Rebound Rates

The Celtics’ demolition of the Lakers reminds me that the sport announcers would do well to put more emphasis on “rebound rates.” Like putt probabilities, the rebound rate basically tells you the probability that a team will get the next rebound.

Can you answer a fairly simple question: In the NBA if a team misses a shot, what is the probability that it will get the (offensive) rebound?

Most people I’ve asked think the probability is 10 percent or less. But it’s closer to 30 percent.

Game six was extraordinary not just because the Lakers had only two offensive rebounds, but because they shot so poorly (42.2) — so there were plenty of misses to rebound — and had only two offensive rebounds. As the great John Hollinger summed up:

[F]or the game [Los Angeles] had only two compared to 34 defensive boards for Boston. That’s a 6 percent rebound rate if you’re scoring at home; normally the offensive team gets around 30 percent.

One question that occurs to me is whether Lakers’ low number of offensive rebounds was just a matter of bad luck. If you have a 34 draws and if each draw has a 30 percent chance of success, then just by chance you might only have 2 successes. But a little analysis (using the same methodology that I used here to analyze political polls) suggests that we can reject the bad-luck hypotheses. The observed rebound rate of 6 percent is more than 3 standard deviations away from 30 percent — so there is less than a 1 percent chance that it would have occurred by chance.

Of course, just as the putting probability turns on the place on the green, the expected rebound probability turns on where the shot is taken and other factors. The website gives a strategy for making the rebound probability turn on additional factors.

But even simple rebound rates can let us see things about the game for the first time.

1. This season Philadelphia had the highest probability of rebounding one of its own misses (31.8 percent), while Miami had a league last probability of 22.1 percent. Almost a 10 percent difference in getting the ball back when you miss can have a huge impact on games.

2. Rebound rates give you a better sense of who are the best individual rebounders. During the playoffs, Tim Duncan had the most defensive rebounds per game:


But Marcus Camby had a much higher probability of grabbing a defensive rebound. Camby himself grabbed more than a third of the other team’s misses:


3. Finally, rebound rates show that the art of the offensive rebound is distinctly different than the art of the defensive rebound.

Camby and Duncan, for example, rank only 35th and 21st among players in the playoffs in terms of offensive rebound probabilities. Who has a high offensive rebound rate? Dwight Howard had the best playoff probability (16.9 percent), but the Celtics’ Leon Powe is close behind grabbing 15.2 percent of the Celtics’ misses. Of course, readers of this blog shouldn’t be surprised at Powe’s success.


In the Spurs system they are taught not to attempt offensive rebounds and instead prepare early to get back and set up on defense rather than the 30% chance of an offense along with getting caught off gaurd.


I disagree with two points here- one, the Lakers shot "so poorly" at 42% against the Celts?!- it should read "so well"- and Duncan having high defense-to-offense rebounding is simply because he plays so much offense- if you were to forbid Duncan from scoring, he would dominate the offensive boards as well


A lot of NBA teams make getting offensive rebounds a very low priority, since sending more players to get offensive rebounds leaves less players to defend the fast break.

Rebounding in general is a mixture of technique, teamwork, effort and luck. There are games when the ball just keeps falling into the other teams hands. But once the Lakers fell behind in game 6, they probably started showing significantly less effort in their rebounding. That and the Celtics had a significantly bigger lineup than the Lakers, who were missing Andrew Bynum who would have been their starting center.


Finally, rebound rates show that the art of the offensive rebound is distinctly different than the art of the defensive rebound.

From somebody who stopped watching the NBA years ago but plays pick-up now and again, yeah. Defensive rebounding is all about boxing out, which should be straightforward if your defensive positioning is sound (you'll be closer to the basket). Offensive rebounding involves more effort and creativity in fighting through or around the box out for good rebound position.

Of course, a lot of pick-up players won't bother to box out and also expect opponents to expend most of their effort on scoring instead of rebounding, making offensive boards a lot easier, and thus a pretty good way to build reputation with new teammates.


Rebounding probability aside, announcers need work in many areas. It is absolutely maddening to hear would-be professionals constantly asking viewers to put themselves in the shoes of the team, coach, or a particular player. For example, Mark Jackson and Jeff van Gundy were incessantly telling us, "If you're the Los Angeles Lakers...," or "If you're Doc Rivers...." I don't know when, where, or with whom this began, but it has penetrated the commentary of just about every sport now.

I am not the Los Angeles Lakers or even Doc Rivers; just be a professional and say, "The Lakers would could make up some ground by focusing on offensive rebounding."



