APBRmetrics

Berri made a post about the influence of offensive rebouding on the defense: http://wagesofwins.com/2012/10/10/is-th ... -rebounds/

Well, I can't comment on his blog, but here is my response to that issue: http://bbmetrics.wordpress.com/crashing ... ive-board/

In short: Teams which had a higher than by their DRB% expected ORB% showed a worse defense (R² = 0.131) and it was statistically significant (p-value=0.000). 235 teams showed a higher than sigma difference to the league average in terms of their discrepancy between ORB% and DRB% (120 lower and 115 higher). The analysis for this sample showed a R²=0.317, that was again statistically significant. Conclusion: Going back on defense helps defensively, crashing the offensive boards hurts the defense. Fun fact, going back on defense helps the overall scoring margin too.
I added the raw data at the end of the blog post as an Excel spreadsheet, if someone is interested to check for himself.

Edit: Just checked out how that effects develops over the time and found that in todays league (2004/05 to 2011/12) the correlation is even stronger. For teams which are more than 1 sigma away from the league average, the correlation becomes R²=0.627 while for all teams it is R²=0.2.

I just split this post off, because I think it warrants its own thread.

The sequence of articles so far (to quote Kevin Pelton):

The second week of training camp seems like as good a time as any to discuss offensive rebounding strategies. This week, ESPN Insider began rolling out John Hollinger’s season previews. In his discussion of the Boston Celtics,Hollinger pointed out that the Celtics’ offensive rebounding rate in 2011-12 was the lowest in league history, and by a fairly substantial margin. Boston is at the leading edge of a lengthy trend toward teams sacrificing second chances in favor of getting back defensively.

TrueHoop’s Henry Abbott noticed, and wondered if teams aren’t better off following Boston’s lead and entirely abandoning the offensive glass. At Wages of Wins, Dave Berri responded by pointing out that there islittle relationship between offensive rebounding and Defensive Rating.

Today came layer two of the analysis, as blogger Mystic looked at a more refined measure of offensive rebounding strategy and found that teams that pay less attention to the offensive glass tend to be better both on defense and overall. I think this latest study gets us about 75 percent of the way there.

Kevin Pelton's response to it all: http://www.basketballprospectus.com/unfiltered/?p=954

The limitation of the study Mystic did is that it only looks at correlation, not causation. We don’t know whether getting back makes teams better, or better teams tend to play more conservatively and defensive-minded because they don’t need to take as many risks. To try to really isolate the causation, I looked at year-to-year changes in offense/defense rebounding ratio as well as team performance. I also limited the study to 2004-05 to the present to consider only the way the game is being played since the rules re-interpretations that opened up the floor for offenses.

This perspective tends to support my view that there’s a trade-off between offense and defense when it comes to hitting the glass. There’s a positive correlation between the change in offensive rebounding and the change in Offensive Rating (+.125) and a negative correlation with the change in Defensive Rating (-.141), indicating that as teams hit the offensive glass more from one season to the next, they get better on offense and worse on defense. Even though the correlation with Defensive Rating is slightly higher, the overall relationship to change in winning percentage is ever so slightly positive. The bigger takeaway is that it’s almost zero. The r^2 figure suggests that about 0.1% of the difference in a team’s record from one season to the next is attributable to the change in their offense/defense rebounding ratio.

The same trends hold up when we look at the extremes. The teams that increased their offense/defense rebounding ratio the most had better offenses and worse defenses and were marginally better; teams that paid less attention to the offensive glass had worse offenses and better defenses and identical winning percentages on aggregate.

I agree that looking only at team level correlation between ORB% and defensive rating is not adequate. Mystic's attempt to identify teams with ORB% that are higher or lower than expected seems to me the right approach, as you really want to isolate positioning/strategy (as opposed to player talent). But I think Mystic's chosen variable, ORB%-DRB% (normalized), fatally biases his study. This is really as much a measure of DRB% as it is ORB% (I'm sure it correlates nearly as well with DRB% as ORB%). And DRB% in turn is very highly correlated with defensive rating. So Mystic had to get the result he found, whether or not a focus on offensive rebounding actually impacts defense. (I'm also not sure why DRB% should be considered a good predictor of ORB% -- for at least the last few seasons, I beleive there is virtually no correlation between the two.)

You need a measure of offensive rebounding that is independent of DRB%, to avoid getting this tautological result. For examply, you might build a simple regression model to predict ORB%, using variables like age, height, eFG%, and opponent DRB%. Then see if teams that overperform on ORB% are weaker than average of defense. You might even include prior-season ORB% for the players, to isolate the impact of strategy.

