Ranking college football teams is challenging due to many possible rankings and factors to consider. The current Bowl Championship Series system uses opinion polls and computer rankings but has issues with bias and lack of transparency. The CMS+ system uses a genetic algorithm with degree of victory and relative distance inputs to rank teams. Researchers improved CMS+ by defining factors for degree of victory like home field advantage and defining a matrix to input rankings were computed faster by reducing generations from 100,000 to 3,500-4,000. Further research could explore more factors and reducing runtime.

1. Background
Ranking college football teams is a significant challenge that has major
implications. With 124 colleges and universities represented in the NCAA
Football Bowl Subdivision (FBS), there are 124! possible rankings. With this
many rankings, it’s hard to tell if it’s the best ranking out of all the possibilities.
Other factors that makes ranking difficult are: what people consider to be
important when ranking a team, how bias of the voters or computer programs
impact ranks, and how conflicting results are handled.
Money is also a huge issue affecting rankings. Getting the rankings right can
have a huge monetary impact on the schools that do or don’t get into BCS
bowl games.
The current system of ranking the teams is the Bowl Championship Series
(BCS), which consists of two opinion polls and six computer rankings. The
opinion polls provide human error and bias. The computer rankings have
controversy due to the fact that all but one of them aren’t published for peer
review.
CMS+ Background
The CMS+ program is a quadratic assignment problem, the program uses a
genetic algorithm heuristic with two inputs: degree of victory (DOV) and
relative distance.
• Degree of victory consists of multiple factors that compare two teams.
• Relative distance shows how the rankings compare with one another, and
culminate to form a bell curve.
Producing Valid College Football
Rankings in Reasonable Time
Mark W. Edwards
Department of Mechanical Engineering
Jonathan A. Shumaker
Department of Chemical Engineering
5th Annual FEP Honors Research Symposium
C. Richard Cassady, PhD
Department of Industrial Engineering
April 20, 2013
CMS+ Problems
Degree of Victory can lead to some issues due to the multiple different factors
that can be included. Defining factors that should be included, which can also
be varied is a difficult task.
Also an issue with the CMS+ is that it currently takes a significant amount of
time to generate a ranking. Decreasing the run time makes the CMS+ more
practical for use.
Platform and Objectives
We believe that a four-team play-off increases the need for a ranking system,
a system should clearly state what factors are included, and a computer
based system should be used.
Our objectives were to improve the CMS+ system for ranking college football
teams by identifying factors to include and defining a way for them to be
quantified. Secondly we worked to improve the time it takes to run the
program.
Degree of Victory
• Defining Factors
We determined that one factor should always be included, and that is
the winner of a game should receive points over the team that they
beat. Four other factors are also in the calculation of DOV and can be
added and removed in any variation:
 Home and Away points are given to away teams if they win on the road. This
also gives half of the points to neutral site wins.
 AP Rank gives points over a team that is ranked higher in the AP poll. This is
done for every single pair of teams.
 Common Opponents points takes into account ever pair of teams, and it gives
the points to teams that have more wins over common opponents.
 Conference Champions are given points over all of the other teams in their
conference.
• Creating Degree of Victory Matrix
A matrix is necessary to compare every single pair of teams. Creating
this matrix is done by giving the points allocated to each of the
specified factors. In our case 15 points are given when the factor is
turned on. The matrix created will be able to be entered into the
CMS+ program with a relative distance matrix to compute a ranking.
• Results
Sixteen files were created where every combination of factors was
turned on and off. A fitness value of 200,000 provides a result of
10,000 standard deviations above the mean with no possible rankings
that are better.
Run Time
Through testing we found two things:
 The number of heuristic replications does not affect run time, therefore
we left the number of replications at 20 throughout testing
 Solution Quality and the Rankings produced is not affected by the
number of generations or replications used in the CMS+
Knowing these two things, we were then able to test the relationship
between the number of GA generations used compared to the run time.
These results are seen in Figure 1.
TABLE OF RUN TIME RES
Table 1: Ranking's GeneratedbyCMS+ System UsingTest Cases
BCS Rankings DOV 01
(OnlyH2H)
DOV 05
(APRank)
DOV 12
(H/A/N, ConfChamp, CommOpp)
DOV 16
(Everythingon)
Fitness 244343 246025 216012 196313
1 Auburn TexasChristian Oregon Oregon Oregon
2 Oregon Oregon TexasChristian Auburn Auburn
3 TexasChristian Stanford Boise State^ TexasChristian TexasChristian
4 Stanford Wisconsin Auburn MichiganState^ Boise State^
5 Wisconsin MichiganState OhioState Boise State^ MichiganState
6 OhioState Nevada^ Nevada^ Wisconsin Wisconsin
7 Oklahoma OhioState Wisconsin VirginiaTech^ VirginiaTech^
8 Arkansas Boise State Stanford Nevada^ Nevada^
9 MichiganState Auburn* MichiganState OhioState Stanford*
10 Boise State VirginiaTech Utah^ Stanford* OhioState
^Gained5 or more spotsfromBCS Ranking
*Lost 5 or more spotsfrom BCSRanking
As seen in the graph, once the generation amount gets past a certain point,
which is in the 3,500-4,000 generation range, the times start to increase.
Going in either direction increases the time to produce a ranking.
Conclusion
We were able to improve both the Degree of Victory and the run time
during our research.
• Factors were found to be included in Degree of Victory and these factors
were quantified then used to compute rankings from the CMS+ system.
• The run time was decreased by lowering the number of generations in
the algorithm from 100,000 to somewhere in the range of 3,500 to 4,000.
Future research should be done on more factors to include and more ways
to include them in Degree of Victory. Also the run time could be further
decreased based on the fact that there are more factors involved in running
the CMS+ system than just the generations and replications.
Figure 1: The Effects of Generations on Run Time