FEI: Head to Head

by Brian Fremeau

The college ratings we publish here at Football Outsiders have been fairly fluid week to week, and as Bill Connelly pointed out yesterday, it's just as important to focus on the big picture as it is the individual team rankings. With 120 teams, there are bound to be outliers and teams that move up or down a handful of ranking positions without much change in their actual rating.

That said, we'd like to think that most of our team comparisons are intuitive for those equipped with a basic understanding of our approach. But inevitably, a few ratings stump us. And then there are weeks when a half dozen examples of head-to-head results don't seem to fit. In the new FEI ratings, Stanford ranks ahead of Oregon, Alabama is ahead of LSU, Virginia Tech is ahead of Boise State, Ohio State is ahead of Wisconsin, etc. What's really going on here?

Ranking violations -- teams ranked incongruently with head-to-head results -- are impossible to avoid entirely, of course. There are "minimum violations" rating systems out there that are specifically engineered to maintain the transitive property as much as possible, but even these systems result in a ranking violation of around 8 percent or so. FEI has a current ranking violation percentage of about 23 percent -- that is, 23 percent of actual head-to-head results on the field are flipped in the rankings. Most computer rating systems hover between 15 percent and 20 percent.

The reasons for individual ranking violations of head-to-head results are many. In the case of FEI, all of the foundational elements are at least partly responsible -- drive data, opponent adjustments, game relevance weights, garbage time, FBS vs. FBS games only, etc. Why might Stanford be ranked ahead of Oregon even though the Ducks handed the Cardinal a 52-31 defeat on October 2? How much weight should that one result receive in comparison with the other 17 FBS games played by those two teams?

I re-ran the FEI ratings under four different scenarios, eliminating one of the head-to-head games listed above in each instance -- Oregon-Stanford, Boise State-Virginia Tech, LSU-Alabama, and Wisconsin-Ohio State. These games alone had little impact on the overall rankings, but they did affect those of the two teams involved in each case. In Stanford's case, its other nine games would rank the Cardinal No. 2 in the nation behind Auburn, and the Ducks dropped all the way to No. 10. The other games had similar results. Boise State would rank No. 13 without the win over Virginia Tech. LSU would rank No. 12 without the win over Alabama. Wisconsin would rank No. 17 without the victory over Ohio State. Virginia Tech, Alabama, and Ohio State would have a slightly better FEI rating in each case, but not significantly so.

Is it possible for both teams to receive an FEI ratings boost simply by playing one another? In isolation, it doesn't appear to be so, but this weekend could put that theory to the test. The FEI ratings are infatuated with the SEC West's best four teams, and they face off in two matchups this weekend. If the games are competitive, I fully expect Auburn, Alabama, LSU, and Arkansas will all remain among the top eight teams according to FEI. Depending on other results, all four might move up. Stay tuned.

FEI Drive Summary Breakdown

Last week, I introduced a new feature in the weekly column -- the FEI Drive Summary breakdown. The FEI system "watches" each game as a series of alternating possession and breaks down the scoreboard value of each possession to the offensive, defensive, and special teams units that contributed to that value. In the final weeks this season, I'll feature at least one drive summary table from the previous weekend.

In the tables below, the white fields represent basic box score drive data. The yellow fields represent the component values that contribute to each team's scoring, according to my efficiency metrics. Offensive drive value (ODV) is the scoring value produced (or forfeited) by the offense in the given drive, including the value of driving into field goal range. Field goal value (FGV) is the value produced (or forfeited) by the field goal unit on attempts. Extra point value (XPV) is the value produced by the point-after unit touchdown drives, including two-point attempts. Field position value (FPV) is the expected score value of the drive based on starting field position alone. The gray fields represent the component values of FPV. Automatic field position value (Auto) is unearned drive value based on national average score expectations from possession alone. Punt or kickoff return value (Ret) is the value above or below average produced from the kick return that initiated the drive. The remaining value (Seq) is produced from the sequence of defensive and special teams events that preceded the drive.

The total score values include only non-garbage possessions and are the only data that is included in the weekly FEI ratings. Garbage possession data is provided as a reference, including first half clock kill possessions. The start of garbage time at the end of a game is calculated retroactively from the game's conclusion as a function of the score margin and the remaining possessions to be played.

The Utah Utes pulled off the biggest comeback of last weekend, erasing a 17-point first-half deficit against San Diego State to win 38-34. Utah's most valuable (and critical) drive was a five-play, 85-yard touchdown drive at the end of the first half that followed an Aztecs interception, but overall, San Diego State's offense produced more drive value than Utah. The Utes' big advantage in the game came from starting field position, keyed by a punt block early in the fourth quarter. Note that the value listed in the return column (3.44 points earned on the punt block) was three times more valuable than the offensive series that punched in the three-yard touchdown drive. San Diego State also had a failed extra point on its third touchdown drive (-.96 points lost in extra point value) which, if successful, would have allowed the Aztecs to drive for a game-tying field goal instead of an attempted game-winning touchdown on their final possession.