Pelton removes a lot of the bias by looking only at the change in ORB-DRB, and seems to find a weaker tradeoff. But as he notes, a lot of the year-to-year change reflects personnel changes, and so still may not be telling us much about the impact of positioning/strategy.

Guy wrote:But I think Mystic's chosen variable, ORB%-DRB% (normalized), fatally biases his study. This is really as much a measure of DRB% as it is ORB% (I'm sure it correlates nearly as well with DRB% as ORB%).

For ORB% difference: R²=0.614
For DRB% difference: R²=0.347

No, the measurement actually correlates stronger with ORB% than with DRB%.

For the cases with a bigger than 1 sigma difference, we get:

For ORB% difference: R²=0.792
For DRB% difference: R²=0.558

So, again, it is more correlated with ORB% than with DRB%.

Guy wrote: And DRB% in turn is very highly correlated with defensive rating.

In the sample the correlation between drb_dif and drtg_dif is: R²=0.338

Guy wrote:(I'm also not sure why DRB% should be considered a good predictor of ORB% -- for at least the last few seasons, I beleive there is virtually no correlation between the two.)

It is indeed not correlated at all. And that's actually the very reason I used that, because I made the assumption that the defensive rebounding reflects the true rebounding abilities of the teams more than either ORB% or TRB%, for the simple reason, that all teams are actually trying to get the defensive rebound and no explicit strategy is known in which the bigs are running away from their own basket before the ball is in the hands of the teams in order to be the first on the offensive end. I think that is a reasonable assumption. If DRB% reflects the real rebounding strength, we can actually use that to gauge that. If you can show that DRB% is actually not a function of the real rebounding strength of the team, my measurement would actually be wrong.
Also, if there would be a high correlation between those two things, we actually would found that better ORB% would lead to better defense.

Guy wrote: You need a measure of offensive rebounding that is independent of DRB%, to avoid getting this tautological result.

No, what we would actually need is a measurement of real rebounding strength of a team, not a good predictor for offensive rebounding in order to seperate rebounding strength from strategy on the offensive glass. DRB% is such a measurement, that's why I used it. If there is something which can actually be used as a predictor for DRB%, we could use that to make a seperation between real rebounding strength and strategy on the offensive glass too.

Guy wrote: Pelton removes a lot of the bias by looking only at the change in ORB-DRB, and seems to find a weaker tradeoff.

Pelton found R²=0.141, I found R²=0.200 for the same sample. So, indeed a smaller tradeoff. But in both cases it is still significant. While my measurement might overrate the effect due to the correlation to DRB%, the result by Pelton is actually still significant and a lot bigger than Berri's method suggests.


Btw, I exchanged an E-Mail with Kevin Pelton in which I agreed with his critism about my used method. His answer suggest that we both are in complete agreement in terms of the limitations and the overall effect. Also, we both agree that the strategy choice depends on the teams and their respective roster.

I also want to point out that my conclusion based on the analysis was that teams should not try to get offensive rebounds at all costs. It is more useful to send the players back on defense, if they are further away from the basket. Especially slow-footed bigger players, which are often used as perimeter shooters in order to create better spacing, should be running back defensively instead of trying to get the offensive rebound. In order to improve that strategy, the work by Kirk Goldsberry comes in handy, in which he showed where the rebounds actually go. And that also made it pretty clear that having the inside position is a huge advantage for the defending team in terms of getting the ball.
My conclusion is NOT that teams should avoid offensive rebounding at all costs.

Good discussion, Guy, but I think Mystic is right in that DRB% should be a very good proxy for true rebounding ability of the team.

For ORB% difference: R²=0.614
For DRB% difference: R²=0.347
No, the measurement actually correlates stronger with ORB% than with DRB%.

For the cases with a bigger than 1 sigma difference, we get:
For ORB% difference: R²=0.792
For DRB% difference: R²=0.558

So, again, it is more correlated with ORB% than with DRB%.

Those are huge correlations, large enough to explain most if not all of your findings.

Guy wrote: And DRB% in turn is very highly correlated with defensive rating.

In the sample the correlation between drb_dif and drtg_dif is: R²=0.338

I said DRB%, not drb_diff. But anyway, you make my point. Again, this large correlation likely explains much of your finding. It's possible, if not likely, that all you have done is shown that defensive rebounding is correlated with defensive rating, which should not surprise us.

