Last evening was the first time this season it was cool enough for a good fire pit, adding to my personal sense that Fall is here and further inspiring me to start the Random Walker First-Last (RWFL) rankings for the 2011 college football season.
We are once again enormously grateful to both Peter Wolfe and Kenneth Massey for making this task easier on all of us. Both are part of the official Bowl Championship Series standings. Wolfe provides the data
in an easy-to-process form. Massey publishes the College Football Ranking Comparison
We have nothing to do with the official Bowl Championship Series standings. We provide these rankings for fun as an example of how the teams might be ranked using a simple "my team beat your team" argument. As described in our papers and elsewhere on this blog and its links, the RWFL ranking system has one "free parameter" p which loosely speaking relates to the balance between strength of schedule and overall record. When p is close to 1/2 (the left edge of the figure below), quality of opponent plays a strong role. As p increases towards 1 (the right edge), single-game victories and going undefeated matter more.
We will continue to post plots representing the placement of the top-ranked teams as we vary the p parameter in the RWFL rankings. Looking at different values of p is of course just one of many ways to modify the rankings; but they sometimes lead to a quick observation about how sensitive rankings are to different ways of valuing the importance of strength of schedule. That said, such changes have elaborate follow-on effects---changing the ranking of one school impacts the rankings of all of the schools they played, and so on---so that it is often difficult to make quick sense of why this one change affects the rankings. Looking at the figure below, Clemson is ranked #1 at almost all values of p, except very close to p=1 where Alabama slides into the top spot. There are some large movements in the figure, with Illinois ranked at #16 near the left edge but moving up to #5 near the right edge. Why do these changes occur? One could try to weave a story, but with so many undefeated teams right now it might just be easiest to wait for more football to be played.
The RWFL rankings at p=0.75 run on the full network of connected teams should appear in Massey's comparisons
for this season starting this week (where the rankings are broken out separately for the FBS and FCS). The rankings on the restricted network including only the FBS teams are equivalent to Eugene Potemkin's "E-Rating" that sometimes appears there too.