On the matter of whether the low offensive rebounds were luck or not.

Before the game you could have been pretty confident that a particular stat you were going to track would not stray to 3 standard deviations without a predicted cause. Looking backward is where the logical traps are. The sample space increases by orders of magnitude and could possibly extend as far as all the nba games ever played.

If it's not clear, I vote luck.


The probability that the Lakers were unlucky might be really small, but when you play as many games as these guys do, all sorts of improbable events can happen.


Regarding small sample sizes in #1 and #2: That reminds me of _Ender's Game_ where Ender was initially at the top of the charts because of small sample sizes.


Two words: Dennis Rodman. Offensive rebounds and free throws are the low-hanging-fruit of both NBA and NCAA basketball. I'm always surprised more teams don't make a bigger effort for the free stuff.


"The observed rebound rate of 6 percent is more than 3 standard deviations away from 30 percent - so there is less than a 1 percent chance that it would have occurred by chance."

Let's be clear. Are you suggesting the Lakers threw the game? I'm no fan of theirs but the recent NBA scandals have hinged on officiating, not the teams.


You can say the deviation from the norm on offensive rebounds isn't about bad luck, and I'd agree with you. However, it does NOT follow that there should be more rebound opportunities just because there are more missed shots.

If they're forcing up shots, with people out of position or not running an offense or sharing the ball, the normal break downs or mismatches that lead to a weakside player being open aren't going to be there. And if a team is getting creamed, players probably will not be crashing the boards in the same way for hustle plays.

In those circumstances, an outcome below the norm is predictable.


If you wanted to inquire about how successful a rebounder is as an individual, you would have to account for how many minutes they play per game (or more specifically the percent of missed shot attempts they snag during a game). For example, rebounder A may only play ten minutes a game which would prevent him from having huge rebound totals. However, if I'm a general manager, and rebounder A is grabbing 35% of all missed shots while he is on the floor, I might want to take a chance on that player.


A big man will have a large disparity between his offensive and rebounding prowess for a number of reasons. In an offensive system like the Spurs, the big man other than Tim Duncan will always be on the weak side, jostling for rebound position. Tim Duncan, on the other hand will have the ball in his hands alot of the time, and it is very rare to rebound your own miss (if your not attempting a flatfooted layup). So, those players who are not very good at rebounding in general but who have offensive rebounding as one of their main goals on offense (Fabricio Umberto comes to mind) will have higher rebounding rates on the offensive end than on the defensive end.

I arrive at this conclusion through deduction, so some body may have to check the statistics to prove this out.


Dan #4, the suggestion is not that the Lakers threw the game, it is that the event could not be explained by chance. In fact, and I set aside my bias as a Celts fan, it indicates that the Celtics were that much better than the Lakers in that element of the game.

Daniel DuBois

"Let's be clear. Are you suggesting the Lakers threw the game?"

No, he's not. He noted the average rate for the entire NBA. Then he noted the observed rate in this match-up. Then he noted the statistical difference, and how unlikely the difference is to occur from chance alone. So if it's not chance, it must be cheating? You jumped right over another possibility the rest of us understood implicitly: skill. The logical implication is not that the Lakers threw the game, but rather that the Lakers "true rebound rate vs Boston", the rebound rate they should expect given the factors of the match-up, is less than the average NBA rate.


I don't think he's suggesting that the Lakers threw the game.

I think a more logical suggestion might be that there is some truth to the proposition that the Celtics get away with a lot more physical play in situations where officials are less likely to call fouls like off-the-ball and loose ball situations.

If the Celtics get away with more grabbing and pushing other players during rebounding situations, that would help explain a much lower than normal rebound rate for their opponent, the Lakers.

Carl Spackler

Leon Powe's number have to be looked at as aberrations only because of the small sample size. Had he seen more consistent minutes, I think you would have a more valid case. What I would look at is the Team Rebounding Rate when Kendrick Perkins is or is not on the floor. Whomever he is paired with in the front court, (KG, Powe or PJ Brown), rebounding number's will go up when he is on the floor. This has to do with Perk consistently boxing out the opponents best rebounder. Thus further proving that Perk Is A Beast.


Here's another stat that's crying to be mentioned, but it's football...

The announcers say something like "65% TD rate when in the red zone." Then say "also 30% FG, and 5% no scores." That's screaming for a single number, such as "The Colts average 5.5 points when they get into the red zone."

I suspect it's because it's a nonsense stat, you can't score 5.5 points, but it's so clearly there that I'm surprized no one mentions it.