There's been an interesting argument going around the web the past few days. Is it beneficial to crash the boards, or are teams better off getting back on defense? Kevin Pelton has a good summary of the arguments over at Basketball Prospectus.
To simplify - the argument appears to be boiling down to trying to correlate stats with winning. This seems logical, but that sentence was a lot easier to type than it is to execute. The strongest argument I've seen is this one, which points out the obvious fact that offensive rebounding percentage is a function of more than just going for offensive rebounds. Teams that are good at rebounding the ball will get more offensive and defensive rebounds, and it doesn't mean they're "crashing the boards" more.
So the breakdown that blogger did was to calculate the "expected" offensive rebounding rate for each team relative to their league average due to their relative defensive rebounding rate. Teams that were better at DR% than OR% relative to their league average were, more often than not, winning teams.
While I don't disagree with that argument, I think you can only make a limited conclusion. The fact that freely available statistics can't differentiate between "crashing the glass" and offensive rebounding makes it impossible to come to a strong conclusion either way.
I would argue that they're looking at the wrong question. I've argued for some time that offensive rebounding is about rebounding skill more than anything else. It doesn't matter how hard you "crash the glass" if you don't have elite rebounders. But at the same time, defensive rebounding is really about sound fundamentals. If your whole team boxes out then they'll almost certainly bring down the defensive rebound.
I'll explain what I mean with a series of plots. Note that each plot below including every Division I basketball team from last season. Each dot represents a team. The "Defensive Efficiency" stats are the Pomeroy adjusted efficiency, which controls for tempo and strength of schedule. Each plot includes a "best fit" line that Excel threw in there for me, with the slope and R^2 in the bottom left hand corner.
The first plot shows what seems to be a counter-intuitive conclusion, that more offensive rebounding means better defense:
Of course, more defensive rebounding correlates even more with defensive efficiency:
The conclusion from those two plots is an obvious one: better teams out-rebound their opponents, and also tend to play better defense. Good efficiency, good rebounding and good shooting all tend to be correlated. This is why we need to look at rebounding stats by comparing defensive rebounding to offensive rebounding. The way I did this was by subtracting OR% from DR% to get "rebounding differential". A team with a larger rebounding differential is better at defensive rebounding relative to how well they collect offensive boards.
The above plot tells us that greater offensive rebounding, relative to defensive rebounding, leads to worse defense. But that does not imply that crashing the glass makes you worse at defense. What it more likely means, as I said above, is that a strong defensive rebounding differential correlates with more sound, fundamental play. And sound, fundamental play correlates with lots of good stuff. For example, it means more assists and fewer turnovers on offense:
To me, these last two plots present a much stronger conclusion than anything that we can say about crashing the glass and playing defense. Offensive rebounding probably makes your defense a little bit worse, but it's impossible to say from the available data that this is certain. But a better rebounding ratio means that a team is better on the defensive glass than the offensive glass, and that tends to correlate with other "good fundamentals" stats.
That doesn't mean you can't have success if you're not good on the defensive glass. Syracuse, Marquette and Baylor are among the elite programs that have had success in recent years despite being much better on the offensive glass than the defensive glass. Syracuse and Marquette have had success with high-risk/high-reward defenses that allow a lot of easy baskets but also generate a lot of transition offense. Baylor just out-athletes their opponents.
But if you're looking to see if your team is playing sound, fundamental basketball? You want to see them preventing turnovers. You want to see them getting a lot of assists. And you want a high rebounding differential. I think that's clear.