Four Factors interactions and the virtues of defensive rebounding
Statistical pioneer Dean Oliver broke down basketball into four fundamental facets: shooting, rebounding, turnovers and free throws made. These four factors encompass every single way in which a team can score points and get opportunities to score points (possessions). However, to say this encompasses the entire game of basketball would naturally be ridiculous.
The game of basketball really takes place in the tensions and synergies between these stats. When Chuck Hayes smartly boxes out his opponent, allowing a teammate to grab a rebound, he is helping his team win more than Troy Murphy ripping the ball away from a teammate off a missed free throw. Similarly, Nate McMillan can choose to emphasize eFG defense and rebounding over offensive scoring efficiency by playing Marcus Camby over Gerald Wallace. He also may choose to emphasize the little-known fifth factor of "age" by playing Kurt Thomas instead using small-ball lineups.
In any case, it's these tensions between different ways of scoring and gaining possessions that makes basketball so interesting. In the case of rebounding, we know that a player's individual rebounding stats don't predict a unit's group rebounding performance particularly well. There are significant diminishing returns effects. Furthermore, a team is better able to control its offensive rebounding percentage than its defensive rebounding percentage. The natural upshot of Witus's work would seem to be that defensive rebounding is one of the least important box score stats.
Peering into the black box
Some teams are better at defensive rebounding than others, though. Even though teams have more control over their ability to get offensive rebounds, they still control 44% of their defensive rebounding performance. What's more, the 10 best defensive rebounding teams from 2010-11 were the Magic, Bulls, Hornets, Heat, Nuggets, Bobcats, Mavs, Bucks, Celts and Spurs. All but the Bobcats were above average in defensive rating, which is a fairly remarkable feature of a stat that is only supposed to be 20% of defense, and is more controlled by the opponent than the team.
Here's the interesting thing:
On a team level, defensive rebounding actually correlates strongly with defensive effective field goal percentage. The RSQ is .36, and the slope is -.55 for you ueber nerds. Numbers from previous years show a similar relationship.
Now what has to be parsed out is to what exactly are the attributes that are causing this correlation of two seemingly totally independent acts? There's no reason to assume causation here. There are two possible explanations in my mind. First, players who are better at defensive rebounding are generally better at defending. When people make fun of Kris Humphries, Zach Randolph and Troy Murphy for hoarding defensive rebounds while failing to contribute to anything else, they forget the multiple strong rebounders who are also very good defenders: Josh Smith, Gerald Wallace and Dwight Howard spring to mind. Additionally, although Witus showed that a strong defensive rebounder doesn't increase the rebounding prowess of the team when he is on the floor at as high a rate as a good offensive rebounder, he did show that individual defensive rebounding did explain over 90% of what difference between units did exist. So the relationship is strong, but not as significant as for offensive rebounding.
The second possible explanation is that defensive rebounding is an effort and scheme issue that ties it to eFG percentage. We see this with the Bobcats when Larry Brown took over the team, for example. Their defensive rebounding percentage skyrocketed right along with a big drop in eFG allowed. The same is true for Monty's Hornettes.
My takeaway is this: Nate sucks as a defensive coach (the Blazers were the second worst playoff team in defensive rebounding percentage, ahead of only the hapless Knicks who don't even try on defense) and defensive rebounding percentage deserves a second look as a stat for evaluating defensive players. If we throw out the Troy Murphys of the world, the best defensive rebounders will probably be good at helping a team force its opponents to shoot worse.