For reasons which should become obvious shortly, I’ve split Part 1 of this series into sub-parts. This section will focus on rating Rodman’s accomplishments as a rebounder (in painstaking detail), while the next section(s) will deal with the counterarguments I mentioned in my original outline.

For the uninitiated, the main stat I will be using for this analysis is “rebound rate,” or “rebound percentage,” which represents the percentage of available rebounds that the player grabbed while he was on the floor. Obviously, because there are 10 players on the floor for any given rebound, the league average is 10%. The defensive team typically grabs 70-75% of rebounds overall, meaning the average rates for offensive and defensive rebounds are approximately 5% and 15% respectively. This stat is a much better indicator of rebounding skill than rebounds per game, which is highly sensitive to factors like minutes played, possessions per game, and team shooting and shooting defense. Unlike many other “advanced” stats out there, it also makes perfect sense intuitively (indeed, I think the only thing stopping it from going completely mainstream is that the presently available data can technically only provide highly accurate “estimates” for this stat. When historical play-by-play data becomes more widespread, I predict this will become a much more popular metric).

Dennis Rodman has dominated this stat like few players have dominated any stat. For overall rebound % by season, not only does he hold the career record, he led the league 8 times, and holds the top 7 spots on the all-time list (red bars are Rodman):

^{Note this chart only goes back as far as the NBA/ABA merger in 1976, but going back further makes no difference for the purposes of this argument. As I will explain in my discussion of the “Wilt Chamberlain and Bill Russell Were Rebounding Gods” myth, the rebounding rates for the best rebounders tend to get worse as you go back in time, especially before Moses Malone.}

As visually impressive as that chart may seem, it is only the beginning of the story. Obviously we can see that the Rodman-era tower is the tallest in the skyline, but our frame of reference is still arbitrary: e.g., if the bottom of the chart started at 19 instead of 15, his numbers would look even more impressive. So one thing we can do to eliminate bias is put the average in the middle, and count percentage points above or below, like so:

With this we get a better visual sense of the relative greatness of each season. But we’re still left with percentage points as our unit of measurement, which is also arbitrary: e.g., how much better is “6%” better? To answer this question, in addition to the average, we need to calculate the standard deviation of the sample (if you’re normally not comfortable working with standard deviations, just think of them as standardized units of measurement that can be used to compare stats of different types, such as shooting percentages against points per game). Then we re-do the graph using standard deviations above or below the mean, like so:

^{Note this graph is actually exactly the same shape as the one above, it’s just compressed to fit on a scale from –3 to +8 for easy comparison with subsequent graphs. The SD for this graph is 2.35%.}

There is one further, major, problem with our graph: As strange as it may sound, Dennis Rodman’s own stats are skewing the data in a way that biases the comparison against him. Specifically, with the mean and standard deviation set where they are, Rodman is being compared to himself as well as to others. E.g., notice that most of the blue bars in the graph are below the average line: this is because the average includes Rodman. For most purposes, this bias doesn’t matter much, but Rodman is so dominant that he raises the league average by over a percent, and he is such an outlier that he alone nearly doubles the standard deviation. Thus, for the remaining graphs targeting individual players, I’ve calculated the average and standard deviations for the samples from the other players only:

^{Note that a negative number in this graph is not exactly a bad thing: that person still led the league in rebounding % that year. The SD for this graph is 1.22%.}

But not all rebounding is created equal: Despite the fact that they get lumped together in both conventional rebounding averages and in player efficiency ratings, offensive rebounding is worth considerably more than defensive rebounding. From a team perspective, there is not much difference (although not necessarily *no* difference – I suspect, though I haven’t yet proved, that possessions beginning with offensive rebounds have higher expected values than those beginning with defensive rebounds), but from an individual perspective, the difference is huge. This is because of what I call “duplicability”: simply put, if you failed to get a defensive rebound, there’s a good chance that your team would have gotten it anyway. Conversely, if you failed to get an offensive rebound, the chances of your team having gotten it anyway are fairly small. This effect can be very crudely approximated by taking the league averages for offensive and defensive rebounding, multiplying by .8, and subtracting from 1. The .8 comes from there being 4 other players on your team, and the subtraction from 1 gives you the value added for each rebound: The league averages are typically around 25% and 75%, so, very crudely, you should expect your team to get around 20% of the offensive and 60% of the defensive rebounds that you don’t. Thus, each offensive rebound is adding about .8 rebounds to your team’s total, and each defensive rebound is adding about .4. There are various factors that can affect the exact values one way or the other, but on balance I think it is fair to assume that offensive rebounds are about twice as valuable overall.

To that end, I calculated an adjusted rebounding % for every player since 1976 using the formula (2ORB% + DRB%)/3, and then ran it through all of the same steps as above:

Mindblowing, really. But before putting this graph in context, a quick mathematical aside: If these outcomes were normally distributed, a 6 standard deviation event like Rodman’s 1994-1995 season would theoretically happen only about once every billion seasons. But because each data point on this chart actually represents a maximum of a large sample of (mostly) normally distributed seasonal rebounding rates, they should instead be governed by the Gumbel distribution for extreme values: this leads to a much more manageable expected frequency of approximately once every 400 years (of course, that pertains to the odds of someone like Rodman coming along in the first place; now that we’ve had Rodman, the odds of another one showing up are substantially higher). In reality, there are so many variables at play from era to era, season to season, or even team to team, that a probability model probably doesn’t tell us as much as we would like (also, though standard deviations converge fairly quickly, the sample size is relatively modest).