By GFEI, the single-game opponent-adjusted measure of team performance, Stanford's rout of California was the second most dominant effort of the season by any team in the nation. The Cardinal offense settled for a field goal on a short field in its first drive (-1.65 ODV), but had touchdown drives of 95, 86, 90, 61, and 64 on its next five possessions. Cal managed to cross the 50-yard line only once on its six offensive possessions. Compare this performance to Oregon's effort against California a week earlier. In that game, the Ducks had 26.89 points of field position value but had a negative offensive drive value of -9.36 points the game. The difference in the games against Cal is a big reason why Stanford leapt Oregon in this week's FEI ratings.

Three and Out

Previous topics:

• Week 3: Three-and-outs, Available Yards, and Explosive Drives
• Week 4: Reaching the Red Zone, Methodical Drives, and Late and Close Efficiency
• Week 5: Converting 10+ Yard Drives Into Scores, Points Per Possession, and Scoring After Three-and-outs
• Week 6: Yards Per TD Drive, Playing With 2- or 3-Score Lead, Third Downs Per First Down Series
• Week 7: FEI Team Resumes for South Carolina, Arizona State, and Utah
• Week 8: FEI Team Resumes for Oregon, Wisconsin, and Georgia
• Week 9: FEI Team Resumes for Iowa, Miami, and Baylor
• Week 10: FEI Team Resumes for Arkansas, Michigan State, and Texas
• Week 11: FEI Team Resumes for Pittsburgh, Texas A&M, and San Diego State

In the tables below, the Game Efficiency, Offensive FEI, Defensive FEI, and "Game" FEI (GFEI) for each team in each game is provided. The ranking of those individual unit and game performances is also provided. Note that there have been 609 FBS vs. FBS game played to date, meaning that there have been 1,218 individual game performances for each category.

The opponent FEI ranking is also provided, as well as a general relevance factor (Rel) for the particular GFEI, OFEI, and DFEI results for that team in that game. As stated in the FEI principles, my system rewards playing well against good teams, win or lose, and punishes losing to poor teams more harshly than it rewards defeating poor teams. In the formula, the relevance factor is partly a function of the relative ratings of the two teams. Across all games, the least relevant results receive about one-eighth as much weight as the most relevant results. For simplicity, I've generalized the relevance data here into three equally distributed categories, High, Med, and Low.

The Bulldogs have played the toughest schedule in the country according to FEI, having played four division mates that currently rank among the top eight teams in the country. They lost all four games, but played Auburn and Arkansas close. Those efforts, along with strong performances against Georgia and Kentucky, all rank among the Top 100 opponent-adjusted defensive games of the year.

On the complete opposite end of the schedule perspective, Nevada's best opponent to date, Hawaii, ranks 60th nationally. The Wolf Pack's overall SOS ranks dead last. Oh yeah, and Nevada lost the game against the Warriors. There simply aren't any impressive opponent-adjusted victories or defeats here, even though Nevada's raw offensive numbers have been eye-popping. The test this weekend against Boise State will be unlike anything Nevada has seen, offensively or defensively.

Per a reader suggestion from "mm," we take a look at Florida International, the top-rated team from the Sun Belt conference. We didn't project much success for the Golden Panthers at the start of the year, but a few close losses in non-conference play set the stage for a strong conference run down the stretch. Florida International hasn't defeated anyone in the top two-thirds of the college football world, but they haven't had to in the Sun Belt. It has been a breakthrough year for a program that had won only 13 games in five seasons of FBS. They can wrap up a conference championship with a victory over Arkansas State this weekend.

If you have a suggestion for an FEI team resume you'd like to see, drop me a line on Twitter or in the comment section here. I'm happy to answer data inquiries or provide team resume tables for bloggers interested in investigating the data themselves.

FEI Week 12 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 does not include 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 RW) represent the average expected team wins for games scheduled but not yet played.

Offensive FEI (OFEI) and Defensive FEI (DFEI) are the opponent-adjusted ratings of all non-garbage-time drives from scrimmage. Field Position Advantage (FPA) is the share of the value of total starting field position for the season earned by each team against its opponents. Field Goal Efficiency (FGE) is the point value per field goal attempt earned by the field goal unit.

Only games between FBS teams are considered in the FEI calculations. The FEI ratings published here are a function of the results of games played through November 20.

FEI ratings for all 120 FBS teams are 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. There are also now separate pages for offensive and defensive FEI ratings for 2010.