Joakim Noah, Russell Westbrook, David Lee And Inscrutable Details Of NBA Rebounding

Rebounds seem like a simple event, but there are plenty of reasons to take a closer look.

What do Chicago Bulls center Joakim Noah, Oklahoma City Thunder guard Russell Westbrook and Golden State Warriors forward David Lee have in common? They are all mentioned in this article on NBA rebounding. And the story is about NBA rebounding. It's a truly fascinating subject that touches on nearly every hidden aspect of basketball, but it rarely gets a second look beyond basic rebounding numbers. Noah, Westbrook and Lee can highlight material differences in opportunities and impact for players and positions, but the important takeaway is that rebounding should be looked at with fresh perspective.

I start by laying out the fundamental limits of box scores, move on to the conceptual underpinnings of why metrics reassign credit for offensive and defensive rebounds in different ways, and how the phenomenon has manifested in the numbers for the trio of players listed in the title. Did I write 3,400 words on rebounding? Yup. Let's get to it.

The Fundamental Problem: The Limits of Box Scores

Basketball is not five games of one-on-one, it's a team game loaded with important contributions and lapses that go completely unrecorded but ultimately help to distinguish the winners from the losers. I don't think anyone would disagree. Then again, official scorers assign full credit for rebounds, assists, points, blocks, turnovers, etc. to a single player in the box score, so it is hard to deny that when we look at the back-of-the-basketball-card stats we all know so well and are deeply embedded in the lexicon of NBA discussions (Pts/Gm, Reb/Gm, Ast/Gm, Stl/Gm, etc.), that we are assenting to a certain degree of misinformation.

A solid screen set on a successful shot isn't recorded. A textbook box out setting up a teammate to grab a rebound isn't recorded. A skip pass that moves defenders out of position from a weak-side drive isn't recorded either. The scorer, rebounder, and assister claim full -- meaning undivided -- credit for these events. The full picture is always a bit out of focus.

As I pointed out in an earlier breakdown of John Hollinger's PER metric, traditional box scores cannot provide a truly comprehensive reporting of game events. Not only do they ignore situational context of game events, they also fail to record important game details that elude simple classifications including, but not limited to, individual defense, help defense, timely rotations, successful box-outs, effective picks, specific locations of shot attempts, and when shot attempts occur within the context of the game.

Should we throw stats out the window and just watch the games and make subjective judgments without any factual points of reference? Of course not. Aside from the inherent flaws of human memory, reliance on unsubstantiated anecdotal evidence does nothing to advance the conversation or our knowledge of basketball. We all get to have opinions, but we can't all be equally correct. There always needs to be some acknowledgement of objective facts. To illustrate my point, I will relay one of my favorite quotes of all-time, spoken by Gene Siskel and retold via the brilliant Roger Ebert (taken from Roger Ebert's Movie Yearbook 2010):

When a so-called film critic defended a questionable review by saying, "After all, it's opinion," Gene told him: "There is a point when a personal opinion shades off into an error of fact. When you say The Valachi Papers is a better film than The Godfather, you are wrong." Quite true. We should respect differing opinions up to a certain point, and then it's time for the wise to blow the whistle...

In sports, I consider stats to be that whistle. Stats help to keep us honest by providing an accurate record of certain valuable on-court events. For example, if someone says Brandon Jennings is a good shooter, they are wrong. It's honestly that simple. Conceptual problems may always persist when tapping traditional box score inputs as a basis for player evaluation, but intelligent efforts are being made to find better ways to break up and reassign credit for important on-court events to individual players. Although the ideas apply in some form to almost any recorded stat, for the sake of clarity the discussion will focus on rebounding.

The Specific Problem: Assigning Individuals Credit for Complex Team Events (The Rebound Problem)

Back of the basketball card stats aren't particularly credible or accurate when assigning credit to individual players in most situations. Better options already exist. Sorting out great players from terrible ones is a facile exercise for anyone with a measure of basketball sensibility, but deciding on value among players in the middle is far more difficult. How much do opportunities and positional assignments affect player performance? How well do we implicitly adjust for these issues in our conversations and evaluations? To explore these questions, let's take a closer look at rebounds.

