by Brian Fremeau
The college football regular season approaches its final act, with a handful of key conference championship games that will ultimately determine the College Football Playoff field, plus a few other FBS games that will clarify the set of bowl-eligible teams and determine the bowl match-ups that will carry us through the conclusion of the season in January. There appear to be more certainties this year than we usually have, but there is still time for the 2018 season to surprise us with chaos. If not, I don't expect much movement in the FEI ratings next week, since single-game results at this point in the year, even in blowout fashion, only carry a fraction of the weight given to the rest of the season's results.
Michigan was blasted by Ohio State on Saturday, but only fell from No. 4 in the FEI ratings last week to No. 9 this week. Ohio State's victory over the Wolverines ranks in the 99th percentile of opponent-adjusted single game performances this year, and was far and away the Buckeyes' best performance this season, but it still resulted only in Ohio State bumping up from No. 9 last week to No. 7 this week. That game carries as much or more weight in the FEI formula than any other results for either team, and yet it only counts as 10.7 percent of Ohio State's rating, and only 11.1 percent of Michigan's rating. My system, by design, doesn't care when results happen as much as it cares about the relative significance of a given result based on the opponent faced.
I have been dabbling recently with yet another modified version of the FEI ratings, one that gives more pronounced weight to more recent results. The idea that a team may dramatically improve or decline over the course of a season is something that I have intended to consider, but I have had trouble with modeling this, in large part due to the small number of games played in college football. And especially since a significant portion of the well-connected non-conference games are scheduled early in the year, it is challenging to have a recency-weighted model reflect both the changes in team performance and a solid footing on which to apply opponent-adjustments.
Still, I thought it would be prudent to share an approach to this modeling problem, and see what may stick or not stick with those that follow FEI and my work more closely. I used the single-game opponent-adjusted GFEI data as is, which is based on my traditional FEI formula, but then applied the recency weighting to it. To use Michigan as an example, the regular FEI weighting structure gives an equal amount of weight to their Week 1 matchup against Notre Dame as it does to their Week 13 matchup against Ohio State -- combined, those losses to strong opponents account for 22.2 percent of Michigan's overall FEI rating. But when I apply a recency weight to the GFEI data, escalating from Week 1 to Week 13, Michigan's loss to Notre Dame is only given 4.0 percent weight and their loss to Ohio State is given 12.7 percent weight.
If we apply a similar recency weighting to every team, how much would that change the FEI ratings? Here are the five teams that would benefit most from this approach. (Note that WFEI column indicates the recency-weighted FEI ratings for each team).
Charlotte is an interesting team to lead this list, in part because they have lost three of their last four games. But their victory last weekend over Florida Atlantic is their best GFEI result of the season, and their worst four GFEI results this year came in their first four FBS games. Their recency-weighted FEI improvement has as much to do with lowering the weight given to their early season results as it does emphasizing the weight of their late-season results. Memphis benefits similarly, downplaying their Week 2 albatross loss against Navy, but also boosting the emphasis on their last few games, including their best performance of the season, a 52-31 victory over Houston. Mississippi State has posted four single-game GFEI performances that rank in the 90th percentile over their last five FBS games, including consecutive blowout wins over Arkansas and Ole Miss by a combined score of 87-9. Lowly Rutgers loses some benefit from their lone victory of the season in Week 1 (over similarly lowly Texas State), but gets a boost from their most recent game, a very respectable 14-10 loss to Michigan State. Army hasn't played an FBS opponent in the last three weeks, but its three 90th-percentile GFEI performances to date this year came in the back half of their schedule.
The flip side of this is instructive as well, as indicated in the table below of the teams that would be most negatively impacted by recency-weighted FEI.
Duke is impacted most negatively by recency-weighted FEI, on the heels of suffering a shockingly bad loss by 52 points to Wake Forest last weekend, and reducing the weight given to their only 90th-percentile performances this year in wins over Army in Week 1 and Northwestern in Week 2. North Texas also loses the benefit of their best win of the season in Week 1 (46-23 over SMU, 36-0 in non-garbage time) and heavier emphasis on a substantially less-impressive 24-21 victory last weekend against a weak UTSA. Maryland loses ground by not getting as much credit for its Week 1 victory over Texas, and though they played Ohio State to the wire two weeks ago, their weakest GFEI performance of the year came this past weekend against Penn State. Michigan State's last three weeks (26-6 loss to the Buckeyes, 9-6 loss to Nebraska, and 14-10 win over Rutgers) get more emphasis in this model than the early season win over Utah State that has kept them relatively high in the regular overall FEI ratings this year. Kentucky's hot start to the season, which included a Week 4 dominant victory over Mississippi State, gets less emphasis, and their ugly 24-7 loss to Tennessee three weeks ago is more of an albatross.
The teams at the top of the regular FEI ratings don't appear on either of these two lists of teams most impacted by this recency-weighted model, but some do shift a bit. Alabama has been consistently dominant all year (10 straight 90th-percentile GFEI victories coming out of Week 13) so they're barely impacted. Clemson also has been very consistent this year and is minimally impacted by recency-weighted FEI. Notre Dame loses a little bit of ground, not because their recent results are poor, but because their best opponent-adjusted win of the year came in Week 1 against Michigan. Georgia's season, like Alabama and Clemson, has more overall balance, and their one loss to LSU came in the middle of the year and receives just about as much weight in the recency-weighted formula as it does in the regular formula. Oklahoma loses a little ground by downplaying the weight given to their 99th-percentile victory in Week 1 over FAU (63-14, 42-0 in non-garbage time). Ohio State gains ground, jumping ahead of the Irish and Sooners in the recency-weighted FEI ratings, due almost exclusively to their crushing defeat of Michigan last week.
Is recency-weighted FEI a good model? I haven't done enough work with it to test its predictive power, or to play with the relative recency weights to optimize its predictive power for that matter either. I do think there's some potential with it, and I'll add it to my growing list of off-season projects to tackle.
FEI Week 13 Ratings
The Fremeau Efficiency Index (FEI) is a college football rating system based on opponent-adjusted possession efficiency. Adjusted Possession Advantage (APA) ratings represent the per-possession scoring advantage a team would be expected to have on a neutral field against an average opponent, calculated as a function of current FEI overall, offense, defense, and special teams ratings.
Strength of Schedule ratings (PSOS) represent the average number of losses an elite team (two standard deviations better than average) would have against the team's regular season schedule to date. Offensive FEI (OFEI) is scoring value generated per drive adjusted for starting field position and opponent defenses faced. Defensive FEI (DFEI) is scoring value generated per opponent drive adjusted for starting field position and opponent offenses faced. Special Teams FEI (SFEI) is scoring value generated per possession by a team's non-offensive and non-defensive units adjusted for opponent special teams units faced. The team's record to date against opponents ranked in the FEI top 10 (v10), top 20 (v20), top 30 (v30), top 40 (v40), and top 50 (v50) are also provided.
Ratings and supporting data are calculated from the results of non-garbage possessions in FBS vs. FBS games.