One of the most widely used stats in the NBA is the grossly misleading rebound. We all discuss how field goals can come from sharp passes, or how a player’s field-goal percentage is lower because he has to take too many of the team’s unassisted shots at the end of the shot clock. Assists are criticized too for their subjectivity and how certain players can have flaming bag assists, holding onto the ball too long and getting a bailout when a teammate hits a jumper. Rebounds, however, are largely taken at face value where players like Roy Hibbert get criticized for for a lack of rebounding while others like Drummond or wings like Stephenson get lauded. Yet rebounding isn’t a singular, independent activity; it’s a team-wide activity. Understanding that, and how individual rebounding doesn’t tell the whole story, can lead to more insights into which players help you more on rebounding and why.
Let’s frame this investigation with the helpful concept of optimization. A player may try to optimize his own stats by positioning himself for every rebound and grabbing any near him. But this is not the same as optimizing his own team’s rebounding. The disparity between individual and global optimization, and the conflation of the two, can be seen in systems like roadways where you can shut down an urban freeway and improve travel time. The problem is that what incentive exists that would urge players to help their teammates rebound instead of themselves? There are some factors like a coach’s influence and the positive or negative response of teammates, and this is getting into concepts like the Nash equilibrium, but there are some players who choose to box out opponents and let their teammates pick up the rebound. Picking out those guys from the available data, however, is a tough exercise.
The Team Rebounders
Based on the available public data, the best way to analyze team rebounding and its relationship with an individual player is using what’s essentially a plus/minus model except that we’re only looking at rebounds. Basically, you use regression to see which players are associated with the most rebounds per available rebound, and you can see an example of that here. This is not perfect, of course, but no stat will be and it uses three years of data to stabilize the results more.
Thus, if you then look at the relationship between individual rebounding rates and team rebounding rates, you can create a list of players ranked by the disparity of their team effect and their own individual numbers — guys who box out and guys who steal rebounds, essentially. In the below table, you see the guys who are overrated the most by their rebounding numbers. Rondo is infamously known for his stat padding, so perhaps it isn’t surprising to see him at the top. There are also a few notable rebounders here like Drummond, Plumlee, Garnett, and Jordan. Garnett set a career high in defensive rebound rate, but his team got killed on the glass and he’s gotten quite old. If you watch guys like Drummond and Jordan play, you do see how they’ll snatch every rebound they can rather than staying on the floor and helping their teammates grab one. You also see a few other wing players. Some teams llke Indiana let their big men box out and their wing players grab the ball and go upcourt.
For an example of a misleading rebound, Gerald Wallace boxes out a bigger player while Rondo waits in an unoccupied space at the end of the clip below. Then Wallace, while his arms are locked with the opponent, jumps up to tip the ball and Rondo quickly grabs it away — Wallace probably could have gotten to it and does not get credit in the box score for boxing out.
Inversely, here are the best team rebounders. Nene is consistently at or near the top of these measures. Besides Jason Collins, he’s probably the best team rebounder. Robin Lopez averages a meek 8.6 rebounds per 36 minutes for his career and he replaced J.J. Hickson, who averaged over ten rebounds a game, in Portland, yet Portland became a better rebounding team and Aldridge set a career high. It’s a list also dedicated more to ground-bound players and there are fewer guards.
For an example, you can see Nene below hold and box out his man, letting Gortat get the rebound:
I included an additional measure too you can now see from SportVU: the percentage of defensive rebounds you grab that are contested. Hence, a low percentage means most of your rebounds were obtained with no opponent within 3.5 feet. If you notice a trend in those tables, it’s that the worst team rebounders grab fewer contested rebounds. Rondo, for instance, has a contested percentage of only 9%, which is extremely low. If you watch him rebound, you’ll notice that like a big man he drops to the basket when a shot goes up and grabs a lot of uncontested rebounds far from another player, but he doesn’t go inside and box out others or do the dirty work and grab tough rebounds. This is also a problem with high rebounders like DeAndre Jordan, which you can see in the clip below. They can “pad” their stats a little by grabbing a lot of the easier rebounds.
Linking SportVU and Team-level Rebounding
With the complete dataset of rebound logs showing details of every rebound from the 2014 season, perhaps we can measure real rebounding impact in a better way. The stats you see on the NBA’s website are incomplete and don’t contain the same level of detail I have access to, via the logs. For instance, I can break up rebounds by offense, defense, field goals versus free throws, rebounding chances, average shot distance for the rebound, and average rebound distance. Since more offensive rebounds are contested, the total contested percentage publicly displayed is misleading and not entirely useful. Offensive and defensive rebounds are two very different stats — breaking them apart is a must. Also, free throw rebounds are easier to grab, so there are some marginal gains in breaking those apart too.
To figure out the value of these SportVU stats and build a better model of real rebounding impact, I used the aforementioned data here and concentrated on defensive rebounding only, using every available statistic I could wrangle and form. For a more technical note, I used LASSO regression in R to select and drop variables — though I also used plain old linear regression just to check things out with a more manual method. Additionally, by using regularization the model is more generalized and will do better with a new season or set of players. You have a better chance of finding the “truth” about the value of variables this way, rather than just fitting data to a specific variable.
