Strength of Schedule: Miami vs. Michigan

Through 25 games, which team has played a more difficult schedule: the Miami Hurricanes, or the Michigan Wolverines?

Seems like a fairly simple question. And the standard sources give you fairly consistent answer: it's close, but Miami's schedule has been a bit more difficult.

Is there any way that's true, though?

Using the current KenPom ratings, I took the opponent and location for each of the 50 relevant games here. For each one, I determined how likely Ohio St. -- currently the #13 team in Pomeroy's ratings -- would be to win in each situation. Here are the 10 most difficult games, color coded by which of the two teams (Miami or Michigan) played them:

(Miami's home game vs. Duke also comes in at 55%.)

So, the team with the supposedly easier schedule has the seven most difficult games. Looking at the 10 easiest games, it becomes clear how this is the case:

So, there you have it. Michigan has seven of the 10 most difficult games, but also eight of the 10 easiest. The strength of their schedule on the top end is cancelled out by its weakness on the bottom.

Except, you really can't look at it like that. As you probably noticed, the range of %s in the first chart (15% to 55%) is quite a bit wider than the range in the second one (94% to 100%). All of the games on the second chart are very likely wins, while the first chart is all over the place.

This has an interesting effect when you're calculating SOS by just averaging the ratings of a team's opponents. For these teams, whether they're playing the 327th best team or the 347th best team, their expected win percentage is going to be about the same. On the other hand, there's a huge difference between playing the best team and the 21st best team.

This is more easily shown with a fairly simple chart, splitting each team's schedule into groups of five games, from most to least difficult:

Probably a good time to say that I think the excepted W% column is very important when gauging SOS, and the average rating column is essentially worthless. We care how likely a comparable team would be to win these games; I'm not sure why we would care about the average rating of opponents.

In that light, this chart is interesting. Michigan has a much lower eW% (meaning a more difficult schedule), but their avgRat is also noticeably lower than Miami's (meaning an easier schedule).

The reason for this is the same issue as before. Michigan's avgRat gets killed in the 21-25 group when compared to Miami's, but it just doesn't matter that much, as can be seen in the small difference in eW%. On the other side of the spectrum, their avgRat isn't that much higher for the 1-5 group, but the difference between .938 and .901 (along with the location of the games) has a huge impact on eW%.

So, what's the point? Well, Miami is currently ahead of Michigan in almost every single bracket projection. Which can partially be attributed to the Canes having one fewer loss, but also the consensus in various metrics that they've done it against a more difficult schedule. I think if you look at SOS in a more accurate way, it can lead you to some much different conclusions in terms of seeding. I've looked at this before, and will revisit it in my next post.