It is indeed not correlated at all. And that's actually the very reason I used that, because I made the assumption that the defensive rebounding reflects the true rebounding abilities of the teams more than either ORB% or TRB%, for the simple reason, that all teams are actually trying to get the defensive rebound and no explicit strategy is known in which the bigs are running away from their own basket before the ball is in the hands of the teams in order to be the first on the offensive end. I think that is a reasonable assumption. If DRB% reflects the real rebounding strength, we can actually use that to gauge that. If you can show that DRB% is actually not a function of the real rebounding strength of the team, my measurement would actually be wrong [emphasis added]

That's a big assumption you're making. In fact, we know DRB% reflects more than "pure rebounding ability," assuming such an ability exists. For example, it is highly correlated with opponent eFG%.

But even if DRB% is a moderately good proxy for "rebounding ability," it doesnt' matter -- you can't use it in this study. Because it is so highly correlated with defensive rating -- indeed, is a component of defensive rating! -- your method ensures your result. If you define offensive rebounding as the relative absence of defensive rebounds, then you will necessarily find that it hurts team defense. You've simply assumed your outcome. You need a measure of rebounding ability that is INDEPENDENT of your defensive metric. So you need to find a better measure of rebounding talent, or a measure of defensive prowess separate from drb%.

I suspect that your (and Pelton's) conclusions are absolutely correct. But your methodology is too compromised to serve as evidence for those conclusions.

Teams that don't shoot well are more apt to go for more offensive rebounds.
Of 380 team-seasons in this century, the top 100 OReb% teams have a median eFG% of .476
The bottom 100 OReb% teams have a median eFG% of .498
Both groups have median W% of .512 (42-40)

Meanwhile the top 1/4 of eFG% teams have had a median OReb% of 26, while the bottom 1/4 have median ORb% = 29.

Guy wrote:You need a measure of rebounding ability that is INDEPENDENT of your defensive metric. So you need to find a better measure of rebounding talent, or a measure of defensive prowess separate from drb%.

Opponents points per 100 possession is not calculated by using defensive rebounds at all. It is simple counting the points and counting the amount of possessions.
What you are asking for, is metric which would be based of the assumption that rebounding ability has no influence on the defense at all. That is hardly a reasonable assumption at all. Whenever I have something which describes rebounding ability, I expect that to correlate well with the defensive strength. Do you really want to argue against that?

Also, and it might be a point you are missing, I did not try to describe offensive rebounds as the relative absence of defensive rebounds, I describe the strategy of crashing the offensive board as relative absence of defensive rebounds while the strategy of getting back on defense is described as the relative absence of offensive boards. That is a big difference here. What you are trying to do is getting the effect of the overall offensive rebounding on the defense, and I can tell you that we can't see such thing to a good enough degree (not statistical significant).
There also seems to be a misunderstanding about what I actually said regarding using DRB% as a proxy for "pure rebounding strength". My assumption here is that it is a better proxy than ORB% or TRB%. We could probably use consistency as an argument here.

We can use the cases in which we know that teams are using such strategy, because we can actually watched them do that, as a point of reference here. We have 4 teams which used "going back on defense" rather than "crashing the offensive board", the Celtics, Mavericks, Heat and Spurs. All 4 teams were below 1/2 sigma in terms of ORB% while being average or clearly above average in terms of DRB% over the last two seasons. All 4 teams are showing the expected relative absence of offensive rebounds. Another example would be the Minnesota Timberwolves. They shifted the focus with the coaching change and ended up being closer to league average in both, ORB% and DRB%,while in 2011 they were clearly much better in terms of ORB%.

Also, and maybe you are missed that too, I actually agree with Pelton's analysis, and agree that this is eliminating bias here. His method is better than my method. I don't question that at all.

ONe thing I should also point out, drb_dif is the difference between the DRB% and the league average DRB%. In that way I normalise the DRB% in order to seperate that from league-wide effects. The Drtg_dif (difference between DRtg and league average DRtg) and drb_dif shows a clearly stronger correlation than DRB% and DRtg over the years. Not normalising those values will underestimate the effect of defensive rebounding on the defensive strength.

If I was redoing the study, I would definitely isolate defensive eFG%. Not sure why that didn't occur to me until after the fact.

Fortunately, the choice of metric shouldn't bias the measure of overall team performance, and that being neutral remains the important conclusion to me.

Kevin Pelton wrote:If I was redoing the study, I would definitely isolate defensive eFG%. Not sure why that didn't occur to me until after the fact.

