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40 |
Michigan St |
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Oregon St |
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Boise St |
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Washington St |
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Colorado |
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Texas A&M |
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Indiana |
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Illinois |
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48 |
Rutgers |
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Navy |
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50 |
Kansas St |
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Colorado St |
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Kansas |
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Nevada |
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New Mexico |
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55 |
Tulsa |
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Missouri |
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Louisiana Tech |
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South Carolina |
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59 |
Fresno St |
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60 |
Toledo |
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61 |
Vanderbilt |
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62 |
Hawai`i |
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63 |
Arkansas |
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64 |
San Diego St |
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Utah |
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Georgia Tech |
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Tennessee |
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68 |
Brigham Young |
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69 |
Wake Forest |
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Baylor |
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Western Michigan |
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Central Michigan |
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Bowling Green |
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Miami OH |
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Wyoming |
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Ohio U. |
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Pittsburgh |
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Cincinnati |
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Connecticut |
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Army |
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Air Force |
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Washington |
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Arizona |
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Southern Miss |
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Central Florida |
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Mississippi |
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Memphis |
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East Carolina |
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Marshall |
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90 |
SMU |
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91 |
Alabama-Birmingham |
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Ball St |
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UTEP |
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Eastern Michigan |
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Houston |
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Syracuse |
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Kentucky |
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Mississippi St |
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Oklahoma St |
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Akron |
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101 |
Utah St |
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102 |
San José St |
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103 |
UNLV |
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Rice |
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Buffalo |
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106 |
Kent St |
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107 |
Duke |
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108 |
Tulane |
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Idaho |
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110 |
New Mexico St |
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Louisiana-Lafayette |
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Louisiana-Monroe |
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Middle Tennessee St |
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Arkansas St |
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Temple |
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Troy |
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Florida Int'l |
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Florida Atlantic |
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North Texas |
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