Argument Stoppers: Rebounds are Overrated rev.1

Posted on 06/09/2011 by


I grow a white rose
in july as in january
for the sincere friend
who faithfully offers me his hand

But for those who cruely tear out
my still beating heart
neither nettles nor thorns do I grow
I grow a white rose
-Jose Marti “Cultivo una Rosa Blanca” as translated by some blogger

Before we get started you need to go read:

  • Jonah Lehrer’s post  Basketball and Jazz at  A post which reviews research explaining the mental aspect of rebounding. In essence, Rebounding more than a learned skill is a rare skill. The implication is that it should sought and prized.
  • Then you can follow up with Prof. Berri’s writeup of the piece:  Rebounding is a Mental Skill .

This is yet another brilliant piece highlighting the value of rebounding.

Don't post Angry

We’ve been here before and old arguments die hard.

I therefore decided in the interest of prevention to beta test a new feature we’ve been debating privately. The intent is to forestall some common arguments by putting together a nice compilation of  some of the rich & varied material that has already been done in a particular vein in one place.

Get ready for Argument Stoppers: Rebounds are Overrated rev.1.

We start simple by quoting Pat Riley: “No Rebounds, No Rings”.

I bet you haven't thought of these guys in a while

We move to one of mine:

The Rebounding Myth

“Insanity: doing the same thing over and over again and expecting different results.”-Albert Einstein

I wrote in a private e-mail today:

Yesterday’s piece was one of those pieces that just happen. I’d been working all weekend on some consulting work I need to hand in and when I went to write the Around the Wow piece the quote “oh the places you’ll go” popped into my head. Before I knew it, I was looking up Dr. Seuss books.

For some reason, my spontaneous/unplanned stuff can be really good (the last 4 pieces were all like that), whereas some of the more thought out stuff leaves me unsatisfied. Weird.”

This is fortuitous because two days ago I wrote a post on the 100 worst seasons/players since 1978. This inspired some familiar responses.

Rebounding Again!!!!!!
The argument is diminishing returns for rebounding .

Now the studies referred have some technical problems ( If you run a regression you must account for other variables that could affect your result). This is why you’ll see me control for small samples (minutes), age, position and teams frequently. Prof. Berri’s covered this before in the comments here or very thouroghly in Stumbling on Wins just buy the book). I’ve covered this before (see The Basics , and here ).

In the book (which I recommend you buy :-)), the finding is that there is diminishing returns with respect to defensive rebound but not for for offensive rebounds. The overall though the effect is quite small.
But the Zombie argument remains unabated and it goes like this:
1. Rebounds dominate Wins Produced
2. Diminishing Returns dominate Rebounds
Therefore Wins Produced as a model is skewed and significantly overrates/underrates players.

I tried a GIS for Zombie Troy Murphy but nothing came up (Image courtesy of

If this were a true statement then season to season fluctuation in Wins Produced would have to be huge and would make predicting the season a ridiculous exercersize (seriously, read any piece on this blog) and rebounding numbers would fluctuate wildly from season to season.
As I said, I cover point one all the time and for the purposes of this discussion (and posterity) I’m going to cover point Number 2. Here’s how:

I pulled every players rebounding numbers from 1979 on (for every player with > 800 minutes played, see controls).
I looked at every player’s:

  • offensive rebounds per 48 minutes (orb48)
  • defensive rebounds per 48 minutes (drb48)
  • total rebounds per 48 minutes (trb48)
  • And for Grins and giggles, looked at all players and a subset of player ages 25-30 (see more controls, this time for age).

For your amusement that table is here. (This also allows for peer review of my findings).

My results? Here:

Do rebounding numbers fluctuate wildly based on teammates and diminishing returns? Short answer is no. Year to year correlation for total rebounds per 48 minutes is at 91% regardless of the age grouping. In fact, 82% of the population in the sample had an absolute error in year to year rebounding of less than 1.5 rebounds. If I break out the Minitab as well and graph it up:

And that looks like the very definition of a normal distribution.

So Wins Produced consistent season to season? Check

Rebounds not varying radically? Check

Unnamed individuals pestered into writing additional material on this? Check and check (You’ll just have to wait to find out).

Scott Meyer needs to get out of my head!!!

