NCAA Football Rankings

Every year in college football there's a big uproar over whether there should be a playoff, which teams are playing for the national championship, if a mid-major should get a BCS bowl (or national championship) bid, whether a dominant team like USC should be left out of the championship game because of one "bad" loss in mid-season, etc. The core flaw in the system is that the rankings are largely subjective and cryptic. What does it mean for one team to have a BCS rating of 0.98 and the other 0.95? What difference does that represent? What if a team beat another team that was thought to be good, but that team plummets through the rest of the season, or vice versa? Are teams getting penalized for not running up scores?

A fair ranking should obey several principles:
1. Every game is equally important
2. A single game can only directly compare the two teams playing in that game
3. Running up the score should not be rewarded
Given that each game is a comparison between two teams, we can then create an oveall tiered ranking that most closely accommodates all the game results throughout the season. In its current incarnation, the ranking considers teams to be equivalent if the score was within 3 points, 1 tier different within 10 points, 2 tiers within 20, and capped at 3 tiers better for a 3TD or larger spread. These tier differences are all compounded, so if team A is 2 better than team B, who in turn is 3 better than team C, we conclude that team A is 5 tiers above team C. If team A is 1 better than team B, who is 1 better than team C, who is 1 better than team A (Each team goes 1-1), they will come out evenly ranked. Each week we add the newest scores into the mix and recalculate a new TopoRank for the season.

Without further ado, here are the results for the last 5 seasons. In each season, the TopoRank correctly identifies over- and under-rated teams, whose performances in the major bowl games corroborate the findings. Here are some highlights:

2008
Was Oklahoma the right choice from the Big 12? Yes. They were better than Texas over the season, and definitely better than Texas Tech. I think this was clear to anyone who watched these teams play.

Was USC over-penalized for its loss to Oregon State? Yes. USC's national title dreams were sunk with a mid-season loss at the Beavers, who ended up #31 in the 2008 rankings. Florida lost to #11 Mississippi, and was the better team regardless. In voters' eyes, Oklahoma's lone loss to #4 Texas was a smaller penalty, however, the lower quality of their wins was not factored in. USC ranked higher than Oklahoma, but was relegated to smack around the Big Ten again.

Was the committee right to not award Utah the national championship game? Yes. Utah played a great game against #5 Alabama in its Sugar Bowl win, but their body of work throughout the season was only good enough to push them to #14. They were clearly hurt here by their conference strength of schedule, winning close non-conference games against [usually strong] Michigan (who finished #74) and #22 TCU didn't give them the push they needed to get into the elite picture.

2007
Ohio State vs LSU or Georgia? Perhaps it should have been Virginia Tech or Florida? VT was never really in the discussion due to getting slaughtered at LSU and then being on the wrong end of Matt Ryan's last second heroics. Florida had 3 regular season losses. LSU and Georgia's losses were most forgiven (while other contenders like Missouri and Kansas were derailed) because they were in SEC play. There was no head-to-head result between LSU and Georgia, and the decision was essentially random. 2007 had no clear top team, a fact that the ratings bear out. Years like this are most compelling for some kind of playoff system.

Was Hawaii a good choice for the Sugar Bowl? Anyone watching that game saw two teams on completely different levels, which is entirely consistent with #46 Hawaii being 1.6 tiers below Georgia. Hawaii outgunned weak teams all season long, but never belonged on the stage with the Bulldogs.

Was Illinois a reasonable choice for the Rose Bowl? Opinions were split over whether Illinois was sufficiently strong to compete in the Rose Bowl against USC (the answer was clearly no). Illinois was the 3rd best team in the Big Ten, and was chosen to keep the Pac-10 v Big Ten tradition of the game. The credibility of the game would have been better served if Cincinnati or Clemson were chosen instead, though the difference was not drastic.

2006
Should Ohio State and Michigan play for the national title? Ohio State had defeated Michigan in an epic 42-39 showdown at the end of the season to earn their spot atop the Big Ten. Debates raged over whether Michigan was the 2nd best team, and if the championship should be a rematch. In a last second ranking miracle, Florida overtook Michigan, quieted doubters by destroying the Buckeyes and really stirred up the Big-Ten-is-overrated discussion. Our numbers vote in favor of this. USC and Florida were the two best teams in the country (though USC sunk themselves with a late-season loss to UCLA), but Ohio State would not be denied with a perfect record.

Did Notre Dame deserve a BCS bowl game? Absolutely not. The Fighting Irish finished 24th in our rankings, right in line with the 41-14 beating they received from LSU. Many considered the Irish to be floating on hype, and this bears out in the numbers and the reality when facing top oppoonents.

How big an upset was the greatest bowl game ever? It wasn't. Boise State finished the season #12 while Oklahoma was #21 (another questionable BCS choice). The Broncos were well on their way to a strong victory when they had a meltdown, necessitating the heroics. #7 West Virginia, #13 Virginia Tech, #14 Rutgers or #15 Georgia would all have been better choices, but Oklahoma rode an 8-game win streak past all of them into the Fiesta Bowl. Again, an argument for why all games should be weighted equally.

2005
No qualms about the USC vs Vince Young championship game. Again we see some teams having stellar seasons degraded by untimely losses (Virginia Tech).

2004
2004 is compelling because it's the only time in the last 5 years that a mid-major really did get snubbed out of the national championship game. Utah dismantled all opponents on the way to a perfect season, but didn't get their chance against USC. Instead they clobbered an overrated (#33) Pittsburgh team while the Trojans had their way with Oklahoma. This was a situation where a mid-major had the quality of victories (strength of schedule and dominant victories) to be rightfully placed in the championship game, but the general voter perception of the Mountain West clouded their judgement. Their situation was differentiable from Hawaii '07, and I can't imagine they would have done worse than Oklahoma.