Strength of Schedule and Notre Dame

FBSchedules.com asked a while ago if Notre Dame's strength of schedule is different that selective "Power 5" conference teams.  Now with Notre Dame playing in the "final four" later, I thought that I would take a look at strength of schedule (SOS) among teams during the regular season (through December 8th).

Conclusion:  Each team has played an average SOS this season.  Details on this follow below.

First, how do I measure SOS?  SOS is the average of each team's opponent's current production ranking using the Complex Invasion College Football Production Model.    Thus team's with a lower SOS numerical value, the stronger the team's SOS.

Thus for the four teams that made the FBS invitational, here is their SOS for this season to date:

Alabama SOS = 63.92;
Clemson SOS = 73.00;
Notre Dame SOS = 75.92;
Oklahoma SOS = 67.77.

Alabama has had the toughest SOS (playing currently ranked #4 Mississippi State and #5 Georgia helped lower their SOS) and Notre Dame had the easiest SOS at 75.92.

So are these two similar or different overall?  To answer this, first note that the average SOS for all games played up to December 8th was exactly 70.00.  Thus Alabama and Oklahoma both had SOS that was stronger than average and Clemson and Notre Dame had SOS that was weaker than average.

But is Notre Dame's 75.92 that much greater than the "league" average?  To answer that, I calculated the SOS standard deviation for this season and it is equal to 9.68.  Thus to determine if one team's SOS is similar or different, I evaluate each team's SOS relative to the "league" SOS.  Since Notre Dame is within one standard deviation of the "league" SOS, and that Alabama's SOS is within one standard deviation of the "league" SOS, I conclude that each team's SOS is average.  Thus both Alabama and Notre Dame have a SOS that is within one standard deviation of the "league" SOS.

What is the current distribution of SOS?  Through December 8th, 83 (or 63.8%) have a SOS that is plus or minus one standard deviation of the "league" SOS.  Team's with an SOS that is between one and two standard deviations lower than the "league" SOS equal 22 (16.9%), as well as 22 teams with a standard deviation between one and two standard deviations below the "league" SOS.  Only 2 teams have a SOS that is greater than two standard deviations (FIU & North Texas) and 1 had an SOS that was less than two standard deviations below the "league" SOS (UCLA).

Historically, SOS has not been statistically significant in determining winning percentage after controlling for points scored, points surrendered and conference affiliation.  That is also true for teams at the upper end of the winning percentage distribution using quantile regression.