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13 Aug 2014

FEI Primer: Degree of Difficulty

by Brian Fremeau

Strength of schedule has never been more important in college football. Probably. We don’t know if the playoff selection committee is actually going to value it, how they are going to measure it, or how much of a factor it will play in their decision making. But we’re sure it is going to be important. Pretty sure.

The new playoff era is upon us, promising a more exciting postseason and a bit more certainty in the process of determining the national championship on the field. The team that takes the crown will have won a pair of games at season’s end against two of the best opponents in the country. The four teams that face off in those playoff games will have taken very different roads to get to that stage, of course. It is probable that the four teams will all be champions of one of the Power Five conferences -– ACC, Big Ten, Big 12, Pac-12, SEC -– but even within those conferences, schedule strength can vary dramatically. It’s even more variable when we consider the myriad ways of calculating strength of schedule.

Readers familiar with the Football Outsiders Almanac and the weekly FEI ratings and analysis posted here know that we take a unique approach in our calculations of strength of schedule. We know that simply measuring the average strength of a group of opponents can be misleading. A two-game schedule against opponents ranked No. 1 and No. 128 presents a fundamentally different challenge than a two-game schedule against opponents ranked No. 64 and No. 65. Strength of schedule measured from the top down, with more weight given to a team’s toughest opponents, provides us more precise data. We have chosen to present strength of schedule (SOS) as something very specific and measurable -– the likelihood that an elite team, two standard deviations better than average, would go undefeated against a schedule of opponents.

If we modify our perspective, we can calculate alternate iterations of SOS data that are just as accurate. What is the likelihood that a good team, one standard deviation better than average, would go undefeated against a schedule of opponents? What is the likelihood that a good team would lose three or fewer games? What is the likelihood that an average team would be bowl eligible, winning at least six games? The schedule of opponents is the same, but the degree of difficulty may be very different if we recalibrate our perspective.

For example, who will play a more difficult schedule this fall according to FEI ratings, the Florida Gators or the Arkansas Razorbacks? The tables below list their respective schedules and the projected FEI ranking of each of their FBS opponents.

Arkansas 2014 FBS Opponents Florida 2014 FBS Opponents
Date Opponent FEI Rank Date Opponent FEI Rank
8/30 at Auburn 8 8/30 Idaho 119
9/13 at Texas Tech 42 9/6 Eastern Michigan 126
9/20 Northern Illinois 50 9/13 Kentucky 79
9/27 Texas A&M 18 9/20 at Alabama 1
10/11 Alabama 1 10/4 at Tennessee 75
10/18 Georgia 13 10/11 LSU 7
10/25 UAB 117 10/18 Missouri 16
11/1 at Miss. State 36 11/1 Georgia 13
11/15 LSU 7 11/8 at Vanderbilt 56
11/22 Mississippi 30 11/15 South Carolina 6
11/29 at Missouri 16 11/29 at Florida State 3

Florida and Arkansas share four common opponents – No. 1 Alabama, No. 7 LSU, No. 13 Georgia, and No. 16 Missouri. Florida will face two other projected top-10 teams, No. 3 Florida State and No. 6 South Carolina, while Arkansas will face only one other top-10 team, No. 8 Auburn. From the perspective of an elite team, the Florida schedule presents more potential pitfalls and rates as tougher than the Arkansas schedule. An elite team would have only a 6.8 percent chance of going undefeated against the Gators’ schedule, and an 8.1 percent chance of going undefeated against the Razorbacks’ schedule.

A good team on the other hand, one standard deviation better than average (approximately ranked No. 20 to No. 25 in FEI) would have a tougher time with Arkansas’ schedule because of the next tier of opponents. Against the Razorbacks’ schedule, the good team would face ten top-50 opponents, and may have difficulty achieving a .500 record. Our calculations give a good team only a 32.0 percent chance of losing four or fewer games against that schedule. Florida’s schedule features only six top-50 opponents. A good team would have a 46.7 percent chance of losing four or fewer games against their schedule.

So which one is tougher? Debates about schedule strength can be very complex and the data can be difficult to process. I teamed up with Andrew Garcia Phillips of Chartball.com to create an interactive visualization of strength of schedule to bring the data to life. Andrew and I will be updating the chart tool throughout the season as new data pours in and FEI ratings are reproduced each week.

Click on the image above to access the interactive

The selection committee isn’t going to need to sort out Arkansas and Florida. They are going to have to wrestle with schedule strength arguments at the top, and that’s where the elite team perspective comes back into play. The committee may want to determine “degree of difficulty” as a way to separate teams that are in the mix for one of the four playoff spots. I’ll define degree of difficulty here as a measure of a team’s overall record against its schedule, and I’ll use the elite team schedule strength distribution as the data to compare teams. The table below presents the degree of difficulty (DoD) faced by each of the 0-loss, 1-loss, and 2-loss teams at the end of the regular season in 2013.

2013 End Of Regular Season
Team Record BCS Rank FEI Rank DoD
Auburn 12-1 2 4 .389
Florida State 13-0 1 2 .431
Stanford 11-2 5 1 .547
Alabama 11-1 3 3 .554
Michigan State 12-1 4 9 .629
Baylor 11-1 6 7 .702
Ohio State 12-1 7 8 .719
Missouri 11-2 8 10 .784
Oregon 10-2 10 11 .786
Oklahoma 10-2 11 20 .811
Central Florida 11-1 15 23 .815
South Carolina 10-2 9 12 .852
Clemson 10-2 12 26 .903
Louisville 11-1 18 22 .913
Northern Illinois 12-1 23 43 .919
Oklahoma State 10-2 13 6 .930
Fresno State 11-1 20 48 .980

Note that degree of difficulty is based on the FEI ratings of opponents, but is not a substitute for FEI. Degree of difficulty is concerned with record against schedule only, not efficiency against schedule.

Michigan State ranked No. 4 overall in the final BCS rankings, and with a Big Ten championship under its belt, may have had a strong argument to reach the playoff had it been in place last year. But according to FEI data, it was more difficult to go 11-1 against Alabama’s schedule (55.4 percent likelihood) than to go 12-1 against Michigan State’s schedule (62.9 percent likelihood). It was even more difficult to go 11-2 against Stanford’s schedule (54.7 percent likelihood). And at the top, it was more difficult to go 12-1 against Auburn’s schedule than to go 13-0 against Florida State’s schedule.

The College Football Playoff selection committee faces a degree of difficulty of its own. By what measure will schedule strength be evaluated and how much will it matter? We hope that their process to answer these questions will be thorough, consistent, and informed. In addition to the SOS and visualization that will be updated weekly on my site, I’ll be adding a column for degree of difficulty to the FEI ratings posted here so that it can be tracked against throughout the season.

Posted by: Brian Fremeau on 13 Aug 2014