Sunday, October 10, 2010

Random Walker Rankings, 2010 Edition

The college football season is already well along and it's past time to bring back the random walker rankings. Of course, college football is understandably a touchy subject at Carolina this season. Ignoring those important issues for the purposes of this blog, we focus back on the rankings, which just became more interesting near the top with Alabama's loss. So, hey, hey, they're the monkeys, let's see what they've got to say this year.

As always, we're grateful to Peter Wolfe for providing the data in an easy-to-process form, and to Kenneth Massey for publishing the College Football Ranking Comparison. We have nothing to do with the official Bowl Championship Series standings. We provide these rankings as an example of how the teams might be ranked using a "my team beat your team" argument. The Random Walker First-Last rankings (at bias parameter p=0.75) on the full network of connected teams appears in Massey's comparisons for this season starting this week. The rankings on the restricted network of FBS teams are equivalent to Eugene Potemkin's "E-Rating" that sometimes appears there too.

Because the full rank order of teams is provided in the comparisons, this season we will only post here the graphical representation of the top-ranked teams across different bias parameter p values, focusing on any interesting changes found there. Looking at different values of p is of course just one of many ways to modify the rankings. Loosely speaking, the overall strength of schedule is more emphasized at p close to 1/2 (the left edge of the figures below), while p close to 1 emphasizes going undefeated and single-game outcomes.

The plot below, including the top 16 teams at p=0.75 for all games played through Saturday October 9th, shows how the rank order changes with varying bias parameter p.  For example, slightly above 0.9, Boise State and Auburn swap places #2 and #3 in these rankings. (Click on the figure to see a larger version.)
At this stage of the season, algorithmic rankings remain at a severe disadvantage because of the relatively limited amount of data available. As more games are played, it will be interesting to see the week-to-week changes in the rankings.