In this post, I will hope to answer the question of whether to be fully depressed about Duke's defense so far, or only mostly depressed because there is some random bad luck going on.
The bad luck would be Duke's sub-300 ranked 3pt% allowed. Pomeroy showed that 3pt% has very little to do with the defense here:
http://kenpom.com/blog/index.php/weblog ... percentage
I'm willing to believe Duke's defense has had very little to do with allowing 41.4% 3pt so far. Let's normalize it and see how big an impact it has on points per possession allowed.
The worst 3pt% Duke has allowed since 2002 was 33.8% (2003 and 2009). Let's assume this team is that bad at defending 3s and deserves to tie the worst mark since 2002.
Let's question that assumption critically and wonder if Duke's small sample of opponents so far this season are great at shooting the 3, so we shouldn't normalize as much. Here are their 3pt percentages, including the games against Duke:
Siena - 31.3%
Bryant - 38.6%
Kentucky - 27.6%
VCU - 38.4%
Georgetown - 40.7%
Duke's 41.4% defensively is already looking like a lot of bad luck, since not a single opponent shoots that well on the season, and Duke typically is not so terrible at this.
We should do some weighting based on how much each team shoots 3s, but I want to go to sleep, so instead let's just average the numbers out. Comes out to 35.3% average 3pt percentage among the five opponents. Especially considering that we're including the bad luck Duke games in these season-long numbers for each opponent, I'm comfortable believing these teams should have shot no better than 33.8% 3pt altogether against Duke (this is the "worst Duke number since 2002" 3pt%).
If we normalize the 36/87 (41.4%) shooting on 3s this season against Duke to be 29/87 (33.3%), this gets us 21 fewer points allowed by Duke this season, over 359 defensive possessions (according to Kenpom). This is 0.058 fewer points per possession, or 5.8 points per 100 possessions.
Now we need to figure out how rebounding works into this (Duke doesn't get 100% of the rebounds off opponent missed 3s) and I'm going to assume it cuts the 5.8 down to about 4.3 just by rough math.
If we normalize for 3pt percentage "luck," then Duke's raw defensive efficiency goes from 105.3 points per 100 possessions to 101.0. Duke's adjusted defensive efficiency being 95.2 reflects Duke's relatively strong strength of opponent offenses and Kenpom's misguided preseason number serving as a sort of anchor, but the adjustment is not so significant from 105.3 that we need to worry about it too much. If we lower Duke's adjusted defensive efficiency by 4.0 instead of 4.3, we get 91.2. That's the 6th best in the country.
So it turns out allowing 7 more 3s than should be expected in 5 games may have a significant effect on defensive efficiency. Having the #199 2pt percentage allowed is harder to explain away, though. Duke's defense is actually benefitting from some good luck on 2pt jumper accuracy (#63 in the country) and is slightly above average in 2pt at rim accuracy. Duke's non-luck-based problem is that they are the 17th worst team in the nation at preventing shots at the rim from being attempted. Opponents are getting to the rim against Duke, and that's not bad luck at all. This is all from hoop-math.com.
I want to believe "if not for the 3pt bad luck, Duke would have the #6 defense," but the other numbers are so bad, I don't see how it's possible. 17th highest frequency of shots allowed at the rim. Nationally mediocre defensive rebounding rate and turnover rate. The only things Duke does well is not fouling and not allowing 3pt attempts. Is that really all it takes to be the 6th best defense?
I think the main problem with this is that we should normalize every team's unluckiest defensive stat as well, and then see how Duke would rank. The most I'm really willing to take from this is that Duke had been unlucky on 3s defensively and it has had a significant effect on the overall defensive efficiency.