Upper Hand: Michigan State vs. Michigan

Welcome to Upper Hand, which I hope will be a recurring feature here at BTP this offseason. Freed from the tyranny of having to write about the latest on-the-court results, I can take this offseason to look at the broader history of the league.

Of course, the main point of looking back at history is to find evidence that your program is better than your rival’s program. That’s what Upper Hand is all about. As BTP’s resident stats guy, I was curious if there was a way to use numbers to break down rivalries in a consistent and systematic way.

In order to do that, we have to keep things simple. For purposes of this column, we’re going to look at head-to-head results and nothing else. Yes, Big Ten titles matter. Yes, national championships matter. But in order to factor those into this analysis, we’d have to come to a consensus on how much they matter relative to each other and relative to head-to-head results. Everybody is going to have a different answer to that question.

But if you look purely at head-to-head results, you only have to answer one question: how much more should you weight recent results vs. results from decades ago?

It makes intuitive sense that this year’s games say more about the relative state of two programs than games from the 1920s. But what about three years ago? Five years ago? Ten?

Rather than drawing an arbitrary cutoff point, I decided to use a principle that should be familiar to everyone from their high school science classes, that of the half-life. Think of a win like a piece of radioactive uranium. As time goes by, its potency decays.

Ah, but what value should we use for the half-life of a win? There’s no definitive answer to that question, but since that’s the only question we’re asking, we can easily show results under several different scenarios. Results are calculated using half-lives of 2 years, 5 years, 10 years, 20 years, 30 years, 40 years, 50 years, and 1000 years.

We’re going to start with the Michigan and Michigan State rivalry. There are a couple of reasons for that:

• Michigan has won the last three games and the most games overall, but MSU won the five games before that and has also won 10 games in a row in the last 25 years. That means we’ll definitely get different results with different half-lives.
• Michigan has an Upper Peninsula and the lower peninsula is shaped like a hand. I couldn’t resist the pun.

The full chart is below. As mentioned above, the columns show different results for different half-lives. I also decided to show who would have had the upper hand at the end of every season over the past 50 years. That’s what you see in the rows.

Interesting results! The Wolverines have the overall head-to-head advantage (as indicated by the rightmost column), but depending on how quickly you believe wins should deteriorate, the Spartans overtook them somewhere around the turn of the millennium. If you think wins have a very short shelf life, then Michigan currently has the upper hand, but that’s only been true twice since Tom Izzo took over in East Lansing.

So what’s the best half-life to use? Whichever one makes your team look best, obviously!