How would you do that? And, the even better question, how can you make sure that the lower eFg% is actually not caused by the reduced 2nd chances after offensive rebounds? Thus, the better rebounding strength actually is partly a reason for the lower eFG% of the opponents?

mystic wrote: Opponents points per 100 possession is not calculated by using defensive rebounds at all. It is simple counting the points and counting the amount of possessions. What you are asking for, is metric which would be based of the assumption that rebounding ability has no influence on the defense at all. That is hardly a reasonable assumption at all. Whenever I have something which describes rebounding ability, I expect that to correlate well with the defensive strength. Do you really want to argue against that?

I am not saying your metric must be uncorrelated with defensive strength, but that it be INDEPENDENT of defensive strength. I don't know how to be any more clear about that. Your findings now are simply tautological. Ask yourself this: if there were zero tradeoff between seeking ORBs and defensive rating, would your analysis still show the correlation it does. The answer is obviously yes, because your metric is in part a measure of DRB%. And defensive rating, while not literally incorporating DRB% in its definition, is obviously determined to a signficant degree by DRB%. The more DRBs you grab, the more often the opponent scores zero points on a possession. Surely there can be no dispute about that.

As Kevin suggests, you could instead look at opponent eFG%. You could also look at opponent turnovers, and/or opponent FTA, if you think there might be effects there.

Or, as I originally suggested, find another way to control for factors apart from effort/focus that impact offensive rebounding. I'm guessing that average age and height might play a role. If you had data on distance of shot attempts, that would likely also help. Teams that over-perform their projection are probably teams that emphasize crashing the glass on offense.

For ORB% difference: R²=0.614
For DRB% difference: R²=0.347
No, the measurement actually correlates stronger with ORB% than with DRB%.

I was a bit surprised by this finding. It implies that the variance in ORB% is much larger than the variance in DRB%. I had thought they were roughly similar at the team level. Is the variance in DRB% much smaller? Any thoughts on why that is?

Guy wrote:I was a bit surprised by this finding. It implies that the variance in ORB% is much larger than the variance in DRB%. I had thought they were roughly similar at the team level. Is the variance in DRB% much smaller? Any thoughts on why that is?

It is, and the difference between the two becomes rather enormous when normalized for league average. I think it gets back to our discussion on why offensive rebounding is more valuable at the individual level than defensive rebounding. A lot of defensive boards are simply the product of showing up, whereas players have to go get--and be told by their coaches to go get--offensive rebounds.

Kevin Pelton wrote:

Guy wrote:I was a bit surprised by this finding. It implies that the variance in ORB% is much larger than the variance in DRB%. I had thought they were roughly similar at the team level. Is the variance in DRB% much smaller? Any thoughts on why that is?

It is, and the difference between the two becomes rather enormous when normalized for league average. I think it gets back to our discussion on why offensive rebounding is more valuable at the individual level than defensive rebounding. A lot of defensive boards are simply the product of showing up, whereas players have to go get--and be told by their coaches to go get--offensive rebounds.

Hmm. When Evan Z looked at this, he found that the SD for ORB and ORB(opp) were virtually the same, and so ORB and DRB had essentially the same impact on team wins: http://www.d3coder.com/thecity/2010/12/ ... rs-part-2/. Anyone have thoughts on the apparent discrepancy?

Guy wrote: I am not saying your metric must be uncorrelated with defensive strength, but that it be INDEPENDENT of defensive strength. I don't know how to be any more clear about that.

I understand what you said, fully, don't worry, I just said that I have a hard time seeing a metric which wouldn't have a similar problem while describing rebounding strength.

Guy wrote: The answer is obviously yes, because your metric is in part a measure of DRB%.

The answer is obviously no. It doesn't matter whether it is in part a measure of DRB%, that is irrelevant to the question. I use the DRB-ORB as a proxy for "crashing the offensive board" and "getting back on defense".

So, in order to check that, we can adjust the DRB-ORB by using the opponent eFG% as predictor for the expected DRB% here. I use league average eFG% - opponents eFG% = eFG%_dif. Then I ran a linear regression and found that 0.576*eFG%_dif = DRB_dif. I use that to determine an expected DRB%, which is then used to adjust DRB-ORB.

For the 235 cases, which have a bigger than 1 sigma difference I found: R²=0.180, p-value = 0.000.

If you would be correct, we shouldn't see a statistical significant correlation.


Also, I already conceded that my method is overrating the effect. Maybe you missed that part too. I'm not defending my method as the best possible way and an absolute perfect measure of that tradeoff. I just used that method in order to determine whether there is such an effect. And I concluded that such an effect exists based on the fact that the bigger than 1 sigma teams in both directions are actually showing a clearly stronger correlation. The teams I suspect will use such different strategies more often than others. I did never propose at any point that my method would be an exact quantification of the tradeoff.