On Strength of Schedule

In any College Football ranking system, Strength of Schedule, is a crucial component. The BCS's method of calculating SoS relies solely on Win-Loss Records (Just like everything else in the BCS). This is a less than ideal situation because a team's record is less an indicator of their strength than their performance in those games. Consider two teams with 5-5 records, Team A won it's five games handily while the losses were close and hard fought. Team B, on the other hand was blown out in their five losses and just barely scraped through the games it won. We all know Team A is better than Team B, but to the BCS they are equally strong opponents. Because of this I use the Team Rating (performance) to determine how tough an opponent is. In my ranking system, a team's Strength of Schedule is simply the average Team Rating of their Div 1-A opponents. I don't think that this is the best system, but it's easy to balance and produces expected results. Below, I'll discuss more about SoS and why a simple average is not always reflective of a schedule's actual difficulty.

What makes a schedule hard?
Is the hardest schedule the one with the greatest average strength of opponents, or is it the one that's hardest to get through undefeated? What's the difference?

Consider two schedules, one with 5 strong teams and 5 weak teams, and a second with 10 average teams. Both have an identical average strength, despite being very different. Given a top tier team, or any above average team, the schedule with 5 strong teams would probably result in a worse record than the one with 10 average teams. As you get to the below average teams, the first schedule becomes the easier one, due to the fact that a below average team has a better chance against the 5 weak teams than against any of the average teams. What we see, is that how hard a schedule is, varies from team to team and that the average difficulty of opponents does not always reflect a true strength of schedule.

A Possible Solution
First, a true SoS solution should be based on performance as opposed to W/L records. Second it should realize that there is a very substantial difference between average teams and the top 20 or so teams. Third, it should rank a schedule with 5 strong teams and 5 weak teams as more difficult than a schedule of 10 average teams.

Strength of Schedule
Rank all teams according to their Team Rating score.
Each opponent ranked in the top 10 is worth 3 points.
Each opponent ranked 11-30 is worth 2 points.
Each opponent ranked 31-70 is worth 1 point.
Each opponent ranked 71-100 is worth 0.5 points.
Each opponent ranked 101-120 is worth 0 points.
Each 1-AA opponent is worth 0 points.

Average a team's total points against the number of games played to find SoS.

This system satisfies the three criteria listed above. We'll see how this pans out over the course of the season and see if any adjustments or revisions need to be made.