Wednesday, November 17, 2010

Measuring Strength of Schedule

Over the last few weeks, I have heard a lot of discussion about Boise State and TCU and why they should not be given the same consideration for the national championship game as teams from automatic qualifying conferences. One of the arguments is couched around the perception that Boise State and TCU play easier schedules than other top ranked teams. This got me to thinking about how to measure strength of schedule. There are existing measures of SOS in both NCAA FBS football and NCAA division I basketball.

The NCAA division I basketball is calculated as: 2/3 opponents' winning percentage and 1/3 opponents' opponents' winning percentage. The Sagarin ratings (linked above for NCAA FBS football) are non-intutive, and frankly I am not sure how they are calculated even after reading the notation at the top, and the NCAA basketball strength of schedule measurement seems arbitrary or contrived.

Since I am unaware of a measure of strength of schedule that I feel is simple I thought that I would come up with my own measure of strength of schedule based on the actual rankings of each FBS school for each team. Thus the most productive team will have a rank equal to 1 and the least productive team will have a rank equal to 120, since there are 120 FBS schools. Here it is. Strength of schedule is the average of each team's opponents production rank. Teams with a high strength of schedule number have a weaker strength of schedule, and teams with a low strength of schedule number have a stronger strength of schedule. That seems simple.

Now, there are some issues with calculating strength of schedule.
  • The first is what to do with FBS schools that played non-FBS schools. What I decided was since there are 120 FBS schools this year, then for each non-FBS school a team plays was to measure all non-FBS schools as having a Strength of Schedule equal to 121. This is not perfect since a non-FBS football team may be better than the worst FBS school, which has a rank of 120.
  • Second, highly ranked teams (i.e. whoever is ranked #1) cannot play themselves, so they may potentially have a lower Strength of Schedule rating. Likewise, low ranked teams may potentially have a higher Strength of Schedule rating, since they cannot play themselves.
  • Third, I am only calculating the Strength of Schedule for the games that have been played, not for games that are currently on the schedule that have not been played. This will change the final strength of schedule measurement.
  • Fourth, the difference in rank from the best to second best team is only 1, but that may not really be the difference in their production, and hence my measure of strength of schedule is not totally measuring the difference in each team's opponents perfectly. I could also base strength of schedule on each team's final production numbers, but have not as of now.

With those four issues presented (and possibly others that I have not worked on) let's use an example to see how the strength of schedule is calculated for each NCAA FBS team.

Thus, for the week ending November 13, my model estimates that Boise State is the #1 ranked NCAA FBS team in the nation. So using Boise State's 2010 schedule here is how I calculate each NCAA FBS schools Strength of Schedule.

Virginia Tech
Oregon St.
New Mexico St.
San Jose St.
Louisiana Tech
Fresno St.


Utah St.

Since Idaho was the last team that Boise State played Boise State's Strength of Schedule is measured as the average of the teams rank in terms of overall production, which for Boise State equals 77.556.

Looking at the number we know that a team that plays a purely average schedule will have a strength of schedule rank equal to 59.5, so overall Boise State has a weaker schedule than an average schedule. Guess what? Of the schools in my top 25 for as of November 13, Boise State does not have the easiest strength of schedule, and the team that has a easier strength of schedule than Boise State is not TCU. Check back tomorrow to find out who!

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