# How much value do rebounders add? Or in the case of Golden State...

The best rebounders add about 1 point per 100 possessions to team point differential. Now that I've got the adjusted four factors going, it's pretty easy to see this.

Recall that O4 and D4 are the rebounding components of A4PM, defined as:

• $O_3=0.35*ORR_{adj}$
• $D_3=-0.44*(OPP)ORR_{adj}$

Here is the 2.5 year list (players > 3000 possessions played):

### Total Adjusted Rebounding Point Differential

According to this, the best rebounder is Kevin Love, who adds 1.16 points per 100 possessions to team point differential through his rebounding alone. Unfortunately, Kevin Love's total A4PM is -0.03, which suggests the rest of his game offsets his rebounding. But if you are in an argument on the internet, and just want to talk about the good parts of Kevin Love, feel free to bandy about this stat. It should be noted how high up on the list Ryan Anderson is, actually above Dwight Howard. That's interesting. And it probably isn't easily explained as a regression issue where he's just drawing away some of Dwight Howard's value, because Brandon Bass is way down on the list at #194 with (-0.15).

The Warriors have had rebounding issues for a long, long time. You can see why here:

Isn't David Lee supposed to be a great rebounder and Ekpe Udoh a terrible one? Well, not according to this. At any rate, you can see that the lineups the Warriors put out most of the time are so bad on rebounding, that it really can make a difference. For example, the starting unit of Curry/Ellis/Wright/Lee/Biedrins is -2.02. That's just awful and difficult to offset. And the funny thing is that we brought in Lee specifically to help improve it.

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What is "position" ? I assumed it's an algorithm to assign position with 1 as PG and 5 as center. But seeing "4.5" for Earl Boykins makes no sense. I don't think he could even handle playing center with Kindergarten kids.

Some of the positions for players who haven't played this year are just completely wrong. It's a spreadsheet error that I didn't bother to correct. As for how the other ("correct") ones are calculated, it's based on initial values from basketball-value.com, which I then further weight based on the actual units on the floor. So, if a "4" is playing with a "4.1", then the "4" will be recorded as a "4", and the "4.1" will actually be recorded as a "5". In other words, the position is a weighted average of the position rank in particular units. Hope that makes sense.

Ok, makes sense. Seeing Boykins as a C/PF was spectacularly amusing though. Made my day. I've been looking at starter basketball leagues recently for my 4 year old daughter. Can't wait to see how the center measures up to Boykins.

The low value of rebounding is hard for me to understand. Let's assume for a second the D-boards have 0 value: In 2011, the top offensive rebounders, Foster/Evans/Dorsey averaged about 4 more per 100 possessions than the average PF/C, the next tier lower Howard/Love/Noah/Bynum... all averaged at least 2 more o-boards over 100 possessions than the average Big. If top rebounders are lucky to earn 1 point per 100 by rebounding and assuming all rebounding value comes from o-boarding alone, the average value on these continued possessions would need to be about 0.25. Given that an average possession is worth closer to 1, and possessions following o-boards are typically better than average, this seems very unlikely. These are the same guys who are a + on the defensive end as well, so factoring in the value of d-boards would only exacerbate this discrepancy. What am I missing? Where is all of the value being lost?

"What am I missing? Where is all of the value being lost?" Remember, what we are looking at is rebounding % at the team level. Let me give a numerical example. Say we have a game where there are 40 rebounding opportunities for Team A (i.e. 40 missed shots). Team A grabs 10 of those, B gets the other 30. In this scenario, Team A has a 25% OREB% (or what I call ORR in the tables above). If Team A grabbed one more offensive rebound, ORR would be 27.5%, an increase of 2.5 %-points. This would equal about 1 point as you suggested. The regression says that it would be 0.34*(2.5) ~ 0.85 points. Not exactly 1, but not so far off. Kevin Love raises his team's ORR by 2.1% according to the regression, so he gets 0.74 points for that. The defensive coefficient is higher 0.44, which would give 1.1 points for the extra rebound. If we average the two coefficients, it would give ~0.95 points. Seems about right to me. There may be some extra value for good defensive rebounders that was found by the regression.

K. I think we have isolated my confusion then. How does Love only improve his team's ORR by 2.1% when hi ORR of 14% is 5% higher than the NBA PF/C mean of 9%? If 1 o-board corresponds to roughly a 2.5% bump in ORR then we have the same degree of concern using ORR that I had with ORB/100poss (this makes sense b/c I generated my ORB numbers using ORR and expected opportunities rather than using real ORB data). Are your numbers showing that when Love (and other good o-boarders) are in the game, they are stealing most of their o-boards from teammates? That isn't something I hear often, but is the only way I can get from Love's 5% advantage over the mean big, but only 2.1% bump to his teams ORR.

"How does Love only improve his team’s ORR by 2.1% when hi ORR of 14% is 5% higher than the NBA PF/C mean of 9%?" I assume you are taking a straight mean of OREB%, but you should weight that by the number of rebounds actually made by each player. There may be many PF/C who have low OREB%, but do not play many minutes (as a consequence!). What I would suggest is adding up the ORR of the starting unit for several teams and then compare that figure to their team's ORR% to get a rough estimate. See how far off it is. (Hint: I've done this, and it's quite close.) And btw, this season Minnesota is averaging 28.6% OREB%, which ranks 10th and is only 1.7 %-point greater than league average. Where's his 5%? Given that he's played roughly 75% of the team's minutes, shouldn't we, er, you expect much higher than that?

I did take the straight mean out of laziness, but now looking at the 2011 "true"-mean ORR of a PF/C player-possession, it is still only 10.1%. That is 3.5% lower than Love's 13.6%. In 2010, the mean level was 10%, which is 4.5% lower than Love's 14.5%. As for this season... Love's ORR has dropped off a cliff. It is only 11.4% or 1% better than the league average of 10.4%. The big question is where did all of Pekovic's ORR (18.8%, though in more limited minutes) go? I would assume into the black hole of suck that is the rest of the Wolves' front-court. So, looking at it more rigorously, the problem is attenuated, but still real. In the last 2.5 seasons, Love has beaten the league ORR for PF/C by about 3.5%, but apparently only helps his team's ORR by 2.1% when he plays.

"In the last 2.5 seasons, Love has beaten the league ORR for PF/C by about 3.5%, but apparently only helps his team’s ORR by 2.1% when he plays." Diminishing returns on offensive rebounding is expected to be about 70%, so that isn't too surprising.

This stat in particular begs to broken down by position. Not sure if the other factors would also be more informative that way.

I have a tough time imagining that Love has a negative overall rating or only adds 1.16 pts per 100 from rebounding. There are a lot issues with box score stats, but he is one of the highest rated players in the league off the box score with any reasonable values assigned to the various stats. He's not that "terrible" of a defender to offset everything else he does well. Not that this means much, but in the 2 games he was suspended Vegas moved the line significantly to reflect his absence.

"I have a tough time imagining that Love has a negative overall rating or only adds 1.16 pts per 100 from rebounding." Everyone is free to believe what they want to believe obviously. You don't seem to have a problem with him being at the top of the list, just the value. That is clearly something that is dependent on the type of analysis being done. I will point out that I found his overall RAPM is +0.93 compared to the -0.03 value for his A4PM. Two different metrics. Jeremias Engelmann has Love rated at +2.5 (which is actually quite a bit higher than last season) total, with just about all of that coming on offense. As I said in the previous article, I need to do more work to test the predictive ability. You might turn out to be right eventually. But certainly, it appears to be within the range of 1-2 points from rebounding, perhaps, with 1 being a lower bound.