Deep Dives: Random Rebound Observations

Somehow, over the course of the last few nights of games, the NBA Twitter topic of discussion turned to rebounding. Specifically, Pau Gasol.

Since he came to Chicago, his gaudy box score totals have become seen by some[1. With some justification, I hasten to add.] as hollow stat-padding, not as impactful in helping Chicago win basketball games as a string of “double-doubles” might otherwise suggest. As is often the case, this sent me down a rabbit hole of exploration of many things rebounding. Especially on a somewhat hot-button topic dealing with a player under fire, I want to emphasize more than usual that a lot of what is discussed below is very much in the “preliminary findings” stage. I might even put some interpretive gloss on the raw results, but that gloss, the explanation of the meaning of what has occurred, is largely conjectural and in need of further study before I’d really like to see “as reported/found by Nylon Calculus” in any sort of citation[2. Hopefully that’s enough of a “proceed with caution” disclaimer.]

Free Rebounds

A topic I return to with some frequency is the value of rebounding. More specifically, the value of individual rebounding. Grabbing boards, or not doing so, is a big component in most holistic rating systems, whether our own DRE, as part of the statistical prior for Real Plus-Minus or in commonly cited single-number metrics such as BPM, PER and Win Shares. Without relitigating the appropriate amount of credit to assign to rebounds in general[3. Seriously, the bitterness of some of the debates over this topic back in the day call to mind Kissinger’s quote about why fights in academia are so bitter: “Because the stakes are so small.”], given what we know now, a rebound is not always a rebound. Offensive rebounds are currently a hot topic, especially with respect to the degree to which so many teams are simply eschewing chances at getting them.

Somewhat paradoxically, this development devalues defensive rebounding to a degree. As I noted last week, a higher percentage of missed shots are simply conceded to the defense than ever before[3. “Ever” being “the three years of the SportVU era”, but given the fairly linear relationship between chasing offensive rebounds and offensive rebound rates, the all-time low OREB% leaguewide almost certainly supports the above statement.]. Meaning there are even greater numbers of “free” defensive rebounds lying around for compilers to, well, compile. Which in many ways brings us back to Gasol the elder.

To better track players who are most guilty of stat-padding, I’ve added “Free” Rebound% — simply the percentage of a player’s rebounds which are uncontested defensive boards, to the Detailed Rebounding page. From there, we can see Gasol is, thru Monday’s game, up to 60.1% of his rebounds being “freebies.” Which sounds bad, until one recalls that around 59.5% of missed FGs result in uncontested defensive rebounds. So Gasol’s number is high, but not egregious. Except for one factor. These days, Gasol plays primarily as a center, a quick perusal of the ranks of those with very low “Free” reb% shows the majority of them are in fact big men, who are forced to fight for more of their boards than those dastardly rebound stealing guards[3. Looking at you, Rajon.]

In fact, using my positional playing time estimates, we can derive averages for each spot on the floor:

Suddenly, that 60.1% for Pau looks more worrisome.

Rebound Value

Of course, acknowledging that uncontested defensive rebounds are less valuable than other boards is not the same thing as saying they are useless. It isn’t right to say only 39.9% of Pau’s rebounds count. Everything else being equal, grabbing more uncontested rebounds is better than collecting fewer, as even if they are easy, at least by snatching them up, he doesn’t give the offense a chance at them. But how to properly discount them? In looking into the topic, I’ve previously found uncontested defensive rebounds are “worth” about half as much as other rebounds via some quick regression analysis. Which makes some intuitive sense. “Contested” rebounds are essentially a 50/50 proposition between offense and defense to see who ends up with the ball. The player grabbing the uncontested board is doing his part by showing up for the contest, which in a vacuum he’d win half the time.

But the inquiring doesn’t end there in terms of rebound value. Going for offensive rebounds, and missing should be penalized to a degree, as chasing and failing to secure offensive rebounds sometimes results in fast breaks the other way. How much of a penalty? Ideally, the demerits would be based to some degree on failed crashes which result in opponent transition play. Unfortunately, public SportVU data isn’t quite there yet — we only know how many offensive rebounds a player chased and his team failed to secure, not which ones. However, on aggregate the difference in eFG% immediately following contested rebounds is about 1% higher than after an uncontested rebound, or about .02 points per possession. For the purposes of this quick and dirty analysis, a possession is worth just over a point, so to make everything simpler, I’m going to estimate the pain of a missed offensive rebound to be worth about .02 rebounds.

