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.