by Brian Fremeau

Boise State essentially clinched an undefeated season with one fourth-quarter drive Monday night against Virginia Tech. College football's regular season "playoff" has barely begun -- 35 percent of teams haven't yet played a fellow FBS opponent -- but it sure feels like the Broncos have already won their bracket. Whether or not their bracket will connect to the BCS championship is the question that will loom over the 2010 season.

If Boise State is one of a handful of undefeated teams at the end of the year, should the Broncos get the nod based on their history of meeting big game challenges? Should a one-loss team from a power conference earn a bid over an undefeated Boise State? How much should strength of schedule factor into the national championship race?

If you follow FEI, you know that my adjustments for opponent strength are significant factors in the formula. FEI is not concerned with identifying "deserving" candidates. It is designed to isolate the strength of each team in terms of its ability to maximize scoring opportunities and minimize those of its opponent. And because there are stark differences between the best and worst teams in college football, the lens through which those raw efficiency metrics should be viewed is critical.

WAC teams are worse than SEC teams. Much worse. That doesn't mean that there is a ceiling for Boise State in the FEI ratings, but it does mean that the Broncos will need to dominate the rest of its schedule to ascend past its projected rating. It would help if a few other WAC teams ascended as well via strong non-conference play, too. But there is little doubt that Boise State's overall strength of schedule will be weaker than most, if not all, of the other national title contenders at season's end. But how much weaker?

Most computer ranking systems use a simple average to calculate strength of schedule. FEI takes a unique approach to SOS calculations that can tell us much more about the relative difficulty of each team's slate of opponents. How difficult is it for a team to win every game? That is a fundamentally different question than "What is the average strength of a given set of opponents?" And it is a better one, too.

If a team played 10 average opponents, how might its strength of schedule change by playing two more teams? Winning two more games must be more difficult than not playing the games at all, even if the opponents are weak and victory is nearly guaranteed in both games. But if we used a simple average to calculate strength of schedule, then the 12-game schedule would actually be measured as weaker than the 10-game one because the addition of two weak teams would drag down the average of the entire slate. The average misleads us.

Instead, we'd like to find out the likelihood of victory in each of the games. The only problem is that the likelihood of victory depends on the strength of both teams, not just the opponent, and the ease of a schedule depends on our perspective. Teams at the top of the college football world would have more success against a bunch of average teams than they would against a schedule that included a handful of elite teams and a handful of chumps. The worst teams in the country would have more success against the latter group, however, because they'd have a shot to win a few games against the chumps.

If we want to measure the likelihood of an undefeated season, we have to take the perspective of an elite team. Only upper echelon teams can reasonably expect to go undefeated in a 12- to 14-game schedule. I chose to standardize SOS from the perspective of a fictional elite team, one with an FEI rating of two standard deviations above average, roughly equivalent to a typical top five team.

To calculate the likelihood of victory, I charted the relationship between power differential and winning percentage for both home and away teams during the last seven seasons. Power differential represents the standard deviation delta between the two teams' end-of-year FEI ratings. The best fit polynomial trendlines for those results are charted here.

Note the nonlinear relationship of these factors and the slight bump in the lines near the center of the graphic. The value of home field peaks when the teams are of relatively equal strength. Note also that a home team with a power disadvantage of roughly 0.2 standard deviations has a 50 percent win likelihood. Conversely, a road team must be better than 0.2 standard deviations in power than its opponent if it expects to win on the road.

Based on this regression model, I calculate the likelihood of victory for our fictional elite team against every game on every team's schedule. The product of those individual game win likelihoods is the overall probability that the elite team could run the table. The lower the probability, the tougher the schedule. SOS isn't permanently fixed at this point in the year. It will fluctuate throughout the season as FEI ratings change, but we get a pretty good idea now regarding the differences among Boise State and other title contenders.

