USA College Football.

Description of a Ranking of Rankings System by Martien Maas.

For ranking the (FBS) College Football teams numerous Ranking Systems have been developed.
A summary of nearly 140 of such systems can be found on a webpage College Football Ranking Comparison which is maintained by Kenneth Massey.
On that webpage Massey also presents some statistics for each Ranking System:

• Correlation to Consensus
• Ranking Violation %
• Top 25 Correlation to Consensus
• Top 25 Ranking Violation %

More detailed information about these statistics can be found on the following webpage About the Ranking Comparison of Kenneth Massey.

A number of College Football fans do produce a so-called Ranking of Rankings Table (Metaranking) based on correlation,
wins, (weighted) violations, agreement with comparison scores, prediction of results et., etc.
On the Ranking Comparison webpage of Massey you can find some links to such metarankings.

My new Ranking of Rankings System in fact is based on the Combination of two qualitative attributes namely: Correlation and Violation.
The ranking of the Ranking Systems is based on the following assumptions:

• The higher the Correlation to the Consensus, the better
• The lower the Ranking Violation Percentage, the better

For the computations for my Ranking of Rankings System I choosed to use the so-called Top 25 statistics from Kenneth Massey's webpage.
Since Correlation and the Violation are two completely different quantities you cannot combine these two by simply add them up.
Top 25 Correlation as presented by Massey has a mean value over all Ranking Systems of approximately 843
while Top 25 Violation has a mean value of approximately 178.
Before adding up Correlation and Violation a standardscore is calculated for each of the two attributes.
Both of these two standardscores have a mean value of: 0.0 and a standarddeviation of: 1.0.
Before adding up the two standardscores the sign of the Violation standardscore is changed: negative values become positive and vice versa.
Now we have created the situation where:

• The higher the Standardscore for Correlation to Consensus, the better
• The higher the Standardscore for Ranking Violation Percentage, the better
• The higher the Sum of both Standardscores, the better

By presenting all Ranking Systems in order of the magnitude of their Sum of both Standardscores we thus create our Ranking of Rankings Table.

Credits.

I am grateful to Kenneth Massey who grants me to use data directly from his College Football Ranking Comparison webpage.