Every basketball fan knows that grabbing rebounds is essential to victory. They are the primary method of securing additional possessions for each team. However, every basketball fans also knows the anatomy of each rebound is unique and complex, even if sometimes unspectacular. Allow me to illustrate my point with the following example: the Bulls defense forces a missed perimeter shot, and Joakim Noah grabs the defensive rebound. Great outcome. The Bulls forced a miss, and prevented the opponent from scoring. That deserves a Finga Gunz. Of course, it's not all that simple.

Possessions are the currency of basketball, and rebounds convert possessions. The tricky part is that the only record in a box score comes in the form of a defensive rebound credit to Noah. Assigning the full value to Noah because he actually secured the possession by grabbing the rebound seems a bit naive. For example, this game charting exercise provides some hard evidence to support the theory that roughly 30% of defensive rebounds go completely uncontested by the opposition. Is there truly nobody else deserving of recognition or credit in this situation?

To understand the logical fallacy underlying the assignment of full individual credit to the rebounder, let's revisit the hypothetical Noah rebound in more detail. Sure he actually grabbed the ball -- and somebody does have to grab the rebound to gain any value at all -- but this event is still the product of a complex network of subtle strategic assignments.

To properly assign credit for ending the opponent's possession, we would need more details in the hypothetical. Who was defending the shooter? Did team defense force a difficult shot attempt, how well did other defenders box out to allow Joakim to get the rebound? Could another Bulls player have grabed the rebound if Noah had not done so? Did any players on the opposing team attempt to snare the rebound, or did they all retreat to prevent Derrick Rose from getting out on the fast break? Quite frankly, there are too many factors and permutations to reasonably play out. There needs to be some focus to the inquiry.

Certain basic factors influence the circumstances of every rebound. Joakim Noah is a center, which is traditionally a position assigned to bigger and taller players rooted on the interior defense. We Intuitively know that interior areas closest to the basket represent the areas of highest likelihood for landing spots of missed shot, and that Cs and PFs and are assigned the greatest responsibility for grabbing the majority of rebounds for the team. It's why everyone has a good time making fun of Andrea Bargnani and Brook Lopez. The fundamental point is that context is very important.

Phil Birnbaum has explored the details of this problem:

Imagine that the NBA institutes a new rule: the offense is prohibited from touching a rebound until it has bounced three times on the floor.

...A defensive rebound still constitutes a change of possession, and is therefore still worth exactly the same [ ] as it was before. But, now, instead of 70% of rebounds going to the defense, the number is now 99%...

Given that there is now no skill at all, doesn't it overrate Rodman to give him credit for those rebounds? Obviously, any excess rebounds picked up by Rodman, instead of his teammates, are positioning, luck, or opportunities given him by his coach and team. Even a caveman could get them.

The argument for 99% also applies to 70%, but to a lesser extent. Some, but not all, of Rodman's rebounds are, in effect, his team "letting him" have the ball more. Those are perhaps better classified as team rebounds, rather than individual rebounds. Since they aren't, Rodman winds up overrated...That's opportunities.

We should know that some portion of rebounding is a matter of opportunities -- rather than a difference in skill -- so the issue cannot be ignored or overlooked. Birnbaum illustrated how ignoring the impact of opportunities can create potentially misleading results. In his next example, he uses the rough assumption that 70% of opponent misses are grabbed as defensive rebounds and 30% of team misses are grabbed as offensive by an average team for his examples...just for reference, the averages this season were 73.6% and 26.4%, respectively, and always hover around the 70-30 marks he uses for estimates:

...[T]here's a second reason rebounds are overrated, a much more important reason...

...As [John] Hollinger writes here, "missed shots can be rebounded while turnovers can't, and ... a defensive rebound is merely the completing piece of a sequence that began by forcing a missed shot."

To get the opportunity for a defensive rebound [ ], the defense must first force the opposition to miss [ ]. The defensive rebound is a combination of the two acts: good defense for up to 24 seconds, and one grab of the ball. Crediting the rebounder with the full value of the defensive play is like crediting the kicker with all seven points of the touchdown.

Shot attempts produce, at a bare minimum, an opportunity for recovery via an offensive rebound. Turnovers do not. I'm sure C.J. Watson and John Lucas III ponder this deep basketball thought before every shot. Okay, maybe not, but it's true that a missed field goal is not as harmful as a turnover, simply because it creates an opportunity for recovery of the ball.