As it currently stands, the Broncos total 2010 schedule ranks 103rd among all FBS teams. A typical elite, top five team would have a 57.9 percent likelihood of winning every game. And the biggest hurdle is already in the rearview mirror. An elite team would be expected to have a better than 94 percent chance of winning each of its remaining games (Oregon State is the next toughest challenge, and they have to visit the blue turf), and an 80.5 percent chance of running the table the rest of the way. That's the fifth-easiest remaining schedule in all of college football.

It isn't as though all automatic qualifying programs have tremendously difficult schedules in comparison, however. Texas and Ohio State rank 62nd and 59th, respectively, by this SOS measure. But it isn't enough to say their schedules are roughly 40 spots tougher than Boise State's. How much tougher is 40 spots?

Let's compare the schedules of Ohio State and Boise State, currently neck and neck in the Associated Press poll at No. 2 and No. 3. FEI produces a strength of schedule rating of .332 for Ohio State, a 33 percent likelihood that an elite team would win every game. If Boise State's schedule were played twice -- that is, 24 total games, two trips to FedEx Field to face the Hokies, two at home against Oregon State, etc... -- it would still be easier than the Buckeyes' 59th ranked schedule. An elite team would have a better chance of going 24-0 against Boise State's slate twice (33.5 percent) than it would going 12-0 against Ohio State's slate this year (33.2 percent).

This phenomenon is not isolated to Boise State or other teams with weak SOS ratings. A 24-0 record against Ohio State's schedule twice would still be easier (11.0 percent) than 12-0 would be against LSU's fifth-ranked schedule (10.8 percent).

Before this gets into Total Cereal territory, we can frame the difference with a little more subtlety. If Boise State replaced one non-conference game other than Virginia Tech this year with another heavyweight, their schedule strength would be on par with Ohio State and Texas. Playing a single game against either Florida or Alabama instead of Wyoming or Toledo, for instance, would produce an SOS at around .320. Adding in one more game of the caliber of Virginia Tech would improve SOS to around .400. The depth of the WAC certainly hurts the Broncos cause, and an SEC-level strength of schedule would be nearly impossible to achieve (it would require three or four elite non-conference dates, at least). But one more marquee matchup would do wonders, both in terms of popular opinion and SOS calculations.

This is not meant to be a criticism of Boise State's scheduling philosophy, but rather an objective approach to the question of schedule strength. There are huge differences in college football between conferences and team schedules. And as long as the BCS pits only two teams against one another for the title, the challenge of weighing performance against opposition requires this level of scrutiny.

FEI Week 1 Top 25

The principles of the Fremeau Efficiency Index (FEI) can be found here. FEI rewards playing well against good teams, win or lose, and punishes losing to poor teams more harshly than it rewards defeating poor teams. FEI is drive-based, not play-by-play based, and it is specifically engineered to measure the college game.

FEI is the opponent-adjusted value of Game Efficiency (GE), a measurement of the success rate of a team scoring and preventing opponent scoring throughout the non-garbage-time possessions of a game. FEI represents a team's efficiency value over average. Strength of Schedule (SOS) is calculated as the likelihood that an "elite team" (two standard deviations above average) would win every game on the given team's schedule to date. SOS listed here includes future games scheduled.

Mean Wins (FBS MW) represent the average total games a team with the given FEI rating should expect to win against its complete schedule of FBS opponents. Remaining Mean Wins (FBS RMW) represent the average expected team wins for games scheduled but not yet played.

Only games between FBS teams are considered in the FEI calculations. Since limited data is available in the early part of the season, preseason projections are factored into the current ratings. The weight given to projected data will be reduced each week until Week 7, when it will be eliminated entirely. Offensive and defensive FEI ratings will also debut in Week 7.

These FEI ratings are a function of results of games played through September 6.

FEI ratings for all 120 FBS teams are now listed in the stats page section of FootballOutsiders.com. Click here for current ratings; the pull-down menu in the stats section directs you to 2007 through 2009 ratings.