Random Walker Rankings for NCAA Football
2007 Random Walker Rankings
The random walker rankings are back for 2007! The 2006-2007 bowl season included Boise State shocking the football world with their big comeback BCS bowl win over Oklahoma, becoming the second "non-BCS" conference team to win a BCS bowl game. The 2007 season brings us one more team in Division I-A---oops, I mean in the "FBS"---with Appalachian State already proving that "FCS" teams can beat major FBS competition. In news more immediate to our lives here at Random Walker Rankings, our peer-reviewed manuscript about the random walker rankings appears this fall in the American Mathematical Monthly.
Below we list the Top 25 according to the Random Walker (RW) system of first-place votes and the Random Walker First-Last (RWFL) system at our selected p=0.75. We also make available rankings of all 120 Football Bowl Subdivision teams at p=0.75. The breakdown of the top teams across different p values for both RW and RWFL can be seen in the figures below. Additionally, we plot the fraction of ranking violations---that is, the fraction of game outcomes that have been contrary to the rankings---for each system across the p values. Ranking violations like these are also included on Kenneth Massey's site, and can be used as one measure of the efficacy of a rank ordering; indeed, one could instead choose p to minimize such errors, but we are more comfortable at the selected fixed values for ease of explanation.
Note added December 2nd: Notice in the figures how much different the rankings of the top teams are comparing the selected p=0.75 against p in the vicinity of 0.8-0.9 where ranking violations are minimized. Such differences are merely more evidence of the topsy-turvy uncertainties at the top of college football this season. It will be fun to see who gets selected to play against whom, and how all those bowl games turn out...
December 20th: The bowl games start tonight, and we've had multiple requests for information about how one might use rankings like these to predict future outcomes and to order the confidence in those picks. For instance, part of playing ESPN's College Bowl Mania (not endorsing it, just using it as an example), involves ranking your 32 picks in order of confidence. We definitely don't want to start a whole discussion here about predictive versus retrodictive rankings; but we do want to remind you of the main philosophy of the Random Walker Rankings: These rankings are not intended to be "best" in any sense; rather, they are an example of a ranking system that is both simple-to-describe and demonstrably valuable. There are more complicated systems out there that one should probably rely on to give better predictions than those here. But if you still want to see what the "my team beat your team" random walkers suggest about the upcoming bowl games, check out our 2007 Bowl Games page.
2007-2008 Post-Bowl Random Walker Rankings
While our primary interest here at Random Walker Rankings is in what the rankings say prior to the bowl games, we again provide rankings as calculated after all the bowl games were played. Unsurprisingly, LSU remains the #1 team. Full ranking details are tabluated in our post-bowl rankings of all 120 FBS teams. We also note that, despite stumbling a little down the stretch, the purely-algorithmic ranking of outcomes and confidences presented in our 2007 Bowl Predictions placed just above the 75th percentile of entries in ESPN's College Bowl Mania.
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