Random Walker Rankings for NCAA Football
2008 Random Walker Rankings
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.
By the way, do you agree or disagree with these comments? Would you like to respond with comments yourself? If so, you can finally do so, as we are very slowly getting with the proverbial program and moving this site to a blog. We expect it won't get properly cleaned up until the off season, but it at least presents a vehicle for comments now.
December 19th: Bowl game predictions are available from our blog.
December 6th: We'll keep the predictions short: Oklahoma will face Florida for the title, and I'm afraid that Ohio State will probably get picked for the last at-large BCS bowl bid over Boise State. Hopefully the bowl game officials will prove me wrong on the latter, because there are only two undefeated teams left in the FBS (Utah and Boise State), and it would be nice to see them both in BCS bowls. But I'd be really surprised if Florida doesn't jump Texas in the Standings to take a spot in the title game. Yes, the computers are still going to rate Texas favorably---last week, 5 of the 6 official systems had Texas ahead of Florida, and 4 of those systems had both Oklahoma and Texas ahead of both Florida and Alabama. Florida will improve with the computers, but they might still be behind Texas there. Again, we're in no way part of the official system, but the family of random walker rankings across varying p values (see the plots below) are sometimes a decent proxy for what the official computer systems will do, and the random walkers keep Oklahoma and Texas in the top two throughout. Don't blame the computers on this one: I don't believe any of them explicitly put value on conference championships, and the OU-Texas-TTech trio is collectively and formidably undefeated as a unit. So Florida will probably need the pollsters to vote them in with sufficient numbers to make up a difference in the computers. But Florida did, after all, just knock off a #1 that got the overwhelming majority (165!) of the first place votes across the two polls last week, so I'm confident that it will happen.
November 30th: We don't have much to add to what we said last week. All eyes will be watching how this week's BCS Standings break the Big 12 South division tie. Using our own random walker rankings as an imperfect stand-in for what the group of computer systems will do, it appears that Oklahoma should pick up ground on Texas in the computers this week. Importantly, Oklahoma led Texas in both polls last week, but ended up far enough behind Texas in the computers to be behind Texas in the Standings (an average of the three). We'd guess that Oklahoma will gain enough ground in the computers, between their win over highly-ranked Oklahoma State and the follow-on effects of Kansas beating Missouri, that they will close the gap with Texas in the computers. So, quite simply, it might end up to the selections of the pollsters; if they stay consistent from last week, Oklahoma will go to the Big 12 Championship, but if they change their collective minds, it could still be Texas. We'll find out soon enough, and then we'll argue about it for at least a week (if not longer)... Boise State's slimmest of hopes for a BCS bowl remain alive, but still slim. As discussed last week (below), it first hinges on the last at-large bid, which might still be up for grabs if USC wins the Pac-10 by beating UCLA next week. If that happens, it should come down to a bowl game selection between Boise State and Ohio State...
November 23rd: Wow, now the fun really starts! Volumes could be (and are being) written about the possible mess on the way to the national championship game selection. I can only hope that the near-playoff we're going to be treated to in the SEC and Big 12 will build some future interest in a true playoff system. From all accounts, it still appears that an Alabama-Florida SEC Championship game will be an unofficial national semifinal, assuming of course they both win out until then. In an amusing twist, the Big 12 conference championship matchup will be determined by the BCS standings if OU, Texas, and Texas Tech all win next weekend, the highest ranked among those three playing Missouri for the conference championship. If that team then beats Mizzou, they're all but assured a spot in the national title game; but if the conference championship goes to Missouri, it's going to be chaos...
Meanwhile, in the "BCS Busters" department, I don't want to say it, but I have to acknowledge the facts, and those facts say it is now more unlikely that Boise State is going to get a BCS bowl bid. Don't send me hate mail over this; I wish it weren't so. But their chances under the governing BCS rules are becoming thinner after this past weekend. Utah has all but officially wrapped up an automatic BCS bowl bid, barring lots of pollsters changing their minds from previous weeks and moving Boise State ahead of the Utes. The special rules that force inclusion of high ranking conference champions outside the big 6 conferences only applies to a single school, which will be Utah, assuming again they stay ahead of Boise State in the BCS Standings. The second such school has to get a bid through the normal at-large selection process, of which there will only be 3 openings left. For Boise State's purposes, a hopeful key phrase in the rules is "No more than two teams from a conference may be selected, regardless of whether they are automatic qualifiers or at-large selections." Importantly, the top of the BCS Standings is packed full of teams from the SEC and Big 12, so it's safe to say that two from each will get BCS bowl bids. That is, two of the remaining three at-large bids will go to these two conferences. So does Boise State have a shot at that last spot if they win out? After yesterday, I'm not confident. Specifically, Oregon State is now one win away from a trip to the Rose Bowl, in which case you have to think that USC is going to get an at-large BCS bid. Indeed, if USC somehow climbs to #4 in the Standings before the end of the season, that at-large bid becomes automatic under the rules. So Boise State fans have to be cheering for Oregon to beat Oregon State next weekend, and for USC to win the conference to take the Rose Bowl bid. Alternatively, USC could drop out of the picture altogether with losses to both ND and UCLA; but that's not something I'd be counting on happening! So, Boise State fans need USC to win the Pac-10. Otherwise, there is no realistic route to a BCS bowl for Boise State. If USC does win the Pac-10, then the last at-large BCS bid appears to come down to a choice, made by the bowl games themselves, between Boise State and Ohio State (ignoring other teams that might become technically eligible but that I think are even less likely to be chosen).
Copyright © 2008 Peter J. Mucha (firstname.lastname@example.org), Thomas Callaghan, Mason A. Porter
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