College Football Rankings
Ranking American college football teams is a challenging task, and there are many different rankings schemes (both human and computer) that rank well in practice. In particular, the Bowl Championship Series (BCS) determines post-season play by building a consensus from several human and computer ranking systems.
But no ranking system is perfect, and a computer system in particular should provide some indication of how confident we can be in its rankings. For example, suppose that the ranks of Team #1 and Team #2 were to switch based upon the result of a single game between Teams #101 and #102. Should we be confident in such rankings?
The rankings below use groups as a way to show confidence. If the ranks of two or more teams cannot be differentiated with high confidence, then they are grouped together. Details of the ranking method can be found in this paper, and the research has been supported by the National Science Foundation through NSF Grant CCF-0545514.
The rankings are a derivative of the Colley Matrix rankings and so do not take into account margin of victory and do not weight later games more heavily. As a consequence, the rankings may not match the conventional wisdom of human polls. (In fact, computer rankings are not intended to!)
Thanks to A. Burer, J. Loefberg, J. Hall, and D. Loots for their ideas and input!