Sunday, November 1, 2009

Concise Definition of RWFL Rankings

The general mathematical description of the random walker (RW) ranking methodology is presented as a sidebar on p.889 of ''The Bowl Championship Series: A Mathematical Review,'' T. Callaghan, P. J. Mucha and M. A. Porter, Notices of the American Mathematical Society 51, 887-893 (2004). These RW rankings, which amount to an amalgamation of first-place votes, depend on a bias value p setting the extent to which random walkers respect each individual game outcome.

The RWFL rankings at bias value p are calculated by the difference between first-place votes (following game winners) and last-place votes (following game losers). This is equivalent to subtracting RW at bias value (1-p) from RW at bias value p.

Starting in November 2009, all of our rankings are calculated on the full connected network of teams connected by games played, of which the FBS teams are a relatively small subset (even when we only report the FBS results). Prior to November 2009, our weekly rankings treated all non-FBS teams as a single catch-all "team" (who played a lot of games). However, our bowl predictions have used the full connected network in previous seasons.