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MinV and MVP College Football Rankings


MinV is a mixed binary integer linear programming model designed to minimize the number of game score violations in the ranking -- that is, the number of times a game's winner is ranked behind the team it defeated. Thus, MinV guarantees the ranking with the best retrodictive accuracy. Stated otherwise, MinV by definition best matches the results (i.e., winners and losers) of the games played thus far in the current season.

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 upwards of 125 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 current ranking is only one of those.

Research has been recently published that modifies MinV such that it selects the most predictive ranking possible from among this large number of minimum violations solutions. Findings from this research suggest that a weighted average of the rankings of Edward Kambour and William Born represents the most predictive composite ranking that is available among existing systems. Thus, the MinV ranking currently presented herein is from a modified MinV model which, as a secondary objective, attempts to match this weighted average ranking and its predictive accuracy as closely as possible, while not exceeding the minimum number of violations.

The MinV-Predictive (or MVP) model simply reverses these objectives: it focuses first on prediction accuracy, and then on minimizing violations as a secondary objective. That is, MVP matches the past head-to-head results as closely as possible without altering its game predictions for the upcoming week, according to the Kambour and Born weighted average ranking. Since it focuses on prediction first, MVP is expected to predict better than MinV -- and as well or better than any other ranking system available -- while approximating (but not necessarily guaranteeing) the minimum number of violations. MinV, on the other hand, is expected to match past games better than MVP (and optimally so), while approximating MVP's prediction accuracy.

"Minimizing Game Score Violations in College Football Rankings," an article describing the original version of 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). A copy of the full article can be downloaded from the link at the beginning of this paragraph.

"Minimum Violations and Predictive Meta-Rankings for College Football," an article describing MVP and the modified version of MinV, as well as their applications to the 2004 through 2011 college football seasons, appears in the February 2014 issue of Naval Research Logistics.

The abstract and bibliographic information for the Interfaces article can also be found under the "Other Sports Research" tab of this site.

B. Jay Coleman, Ph.D.
Richard deR. Kip Professor of Operations Management & Quantitative Methods
Department of Management | Coggin College of Business | University of North Florida | Jacksonville, FL 32224