We continue with another one of mine:

Re-examining myths and explaining how regression works

You know, sometimes it’s fun to poke the bear.

Did you know that when the bomb squad wants to defuse a bomb and they don’t know how to, they take it out to an empty field somewhere and blow it up? That’s kinda the opposite of what we do here. My defining trait is that I’m an engineer and a scientist. I don’t want to ignore questions and problems, I want to take a tool to it and try to solve or understand it.

Yesterday’s post was a result of this. I knew I was kicking an anthill. Today is no different.

Grab a drink, take a bathroom break, because this will take a while.

One of the hallmarks of society is intelligent polite discussion. If any argument,tool or theory is worth anything it can stand up to scrutiny and review (such as Wins Produced see The Basics) . I may not agree with you but this is why I take the time to respond to the questions. I typically arrive at surprising and unexpected conclusions.

The point of having a blog is to invite discourse. As long as everyone has a thick skin and is prepared to be wrong (and right ) , including me. We’ll keep advancing our understanding. Together.

And you know in this case, Guy is right.


Not like you think (sorry, couldn’t help myself 😉 ). We do have the data to answer some of these questions and some of the answers are really surprising.

Before we get to that, lets talk a bit about linear regression.

Let's put that Ivy League education to good use

Linear regression is one of the most commonly used approaches to modeling the relationship between an variable y (say wins) and one or more variables X (say box score stats). Linear regression is simple, useful and well understood and in a lot of cases it works. It’s typically used for two things:

  • Predicting or forecasting Y (say Wins) based on a know set of X’s. This is something we continually do here at ASLS.
  • Given a variable Y (say wins again) and a numbers of variables (say, I don’t know, points, def. rebounds, offensive rebounds, assists, etc.) then linear regression analysis can be applied to quantify the strength of the relationship between them. This is what Prof. Berri did. He did it again in Stumbling on Wins. I did it here and at least five other times.

What does this mean for this discussion? I’m happy with the coefficients math gave me for rebounding and other variables, I’m not changing them.

You shut your mouth when math is talking! (Image courtesy of

Ok, let’s get to the question and answer portion of the program. First let’s look at rebounding. Are there diminishing returns for rebounding? As I said, I have the data (yeah, every single player and season since 1979, I made excel tap out today), let’s take a look:

If I look at the best rebounder (by qty i.e the most rebounds for that team) rebound rate per 48 minutes for every team vs. the rebounding rate there appear to be a diminishing effect. A correlation of 3.4% does not much water. Did I just prove diminishing returns for rebounds? Not so fast there Kemosabe:

If I take out the best rebounder (by qty) for every team, I may not be getting the best rebounder by rate (per 48 minutes), however if I take out the best two rebounders on each team I get a surprising result. There is a positive relationship between the two best rebounders on each team. So having two good rebounders next to other increases returns (everyone else does see some mild dropoff at the extreme). Who knew?

Phil Jackson knew that's who!

Again fairly weaksauce correlation though.

The second question had to do with above average rebounders. Can I find one with >15 treb per 48 whose teamates where above average. Here’s a list of all the players whose rebound rate is >15 per 48 who led their team’s in total rebounds since 1979 :

So the average rebound rate per 48 for teams without their best rebounder is 7.65. By my count 40% of the people on this list qualify.This concludes the rebounding portion of our program.

Let’s talk Wins Produced. If I repeat the exercise I did for rebounding of comparing the best player on each team (in terms of wins produced) vs the rest of the team:

No diminishing returns here. The data is a little stratified so let’s repeat the trick of looking at the second best separate from the rest but this time let’s add the third best:

Now Color coded for your protection

Hmm. Fascinating. Playing with good players makes you a better player. Instead of diminishing returns for WP48, we see increasing returns, and it holds for your top three. And it doesn’t affect the rest of the team that much. Again who knew?

Anything is Possible

We end with

Some links:

  1. First the Wages of Wins FAQ
  2. My FAQ (the Basics)
  3. If you still feel that rebounding is being misrepresented (and have a few days to spend being entertained) go read Ben Morris’ Rodman Opus and don’t miss the bit about rebounding being undervalued.

Drive safely and remember some things never change.

Although New Actors may play old roles

Posted in: Uncategorized