Rather than asking how abstractly probable or improbable Rodman’s accomplishments were, it may be easier to get a sense of his rebounding skill by comparing this result to results of the same process for other statistics. To start with, note that weighting the offensive rebounding more heavily cuts both ways for Rodman: after the adjustment, he only holds the top 6 spots in NBA history, rather than the top 7. On the other hand, he led the league in this category 10 times instead of 8, which is perfect for comparing him to another NBA player who led a major statistical category 10 times — Michael Jordan:

^{Red bars are Jordan. Mean and standard deviation are calculated from 1976, excluding MJ, as with Rodman above.}

As you can see, the data suggests that Rodman was a better rebounder than Jordan was a scorer. Of course, points per game isn’t a rate stat, and probably isn’t as reliable as rebounding %, but that cuts in Rodman’s favor. Points per game should be more susceptible to varying circumstances that lead to extreme values. Compare, say, to a much more stable stat, Hollinger’s player efficiency rating:

Actually, it is hard to find any significant stat where someone has dominated as thoroughly as Rodman. One of the closest I could find is John Stockton and the extremely obscure “Assist %” stat:

^{Red bars are Stockton, mean and SD are calculated from the rest.}

Stockton amazingly led the league in this category 15 times, though he didn’t dominate individual seasons to the extent that Rodman did. This stat is also somewhat difficult to “detangle” (another term/concept I will use frequently on this blog), since assists always involve more than one player. Regardless, though, this graph is the main reason John Stockton is (rightfully) in the Hall of Fame today. Hmm…

This is the most thorough deconstruction of rebounding statistics I have ever seen. As a longtime fan of the Worm, I am impressed and eagerly awaiting the rest of this series. In an eloquent series of articles arguing for Barry Bonds as MVP of the 2004 season by King Kaufman of Salon.com (http://www.salon.com/news/sports/col/kaufman/2004/09/21/tuesday/), a commenter introduced an Australian horse racing term “daylight second” to indicate a situation in which the distance between first and second is truly gigantic. You have demonstrated that it’s Rodman in first, with daylight second in rebounding.

Bonds practically broke the game, in more ways than one. I’m glad you’re enjoying the series so far — believe me, it gets crazier.

i rate rodman a 2

This is devastating analysis overall. One question I have which I have not seen accounted (or not understood how it was accounted for) is the context of the team. For instance, you correctly point out how many more opportunities there were for rebounds in 60-61 as compared to Rodmans era and accounting for these different league contexts reveals Rodman was more impressive using just this simple adjustment, forget more sophisticated methods. But league context is not the only important context. Team context and coaching assignment it would seem to me could matter as well, without having the foggiest idea exactly how to assess their impact. What do I mean but team context and coaching context? In principle Rodman could get more rebs per opportunity because he is a much better rebounder than RC. It could also be that all his teammates were much worse at getting rebounds than were Russell and Chamberlain’s teammates. In such a case his individual rebounding prowess could be the absence of their skill in rebounding. Moreover, I could imagine that if a rebounder is surrounded by other good rebounders the smaller number of rebounds they get relative to a good rebounder surrounded by schleps would have no material impact on the team overall; other good rebounding teammates would get those rebounds. The other potential confounding factor I will through at the wall is coaching strategies. This is likely related among other things to the decline in the number of rebounds overall. What I mean by coaching is this: Did Rodman’s coaches encourage other players vacate rebounding zones in favor of pushing further out. By the same token, Auerbach coached his non-Russell players at times to take off with once the shot was in the air in confidence that if missed Russell would likely get the rebound and they could receive the outlet pass. That particular example, of course, would strengthen your case. But either way it suggests – no more – another factor that should be explored: Do coaching decisions influence the opportunities for players to obtain rebounds? If the answer is yes, or more accurately yes and the size of the impact matters, then it is not enough to isolate individuals from their team context or to ignore the impact of coaching, both the coaching decisions of the focal player and other team they are playing.

I love the analysis, and given that Rodman’s sole focus was on rebounds its not hard to understand why his TRB% was so much higher than that of Chamberlain or Russell…but I don’t appreciate the slights against Chamberlain here. Let me explain. Lets remember that Chamberlain was a huge scorer earlier in his career. In particular, he had a fadeaway jump shot and extended finger roll that in effect lowered his TRB%. In addition, it could be argued that the faster pace actually makes it harder to garner a higher % of your teams rebounds due to the constant running up and down the floor than in the half course set where rebounds become more predictable. I won’t diminish what Rodman did there because he did it better than anyone, but I’ll continue to argue that it was more predictable. The reason I make a case for Chamberlain here and not for Russell goes beyond their roles: the Celtics always played one of the fastest paces in the league. Before 1969 Chamberlain averaged, AGAINST RUSSELL, 30 rebounds a game(I don’t like including 1969 because it wasn’t a legit year for Chamberlain due to his coach and his situation). Russell’s rebounds, I feel, were inflated due to this reason. I also don’t include the other roles Chamberlain normally assumed, like being a huge shot blocker(in 2 separate years the statistiican Harvey Pollack says he swears Chamberlain must have averaged double digit blocks). I think you should do an analysis of Chamberlain as well so we can see how much of an outlier HE was.

