Kansas St vs. Oregon vs. Notre Dame: by the math

We know you’ve been inundated with debate about the undefeateds in college football. Here’s a statistical tidbit by Joe Kaboski, an economics professor at Notre Dame. So you know it’s going to be very biased towards ND.

It’s still worth reading though; as it raises some valid numerical and statistical points.

Prof. Kaboski makes a “very simple statistical argument.”

Here is Prof. Kaboski’s thoughts on sorting out teams 1-3 in this week’s BCS standings:
People seem to give KSU (and also Oregon) the benefit of the doubt over ND based on scoring differential, but it is an argument biased toward teams with relatively strong offenses rather than strong defenses. For example, a team with strong offense wins 60-30, while the team with a strong defense wins 20-10. The former score looks like more of a blowout, but both teams were twice as good as their opponent.

That is effectively what has happened with KSU (average score 42-18) and Notre Dame (26-11), but KSU has been 138 percent better than their opponents, while ND has been 135 percent better. That is effectively a wash, especially since ND has played a slightly stronger schedule. (Oregon has been 169 percent better, but they’ve played a much weaker schedule). Moreover, when you look at common opponents, the numbers overwhelmingly favor ND. Notre Dame averaged 343 percent better than Oklahoma and Miami (35-8 score), while KSU was only 109 percent better (34-16 score).

In baseball, we never think that being down by 3 runs is the same in Coors Field against the Rockies as it would be against the pitching staff of the San Francisco Giants. Indeed, sabermetricicans use what is called a Pythagorean formula to predict wins based on runs scored and runs allowed. If we use the football Pythagorean formula, one would predict that both KSU and ND would have won 88 percent of their games.