Looking at the totals for everyone in the league, including the half-value of free rebounds and the minor penalty for failed attempts to offensive rebound, we’re left with total rebounds equaling about 71% of the actual number of rebounds. So to make the numbers more familiar to the scale we are used to from the box score, I used the ratio of “new” and “old” rebounds as an index with which to derive the following “adjusted” rebound totals:

Rebound Value Index simply compares the players raw rebound totals with the new adjusted totals and scales to an average of 100. Which coincidentally happens to be Pau’s exact score thru Monday’s games. Again, not that bad, except for the fact that he’s a center, being compared with every player in the league, and very few full time bigs have RVI’s of less than 100[2. And RVI itself is a pretty raw measure. Players with high “grab-and-go” ability such as Draymond Green or Giannis Antetokounmpo probably provide more value on than many even uncontested defensive rebounds because of their ability to grab the ball off the backboard and lead a fast break themselves.], again, indicating the raw totals overstate the Spaniard’s effectiveness.

Rebounds Conceded

Especially on the defensive side of the ball, preventing opponents from grabbing offensive rebounds is of similar importance as securing the rebound oneself. As with many defensive metrics, measuring the absence of a bad outcome is quite difficult, so directly cataloging these “preventions” without either detailed play charting or extensive access to raw SportVU data is near-impossible. However, we can at least begin to identify failures in this regard. Again, using the positional playing time estimates, we can make some educated guesses as to how often a player’s positional matchup grabs an offensive board. Now these totals should be taken with a spoonful of salt, as a lot of different things could be getting in the way of straight assignment of blame or credit.

First of all, the position estimates themselves are…estimates. I haven’t watched every minute of every game to know exactly which players are filling which general roles in any given lineup, nor is there anyway I can account for crossmatches, switches or rotations. The last of which is most problematic, as even if I have the matchup correct, sometimes the opponent a player is assigned to guard will get a putback because nobody “helped the helper” when a big is forced to rotate to protect the rim.

That said, I like it as an interesting first pass.

Before diving into the analysis, we need a baseline for what a reasonable expectations for opponent offensive rebounds might be. In a neat bit of symmetry, positional averages for offensive and defensive rebound rates can be used as a baseline for the opponent. So far this season, here are those rates, again by position a player is currently occupying:

So, a full time center should expect to give up about 1 offensive rebound every 10 misses to his opposite number. Looking at the more or less full-time centers in the league this year, here is how they shake out:

And to some degree, it’s worse than that even. Gasol has allowed[2. An estimated.] 123 offensive rebounds through Monday, more than any other player. Ninety-eight of those rebounds have been contested. In other words, Gasol might not be winning his share of fights for rebounds, which probably exacerbates the discontent among fans already somewhat skeptical of his performance.

Digressing for a moment, in the last column, it is interesting to note the presence of a great many rim protectors among those players who have conceded the most uncontested offensive rebounds. As alluded to above, it’s hard to say the degree to which this represents failings of the player in question, or if their respective teammates aren’t doing well enough picking up the slack. Further, it is somewhat to be expected that players who defend the rim well might give up more offensive rebounds. After all, missed layups are more frequently gathered by the offense than are jump shots, which is a small price to pay for, you know, not allowing easy layups in the first place. In fact, there appears to be a fairly direct correlation between contesting shots at the rim, and giving up offensive rebounds:

That said, the relative placement of Jordan and Tim Duncan on the above chart could well illustrate a real skill difference. One of the main arguments against Jordan as an elite defender is the perception that he “sells out” too frequently against players driving against the Clippers, leaving opponents’ free for easy dump offs or putbacks. By comparison, Duncan is an expert at bothering the initial shot without fully committing[5. Or even jumping often times.], allowing him to effectively fill both his rim protecting and rebounding duties, one of the main reasons why his defense remains elite even in the very twilight of his career.

Returning to the topic of Gasol, unfortunately the charges against him do appear to have merit on first pass. He does fatten up on free rebounds, leading to relatively low rebound value, while at the same time doing a very poor job of preventing his opposite number from hitting the glass. Or, all of the above could represent failings of the Bulls as a whole and Gasol is just a convenient scapegoat for fan ire. Only more research can determine which.