An offensive rebound should not be treated like a singular event, because it's fundamentally a product of teamwork, opportunity, and on-court assignments. Yet in the box score, the shooter is charged with minus one possession (in the form of a missed FG), and the rebounder is credited with plus one possession (in the form of an offensive rebound). Let's allow Birnbaum to bring the whole thing home:

Any field goal attempt has, intrinsically, built into it, the embedded feature that a missed shot results in a 30% chance of getting the ball back. The miss includes a consolation prize, a lottery ticket with a 30% chance of winning back the possession. The shooter figured that into his decision about whether to make the shot. That 30% chance belongs to the shooter. In effect, he hasn't wasted a whole possession with his miss, he's only wasted 70% of a possession. Remember Hollinger's point - a missed shot gives the team a chance to recover, but a turnover doesn't. Obviously, the shooter should be debited less for getting a shot away than for letting the shot clock expire.

The willingness and ability of analysts to think about a missed shot as losing only 70% of a possession, or 70% of a defensive rebound being the function of opportunity determined by a player's assignment/role, help to quietly incorporate complex team components into individual evaluations. The next time you sneer at a PER value you don't agree with, stop to consider the amount of effort that goes into understanding player value.

You may not agree with the particular ratios used to reassign credit for rebounds, but committing to a concrete split isn't really the point of this piece. The point is to get you thinking about new and interesting ways to reconcile the endless list of inter-connected and unrecorded team assignments with the goal of evaluating individual skill and talent. I think it is pretty clear that a 70-30 division of credit for rebounds is closer to being correct than the 100-0 split imposed by traditional box scores. If you remain unconvinced that there is any problem with the 100-0 split, I want to take you through a few illustrative examples.

(1) Joakim Noah - The floppy-haired firebrand led the Bulls in offensive rebounds, defensive rebounds and total rebounds per game for 09-10, and did the exact same thing in 10-11, save being edged by Carlos Boozer for the defensive rebounds title by a margin of 7.4 to 6.6. In any case, he's an offensive rebounding machine. Anchoring in the paint and crashing the boards helps him gain premium position on offense, and he makes the most of it by turning the Bulls into one of the best teams in the entire NBA at grabbing their own misses. Offensive rebounds are hard to earn -- even the best teams grab just around 30 percent of their errant shots -- but Noah is one of the best in the league at maximizing that added value and sometimes taking care of the new scoring opportunity himself. Take a look:

Here are 2010-11 Chicago Bulls team rebounding rates relative to Joakim Noah's court time.

On Court Off Court Net
Offensive Rebounding 33.0% 31.0% +2.0%
Defensive Rebounding 71.1% 74.5% -3.4%
Total Rebounding 52.1% 52.8% -0.7%

Here are the 09-10 Bulls rebounding numbers for further reference:

On Court Off Court Net
Offensive Rebounding 32.1% 27.0% +5.1%
Defensive Rebounding 71.8% 72.7% -0.9%
Total Rebounding 51.9% 49.9% +2.1%

(2) David Lee - He's a scrappy PF/C with a history of high per game rebounding numbers, who grabbed nearly 10 rebounds per game this past season, which was good for the 11th highest average among all NBA players. You can't really argue with that level of performance. Well, actually you can, and in a pretty profound way.

Here are 2010-11 Golden State Warriors team rebounding rates relative to David Lee's court time.

On Court Off Court Net
Offensive Rebounding 27.6% 30.7% -3.0%
Defensive Rebounding 66.8% 67.7% -0.9%
Total Rebounding 47.2% 49.2% -2.0%

Now 09-10 with the New York Knicks.

On Court Off Court Net
Offensive Rebounding 25.0% 28.0% -3.0%
Defensive Rebounding 70.6% 69.9% +0.7%
Total Rebounding 47.8% 49.0% -1.1%

With David Lee on the court in 2010-11, the Warriors are the worst rebounding team in the entire NBA. Sure the high-pace systems Lee has played in have inflated his numbers, but would anyone have guessed his presence on the court would coincide with the Warriors grabbing a league-worst percentage of available rebounds? Increased opportunities in high-paced action helps Lee post nice raw rebounding numbers, but he doesn't really outperform his counterparts on the floor. He isn't nearly the talent on the boards that his basketball card numbers suggest.

When Lee went to the bench, the 10-11 Warriors jumped all the way up to the equivalent of the 22nd ranked team in rebounding rate, and they also become the equivalent of the best offensive rebounding team in the entire NBA. Take away the NBA's 11th ranked per game rebounder and the team becomes a substantially better at rebounding. This is the type of stuff we are dealing with people. Let's do another player.

