How Much Of A Problem Is Michigan's Defense?

The mantra that "defense wins championships" isn't restricted to football, and that's starting to get kicked around as a potential problem for Michigan when the bullets start flying in March. Luke Winn gets the first kick at the can by leaving them out of a five-deep Prime Title Contenders tier in his recent column:

You might be asking, what about Michigan? If the Wolverines' profile stays the same, they could be the most interesting test-case of this NCAA tournament. They have the nation's best offense but only the No. 45 defense -- not red-flag-worthy, but well worse than any champ from the past 10 years. Michigan cutting down the nets in Atlanta would be a breakthrough statement for the power of offense.

Despite not playing, Michigan has risen to 39th since he put up his column. There is plenty of time for Michigan to get right in this metric.

But let's say they finish the season about where they are now. This seems like something of an issue. Winn assembled the last ten years of Elite Eight teams and found that relatively few found themselves outside of the top 25 in defensive efficiency.

If Michigan was to make the Final Four with its current defensive numbers they would be better than only four teams in the past ten years—the dual outsiders from a couple years back, Dwyane Wade's Marquette team, and TJ Ford's Texas team. Those are kind of grim odds.

However, not many of the teams to make it were the #1 offense in the country, either. And the ranks can be misleading here. As mentioned, they have slid up six spots whilst eating cheeseburgers the last few days, and if thy were to shave a single bucket off 100 Hypothetical Opponent possessions, they'd leap up another 11 spots. The margins here are slim.

Meanwhile Michigan is leading the charts on offense by a mile. Their adjusted efficiency is 3.6 points clear of #2 Florida. You could hack off 3.5 points of that, toss it on Michigan's defensive numbers, and come up with a pairing of the country's #1 offense with the 16th-best defense and then you're looking at a tier I contender, no questions asked.

The point is that maybe the margins matter here, and the wheat gets separated from the chaff by differential. How does Michigan stack up there? Pretty well.

[numbers collected before last night's games, so this overrates Louisville a little.]

Florida has wrecked everyone they've played save K-State and Arizona and are far-and-away leaders here; Michigan is second. This is pretty close to the Kenpom rankings themselves, obviously.

Defense Wins Just As Much Championship As Offense

First: the Defense Wins Championships cliché doesn't stand up. I took Winn's data set, grabbed their year-end adjusted efficiency numbers, and got their efficiency differentials. I gave each team a point for each win they acquired after reaching the elite eight (3 for the champ, 2 for the runner up, etc.), and then acquired r values* between those three metrics of quality and wins. Over the decade-long sample there is basically no difference between offense and defense when it comes to acquiring wins—offense is actually ahead fractionally—and looking at the two metrics together is significantly more predictive:

• AOE R value: 0.28
• DOE R value: 0.26
• Efficiency Differential R value: 0.39

If you were so inclined you could argue that there's a winnowing effect that prevents poor defensive teams from reaching the Elite Eight, but then you're trying to find a mechanism that works for the first three games of the NCAA tournament only to abandon teams in the crunch—not likely.

I like this result. It is intuitive. It implies that scoring two points at one end is as valuable as preventing two at the other. It won't get me on Malcolm Gladwell's Christmas card list or acquire me a professorship at Princeton, but unlike the things that do bring those benefits this result makes sense.

So… as long as Michigan's efficiency differential remains sky high, they've got as good a shot at the title as anyone. Except Florida. Long way to go, obviously; if Michigan ends the season as they stand today they should be amongst the title favorites.

*[A brief word on R values: these are not significant, but something can be suggestive without reaching levels of statistical rigor necessary to declare you've found the Higgs Boson. In this case they're just one datapoint we are making a reasonable argument with, instead of flogging ridiculous things like David Berri does. As always, R can change wildly depending on the parameters you set.]

A COUPLE OF OTHER THINGS

I took the top eight teams so far this year and threw them in with the 80 teams already in this sample and ranked by efficiency margin. There's good news and bad there. The good: Michigan is a notch above last year's Kentucky outfit! The bad: Florida is #2 in the entire sample, behind only the dominant Kansas title team in 2008 and just ahead of the dominant UNC title team in 2005. Florida is ridiculous right now.

Everyone looks good, in fact. Five of the eight teams from this year are in the top quarter of the sample and all are in the top half. I assume there's a flattening effect that goes on as conference play and mean regression brings high-fliers to earth; also this group of teams has not been ruthlessly culled by the VCUs and Butlers of the world. Strong teams also cry, Mr. Lebowski.

The table is after the jump for anyone so inclined.

[AFTER THE JUMP: A TABLE! WOO!]

Champs are bolded. This year's top eight in italics.

As this should make clear, efficiency is an edge but randomness is gonna random. Unless Michigan can significantly distance themselves from the pack their median expectation in the tournament is an Elite Eight loss.