Just wanted to point out that team offensive rebound are worth exactly the same as defensive rebounds, for symmetry reasons. That is, since an offensive rebound gained is also a defensive rebound taken away from the opponent, they must be equal on average. There might be teams that prefer an offensive rebound over defensive (or the opposite), but in every game the advantage of offensive over defensive for team A is exactly the advantage of defensive over offensive for team B.

Yes, though I acknowledged the symmetricality:

If you could have one or the other (offensive rebound or defensive rebound), an ORB is prob slightly more valuable b/c their possessions are more efficient. But on the court, the choice isn’t between ORB and DRB, it’s between getting an ORB and giving up a DRB, or vice versa, which is where symmetricality comes in. In analyzing team stats though, we’re usually doing the former.

And in evaluating player stats, it’s a whole different issue: it doesn’t matter that an ORB and DRB are technically worth the same thing, what matters is the marginal expectation added to the player’s team. If his team would have been more unlikely to get the rebound without him, it is worth more.

All that said, I’m actually reconsidering the value of offensive rebounds predictively. Despite the prima facie case for them, their performance in regressions is actually somewhat poor.

Good stuff Ben. Love this dude. Appreciate your hard work and analysis of my career. I can honestly say I’ve never seen my numbers broken down this way. Much love honey.

Really love the breakdown here. Had a thought about rebounding rate, though. I wonder if there’s any correlation between offensive rebounding rate, and playing with elite players who attack the rim. It seems like (I.e. I don’t know for sure) many if not most offensive rebounds are the result of a defensive player having to give help, and leaving his man available for the board.

Anyway, not trying to argue the numbers here, just a thought.

What do you think of Reggie Evans?

He’s long been a great rebounder and an under-the-rim scrapper, but he put up a truly Rodman-esque rebounding seasons (actually better than nearly every Rodman season, albeit next to Brook Lopez) and it seems he’s kicked into this high gear at the same age Rodman did, including the season year when he didn’t get very many minutes. Obviously, he was never the defender Rodman was, but how does his rebounding impact stack up? And what’s missing exactly from his game that he’s not Rodman circa 1996?

Other than the fact that he put up a sick TRB% this year (actually the highest ever for that number of minutes played), I don’t know much about him. Just glancing at 82games (http://www.82games.com/1213/12BKN13.HTM), it looks like he didn’t put up a good adjusted +/-. That’s a high variance stat, but clicking back a bit and he’s actually negative for at least the last few years. How that happened and what it means, I don’t know yet.

This is a very interesting analysis. I agree that the rebound percentage is a much accurate measure than the total rebounds. But you can not simply assign each player an equal chance, which results 10%. In a game, a guide is usually further awAy from basket than a forward and even more so than a center. The guide certainly has less chance than center for rebounding. so I think a weight coefficiency should be introduced to account this position factor. It can be based on average rebound percentage of each position of the entire league by assuming the rebound difference between two different positions is soly caused by their distance difference from the basket.

Then, this introduces another factor. Players like Rodman whose assignment in a offense play is to grab rebound. So he always tries to get as close to basket as possible. While others who have to take shoots cannot do so. I don’t know how to calculate this assignment factor.

I do not try to deny the greatness of Rodman. He is certainly a very unique player whose impact to a team, to basketball and to sports business in general is profound. this just shows how complicated a game can be.

Would Michael have tried to score more to increase his standard deviations from avg, if he knew he would one day be competing against Rodman (in the context of this great analysis)?

Very interesting article, but the graph only goes up to 2011 and something happened beginning in 2012. Andre. Drummond. He is looking very Rodmanlike in his 5 seasons so far. Rodman’s peak was in his 9th year in the NBA. What’s truly amazing is how Rodman could dominate the rebounds without being very tall. I’m sure we will never see another guy do anything like that again.

Wilt could bench 500 lbs. and had a better vertical than Jordan. His endurance is well documented. Rodman was athletic with a high energy level. My opinion is if both of them are close to area where a missed shot is heading Rodman is not getting the ball very often. Early in his career I thought Barkley was the most dominant rebounder of modern times as he often converted offensive boards into points..Have you ever done your analysis on Oscar Robertsons game … 5-yrs at close to30_10_10-is impressive..thank you for your hard work and intriguing analysis.

A sentence here made me wonder if I understand possessions. Can a possession ever start with an offensive rebound? Asked another way: Can a possession have more than one shot attempt?

I don’t even know if you are still taking comments on this, but I’m curious as to how the league leader is percentage points less than the league average in some graphs?

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