Random Walker Rankings for NCAA Football




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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.

We remain grateful to both Kenneth Massey for maintaining his comparisons page and to Peter R. Wolfe for making game results available online.

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 Random Walker Top 25 (p=0.75)
Games Through Saturday December 1st
RW RWFL
RankTeam (Wins-Losses)% of Total Votes Team (Wins-Losses)%(First)-%(Last)
1LSU (11-2)2.0693LSU (11-2)1.7846
2Virginia Tech (11-2)1.8742Virginia Tech (11-2)1.5748
3Georgia (10-2)1.8414Georgia (10-2)1.5516
4Oklahoma (11-2)1.8215Missouri (11-2)1.4813
5Missouri (11-2)1.8050Arizona St (10-2)1.4488
6Southern Cal (10-2)1.7972Southern Cal (10-2)1.4375
7Arizona St (10-2)1.7367Oklahoma (11-2)1.4367
8Ohio State (11-1)1.6861West Virginia (10-2)1.3391
9West Virginia (10-2)1.6794Ohio State (11-1)1.3249
10Florida (9-3)1.5953Florida (9-3)1.3143
11Kansas (11-1)1.5612Kansas (11-1)1.2021
12Boston College (10-3)1.5394Boston College (10-3)1.1856
13Hawai`i (12-0)1.4610South Florida (9-3)1.0671
14South Florida (9-3)1.4487Tennessee (9-4)1.0573
15Tennessee (9-4)1.4291Hawai`i (12-0)1.0500
16Oregon (8-4)1.4263Oregon (8-4)1.0209
17Cincinnati (9-3)1.3473Clemson (9-3)0.9761
18Clemson (9-3)1.3447Brigham Young (10-2)0.9422
19Virginia (9-3)1.3406Virginia (9-3)0.9400
20Brigham Young (10-2)1.3381Cincinnati (9-3)0.9039
21Illinois (9-3)1.3262Oregon St (8-4)0.9009
22Oregon St (8-4)1.3006Illinois (9-3)0.8699
23Auburn (8-4)1.2581Auburn (8-4)0.8621
24Connecticut (9-3)1.2171Connecticut (9-3)0.7887
25Arkansas (8-4)1.1909Texas (9-3)0.7332




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.


GT UNC Copyright © 2007-2008 Peter J. Mucha (mucha@unc.edu), Thomas Callaghan, Mason A. Porter

THIS PAGE IS NEITHER A PUBLICATION OF THE UNIVERSITY OF NORTH CAROLINA (UNC) NOR THE GEORGIA INSTITUTE OF TECHNOLOGY (GT), WHERE THIS WORK BEGAN. NEITHER UNC NOR GT ARE RESPONSIBLE FOR EDITING OR EXAMINING ITS CONTENT. THE AUTHOR OF THIS PAGE IS SOLELY RESPONSIBLE FOR THE CONTENT. THE RIGHTS TO ANY AND ALL MATERIALS CREATED BY THE AUTHOR OF THIS PAGE ARE RETAINED BY THAT AUTHOR.