I majored in computer science and minored in math, so I thought about how it might be done, and I came up with this. If anyone sees any errors in my thinking, please feel free to say where I went wrong. Here’s a simple example, using four teams:
First week, A beats B by 20 and C beats D by 10. So we say A is better than B by 20 points and C is better than D by 10 points. But so far, we have no way to compare A and B to C and D.
Second week, A beats C by 10 and B beats D by 10. So now we have a way to compare all teams.
Using A over C exclusively (where we say A is 10 points better than C), and assigning an arbitrary 100 strength points to A, we have:
A 100
B 80
C 90
D 80
Next, omitting the A over C result and using the B over D result exclusively:
A 100
B 80
C 80
D 70
Now, we must average the points for all teams to get a final result:
A 100
B 80
C 85
D 75
Although A defeated C by 10 points, when the results of other games are factored in, they are considered to be 15 points stronger. This is why Sagarin gets some apparently head-scratching ratings, such as Michigan being 3 points stronger than Notre Dame when the Irish defeated them by 7.
As I’ve pointed out before, the weakness of this system is it ignores how teams, in effect, “choose” to win. Some keep the gas pedal on the whole game. Others, such as Notre Dame at times, tend to go conservative with the lead and are content to milk the clock. If Sagarin would give a points bonus for winning the game, it would negate the pure points aspect and would likely result in ratings that would appear to make more sense. Would it be more accurate? I don't know.
Running up the score is apparently a big factor in his rankings. He can explain it all he wants it has zero credibility.