Sunday, October 31, 2010

Rankings through October 30th

And then there were five left. Five undefeated teams, that is. The drama will continue to be the discrepancies between the polls and the computer rankings, at least in the short term. Ivan Maisel makes the argument that the relatively poor ranking Oregon currently has in the computers will be at least partially remedied down the stretch when they play Cal, Arizona, and Oregon State. Of course, they have to keep winning, and their mascot has to keep up with the push-ups.

Our rankings for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

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Sunday, October 24, 2010

Rankings through October 23rd

The rankings appear to tighten up a little with some more teams encountering their first losses of the season this weekend.  The most interesting items in the plot below are the bias parameters (the values of p) at which one-loss Oklahoma and LSU are ranked ahead of undefeated Boise State, Oregon, and Utah.  That said, other than making the observation, we're happy to just sit back and watch more football right now.  We continue to post our rankings for the full FBS and FCS on Kenneth Massey's College Football Ranking Comparison.


Sunday, October 17, 2010

Rankings through October 16th

Another week, another defeat for a #1 team. We still have a lot of football to play, and plenty of undefeated teams left. The first official BCS Standings for the year are released tonight, and much attention will rightly be paid to these rankings to see who has the proverbial pole position to possibly reach the championship game.

Meanwhile, check out Fuzzy math by the BCS by Jon Solomon, bringing to light some of the potential problems with the fact that most of the computer systems used by the BCS are black boxes. Don't get me wrong, I think that the service provided by the authors of these systems should be rewarded (and not just with the hate mail they all get). Colley and Massey once did me the favor of speaking at a minisymposium at a math conference, and I know they do this out of love of the game. But the built-in verification that would come with greater transparency would be most welcome.

As an aside, regarding the actual error of changing team lists noted in the article, we made the same error at a bookkeeping level last week. That is, our current calculations here are independent of such lists because we work on the full connected component of teams connected to one another by games played. But when we sent in our lists of FBS and FCS teams to Kenneth Massey, he caught that we didn't send him the correct lists. It's a completely understandable error, demonstrating the value of the verification that would come with greater transparency.

In the plots below, the order of the undefeated teams jumbles around as you vary p, the bias parameter value. Full "Random Walker FL" rankings of the FBS and FCS for the week will be posted on Kenneth Massey's College Football Ranking Comparison.

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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.