For the first level of analysis, splitting contested defensive rebounds from uncontested did indeed improve the model, and, depending on the method, contested rebounds are roughly about two to three times as valuable as uncontested rebounds. When we first saw these SportVU stats, we all assumed contested rebounds were more valuable, but it does very little to evaluate players if we don’t understand the magnitude.
Secondly, free throw rebounds have a weak significance and the model usually discards those variables. In fact, in the most developed models, free throw rebounds are negatively correlated with rebounding impact. Additionally, the results are better when rebounds are split by field goals and free throws, rather than lumping all rebounds together. Few analysts online split rebounds like that, but it’s intuitive to do so and it’s backed up by statistics. Unfortunately, average shot and rebound distance do not appear to be useful. There might be something to the fact that a player who picks up longer rebounders might be relying more on luck than skill, and that the players picking those up aren’t working hard to create those opportunities by boxing out, but there’s nothing to support that conclusion now.
There were only a couple of other factors that proved to be significant. The number of defensive rebounding chances (i.e. how many times you’re near a rebound) per defensive rebound opportunity (i.e. whenever the opponent misses) was positively correlated with team-level rebounding. Remember, rebounds grabbed are already accounted for, so this is finding another gain. Perhaps it’s identifying players who know where to position themselves and they don’t get strongly docked for grabbing a lot of uncontested rebounds. (This was significant even when free throw rebounds were included.) Lastly, position by itself (coded where a PG was 1, a SG 2, etc.) was another useful variable. I tried a few interaction terms like with position and rebound percentage, but solely position worked best.
The Results
For a quick summary, here are the pertinent significant factors and their coefficients:
(Intercept):
9.41
DRB.FG.Contest:
19.7
DRB.FG.Uncontest:
6.94
DRBC.Opp:
8.73
Position (1 through 5):
0.339
After the intercept, the two following variables are percentage of rebounds grabbed that are either contested or uncontested per available rebound (i.e. missed shot.) DRBC.Opp is showing the number of times a player is near a rebound per available rebound.
Also, I quickly did a model for offensive rebounding, but the dependent variable was a bit different using the numbers from Gotbuckets.com and it distracts from the point of this article. However, I knew someone would be curious about offensive rebounding, and there was an interesting result: contested rebounds are a lot more valuable, on the order of ten times the magnitude, although rebounding opportunities (i.e. simply being near a rebound) are positively correlated too. This is probably due to the fact that contested offensive rebounds are more about skill and something the player directly manufactures, while uncontested ones are more often a lucky bounce. Position, by the way, didn’t matter, and there was a smaller model error — basically, offensive rebounding numbers do not lie as much as defensive rebounding numbers do.
Getting back to the main point, who are the best defensive rebounders by this metric? Asik, Love, Garnett, Varejao, Bogut, Duncan, Jefferson, Dieng, Cousins, and Jordan. The worst? Augustin, Parker, Mo Williams, Nate Robinson, Crawford, Brooks, Jennings, Will Bynum, Sessions, and Watson. Basically, the same list as we have with rebound percentage except that perimeter players get penalized. If you look for team rebounders like Nene and Robin Lopez, the bellwethers here, they’re further down the list near guys like Matt Bonner and small power forwards.
Basically, the exercise here is a failure — we cannot identify team rebounders with the information given.
But was this entirely pointless? Of course not. We know that with a variety of facts that perimeter players are often a bit overrated in defensive rebounding. We know that contested rebounders are a lot more valuable. We know there exists a subset of players who help their team rebound at significantly higher levels beyond what their individual numbers suggest. And we know that with the rebound logs publicly available you cannot identify these players. That’s a useful warning to give people who think the overrated rebounders are entirely those who subsist on uncontested rebounds — that’s not entirely true. We’re missing at least one more piece of information.
The best example of a team rebounder in modern league history is Jason Collins, who despite grabbing as many rebounds as an average small forward, is one of the best rebounders in the league over this seven-year period. Nene and Robin Lopez are two other examples, as well as Roy Hibbert. What do they have in common that we can see with the stats they have? Pretty much nothing — Hibbert blocks shots, Nene grabs more contested rebounds than Lopez, and Nene and Collins don’t grab a lot of offensive rebounds.
What we need is something that’s like a rebound assist — you box out or otherwise clear an opponent from crashing the glass, allowing a teammate to grab the rebound. We also need information on players who grab rebounds when teammates are nearby — aka rebound stealing. What we have now is incomplete and lacks the detail to bridge the gap from individual to team rebounding. So drop the criticism of Hibbert’s rebounding and allow for the possibility of his real rebounding impact to equal that of DeAndre Jordan’s. We don’t quite understand all the interactions here, but we know they exist. And insisting otherwise would lead you down the wrong path.
“The more I learn, the more I realize how much I don’t know.” — Einstein
