Fremeau Efficiency Index: Week 13

by Brian Fremeau

The Fremeau Efficiency Index (FEI) principles and methodology can be found here [1]. Like DVOA, FEI rewards playing well against good teams, win or lose, and punishes losing to poor teams more harshly than it rewards defeating poor teams. Unlike DVOA, it 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, a measurement of the success rate of a team scoring and preventing opponent scoring throughout the non-garbage-time possessions of a game. Like DVOA, it represents a team's efficiency value over average.

Only games between FBS (Division 1-A) teams are considered. The Week 13 Ratings represent the results of games played through Saturday, November 24, 2007.

Offensive Efficiency (OE) represents the raw per-possession scoring rate for each team, and Defensive Efficiency (DE) represents that of its opponents. Adjusted Offensive Efficiency (AOE) and Adjusted Defensive Efficiency modifies OE and DE for field position and opponent. Field Position Advantage (FPA) represents the difference between a team's average offensive field position and its opponents'.

Click here [2] for rankings of all 119 teams. Click here [3] for Offensive/Defensive Efficiency rankings for all 119 teams.

After yet another weekend of rankings carnage and thrilling finishes, including a remarkable total of 24 overtime possessions, the BCS title game picture has almost come into focus. No undefeated teams remain among the championship game contenders, unless you agree with Les Miles' suggestion [4] that his LSU Tigers, fresh off their second triple-overtime loss of the season, are actually 10-0-2. But why stop there? If not for their fourth quarter drama against Florida, Auburn and Alabama, they could be standing atop the college football world with an undefeated 7-0-5 record.

None of those games were ties, however, and LSU properly gets credit for the victories and absorbs the consequences of the losses. That they destroyed Virginia Tech in Week 2 and efficiently disposed of the rest of their opposition keeps the Tigers in the FEI top spot for the seventh straight week. That body of work is enough to maintain the separation from the pack for LSU in a 2007 season chock full of blemished resumes. How blemished? LSU's current rating would be good for only third place in the final FEI standings of 2004 (behind USC and Auburn), 2005 (behind Texas and USC), and 2006 (behind Florida and USC). In 2003, only that year's LSU team would rate ahead of the 2007 Tigers.

FEI's No. 2 West Virginia and No. 3 Ohio State currently match the BCS standings and probably require only an Oklahoma victory over Missouri in the Big 12 championship game to set the stage for a championship showdown. A Mountaineers/Buckeyes game would feature the second best offense according to AOE versus the top defense according to ADE, a match-up quite similar to Saturday night's Missouri/Kansas game. For their part, Missouri can extend their dream season by exacting revenge on Oklahoma team still rating as one of the most balanced, if not tested, in college football. The winner will probably get a boost further up the FEI Top 10 standings, though not enough to make up for the Big 12's missing marquee OOC wins (Illinois and ... ?), head-scratching second-tier (tsk, tsk, Texas), and free-falling third-tier (Kansas State and Nebraska went from AP Top 25 teams to uncompetitive conference laughingstocks in just a few weeks).

Hawaii actually is the only undefeated team in the country, and received the biggest FEI ranking bump of the weekend after knocking off Boise State to clinch the WAC crown. The conference looks to be a big winner, too, if Hawaii can remain undefeated and earn a coveted BCS bowl berth and payout. All that stands in their way is a 4-8 Washington team ... one that also beat Boise State (Hawaii's best opponent) and played mostly competitively against eight other opponents rated higher than BSU this season, including four of the FEI Top 15. Saturday's game also pits Hawaii's 2.26 Wins over Pythagorean Wins (most in the nation) against Washington's 1.53 Wins under Pythagorean Wins (fifth most in the nation). If the rest of the season hasn't convinced you, it might be best to wait until this game and the others play out before penciling in any of the BCS bowl berths.

Strength of Schedule

I have received a number of questions about the way FEI employs strength of schedule in its opponent adjustments of Game Efficiency data. In the Week 10 FEI Ratings article [5], I charted the frequency and GE margins of games between teams of varying strengths, shedding some more detailed light on the broad distribution of teams in college football. I used data from the 2005 and 2006 final Massey Consensus Rankings for the following analysis.

This table was originally provided in Week 10 to illustrate the general frequency of competition between teams of different types in college football. To more specifically explore the schedule strength of each team type, I decided not to take an average ranking of opponents faced by each team, but instead separated each team's schedule into an ordered list of its opponent's Massey Consensus (MC) ranking, best to worst. For example, the 2006 Florida Gators faced Ohio State (MC No. 2) as their best opponent, LSU (MC No. 5) as their second best opponent, and so on. I then took the average opponent ranking of each team type's best opponent, second best opponent, etc., to produce the following table. I did not calculate average opponent rankings past the eighth best opponent faced because not every team in 2005 and 2006 played more than eight FBS opponents.

It should come as no surprise that the Elite, Very Good and Above Average team types play stronger opposition than the national average, since those team types are dominated by BCS conference teams that play seven or eight conference games each year against one another. It should also not be a surprise that Elite teams play better teams throughout -- not only do Elite teams often get opportunities to play an extra Elite team in a bowl game, the status of their other opponents may be boosted somewhat simply by having played the Elite team in the first place.

These are averages, of course, and not every Elite or Very Good schedule is created equal. The 2007 LSU Tigers, for instance, have faced the FEI No. 4, No. 14, No. 18, No. 19, No. 26, No. 27, No. 31, No. 44, No. 74, No. 91, No. 93, and No. 96 teams this season. Is it fair to say that the average ranking of its opponents (44.75) is indicative of LSU's strength of schedule? Or should LSU's best opponents and, therefore, more important games (Florida, Virginia Tech) be given more weight than its worst and least important (Louisiana Tech, Tulane)? As described in the basic methodology, FEI takes this latter approach, weighting the value of the top of a given team's schedule more heavily than the bottom.

Since each game outcome is weighted independently, a traditional strength of schedule metric is not employed by or calculated from the GE and FEI ratings. In other words, to describe and compare LSU's strength of schedule as the difference between its GE and FEI (0.030) versus West Virginia's (-0.065) is imprecise. A comparison of LSU and West Virginia game-by-game is better.

Based on schedule, the top opponents for each team are rating as a virtual wash, but LSU gains a clear edge over the next five. LSU's schedule appears more like the average Elite schedule listed above, while West Virginia's is more similar to that of an Above Average team. The final column represents Adjusted Game Efficiency (AGE), or Game Efficiency modified not only for strength of opponent but also weighted for the importance of the game outcome in terms of its relevance -- top games are given more weight than bottom games, and bad losses more weight than wins over poor teams. FEI is calculated from the multiple-order AGE data.

Considering all of this information, LSU's top two games are clearly better than West Virginia's, but WVU's strong performances against its next best opponents beats out those of LSU's, particularly because of the Tiger losses. Both teams handled a reasonably comparable bottom portion of their schedule well on the whole, and in total, LSU finds itself perched just ahead of West Virginia in the current FEI ratings.

There are, of course, a number of other considerations that could be made when determining strength of schedule, including sequencing of games, number and sequencing of off-dates, etc., though measuring these would take a great deal more research. The current FEI method for comparing schedules and strength of opposition may not settle any barstool arguments, but perhaps it positions the terms of the debate more openly.