(3) Russell Westbrook - He is one of the top rebounding PGs in the league, 4th among PGs with an average of 4.6 rebounds per game in 2010-11, and 1st among PGs in average offensive rebounds per game and per minute offensive rebound rate. Any time you can get that type of rebounding production from your PG, you are gaining an advantage over your opponents, right?

Here are Oklahoma City team rebounding rates relative to Russell Westbrook's court time.

On Court Off Court Net
Offensive Rebounding 29.0% 30.2% -1.2%
Defensive Rebounding 70.8% 71.4% -0.5%
Total Rebounding 49.9% 50.8% -0.9%

Here's a look at the 09-10 Thunder.

On Court Off Court Net
Offensive Rebounding 30.9% 31.0% -0.1%
Defensive Rebounding 70.7% 71.3% -0.6%
Total Rebounding 50.8% 51.2% -0.4%

In 10-11, the Thunder actually grabbed a lower percentage of available rebounds when Russell Westrbook was on the floor. Let that sink in for a minute. Now you might be thinking "a one percent difference in total rebounding isn't really a big difference," but in fact a one percent difference is a pretty big deal because there is generally a small standard of deviation for rebounding at the team level.

For example, using these hoopdata numbers, a one percent drop in total rebounding percentage would knock the 6th ranked Thunder all the way down to the 14th ranked team in 10-11. The team went from well above-average to almost exactly average in rebounding when Russell Westbrook stepped on the court. This isn't something you would guess by looking at the back of Russell's basketball card, or even by looking at the leaderboard for PG rebounding, but it is an important fact worth knowing and understanding. These are the types of things advanced stats can help to uncover. This is what actually happened.

When it comes to the reasons why the Thunder are a worse rebounding team with Westbrook on the court, the topic is open for discussion and debate. Maybe with Westrbook crashing defensive the boards, opposing teams did not have to commit players to transition defense and could use all of their players to pursue the offensive rebound. Maybe with Westbrook crashing the offensive boards, the counterpart defender became involved in rebounding when he otherwise would not have done so. Maybe Westbrook occupied premium space trying to grab rebounds that would otherwise have been occupied by a taller Thunder player with longer arms and a bigger body, leading to less rebounds being grabbed by his team.

There are countless possibilities that provide new angles and perspectives to apply the next time you take in a Thunder game, right? This is just one way advanced stats can add new knowledge and make watching the game more enjoyable. Every could stand to sharpen their basketball sensibilities and expand their basketball acumen.

One of the biggest complaints I hear about advanced statistical analysis is sports is that it sucks the fun out of the game. I understand that nobody wants an informal statistics course to break out in the middle of a basketball discussion, but statistics aren't meant to take the fun out of basketball, they are meant to enhance our knowledge and refine our level of observation and understanding.

For being so simple, basketball is exceedingly complex; I encourage you to find ways to use advanced stats and the underlying concepts that inform them to find new ways to view the game and digest the story of what is happening on the court. Rather than find a few more creative ways to say I think an understanding of advanced stats is worth pursuing for every basketball fan, I want to leave you with a more eloquent and timeless message that Roger Ebert used to follow up the wonderful quote I included above (again from Roger Ebert's Movie Yearbook 2010):

What I believe is that all clear-minded people should remain two things throughout their lifetimes: curious and teachable. If someone I respect tells me I must take a cloer look at the films of Abbas Kiarostami, I will take that seriously...I will try to do what Pauline Kael said she did: Take everything you are, and all the films you've seen, into the theater. See the film and decide if anything has changed. The older you are and the more films you've seen, the more you take into the theater. When I had been a film critic for ten minutes, I treated Doris Day as a target for cheap shots. I have learned enough to say today that the woman was remarkably gifted.

Those who think Transformers is a great or even a good film are, may I tactfully suggest, not sufficiently evolved. Film by film, I hope they climb a personal ladder into the realm of better films, until their standards improve. These people contain multitudes. They deserve films that refresh parts others do not reach. They don't need to spend a lifetime with the water only up to their toes.

The real point of this story is to encourage us all to remain curious and teachable when it comes to basketball, and to remind us that we never need to settle for spending a lifetime with the water only up to our toes.

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