Crashing the offensive boards does come with a cost!

Dave Berri over at engaged in a conversation with Henry Abbott from ESPN about the influence of offensive rebounding on the defensive efficiency. Abbott argued that crashing the offensive board might cost a team points on the defensive end, while going back on defense would make them play better defense. Abbott’s idea has some merit, because going back on defense instead of crashing the board would have an influence on the fast break opportunities of the opponents, which is the most efficient opportunity. Thus, reducing the amount of fast break opportunities should lead to a better defensive efficiency.

Now, Berri argued that offensive rebounding does not show a statistically significant influence on the defensive efficiency. I can confirm that, because just looking at the ORB% and the ORtg from 1987-88 to 2011-12 will give the R² and the p-value Berri reported in his blog post. Also, the 2nd argument by Abbott (shots per possessions) is not something worth talking about, I agree with Berri on this one too.

Well, there is obviously a “but” here, because otherwise I wouldn’t write this blog entry at all. The issue is neither of the two statistical analyses Berri did was actually able to answer the question at hand. Is crashing the boards actually hurting a team defensively? We can’t answer that by looking just at ORB% and DRtg, because a team with a higher ORB% might just be able to be a better rebounding team overall, thus a better defensive rebounding team as well. And we know that DRB% has a great influence on the team defensive efficiency.

In order to control for that, we can look at the DRB% of each team and compare that to the DRB% of the league in average. We can do the same for ORB%. If a team gets relatively more offensive rebounds than defensive rebounds, we can reasonable assume that they actually crashed the board more often offensively, while if it is the other way around, they probably chose to go back defensively instead more often. The actual comparison was the difference to the league average in terms of DRtg (Drtg_dif) versus the difference to the league average in terms of DRB% (DRB_dif) minus the difference to league average in terms of ORB% (ORB_dif). The difference between DRB_dif and ORB_dif will be called DRB-ORB. For those selected 711 team seasons from 1987/88 to 2011/12 we are getting R² = 0.131 and a p-value of 0.000. Thus, we are actually noticing that a team which has more offensive rebounds than expected by their DRB% will tend to have a worse defensive efficiency. That is statistically significant as seen by the p-value.

We would also expect that a team which crashes the board even more often offensively or a team which actually goes back on defense even more often, essentially teams which have a distinct strategy for that matter, would actually show a bigger discrepancy between their difference to the league average in terms of ORB% and DRB%. In order to check those cases, I looked at the standard deviation (σ) of the DRB-ORB in the sample and found it to be 2.9. Then the sample was reduced to all teams which showed a bigger than 1σ difference between ORB% and DRB%. That eliminated 476 team seasons and left us with 235 cases. Now the same correlation analysis was made as previously with all teams and the result was: R²=0.317 with a p-value of 0.000. As we can expect, teams with a bigger difference showed a bigger correlation. We can essentially use that as a proof that crashing the offensive board is actually hurting the defensive efficiency while going back defensively will actually increase the chances of having a better defense.

And while we are at it, we can check some other things:

How does being better than league average at ORB% influences the team’s offense? R²=0.011, p-value=0.005
How does being better than league average at DRB% influences the team’s offense? R²=0.025, p-value=0.000
Well, as it seems being better at defensive rebounding is more statistically significant and shows a better correlation than being better at offensive rebounds in terms of team offensive efficiency.

How does being better than league average at ORB% influences the team’s overall scoring margin per 100 possessions? R²=0.005, p-value=0.058
How does being better than league average at DRB% influences the team’s overall scoring margin per 100 possessions? R²=0.217, p-value=0.000
While ORB% advantage is not statistically significant in the sample from 1987/88 to 2011/12, having an advantage in DRB% is.
How does the DRB-ORB reflect on the scoring margin? R²=0.054, p-value=0.000
And for the 235 cases which showed to be further away from the league average DRB-ORB than 1σ? R²=0.119, p-value=0.000

All those numbers are suggesting that going back on defense is indeed the superior strategy for NBA teams than crashing the offensive board. Teams which tend to go back on defense will not only see a better defensive efficency, but also a better scoring margin per 100 possessions. But they also say that being better at rebounding is actually a helpful trait in order to win games; just that being the better defensive rebounding team is much more important than being the better offensive rebounding team. Thus, a metric which wants to reflect the reality should show the same things.

Here is the raw data as Excel file which was used for the statistical analysis (derived from rawdata_orbcost

Edit: There might also be the question whether that has a bigger influence today. To answer that question we can check the data from 2004/05 to 2011/12 (since the new interpretation of the no-handchecking rule is in place). For those 240 team seasons we get a R²=0.200 and a p-value of 0.000 between Drtg_dif and DRB-ORB, while for the 78 cases which are further away from the league average than 1σ (the standard deviation for that sample is 3.0) we get R²=0.627 and the p-value is 0.000. Thus, we can conclude that in today’s league the strategy of going back on defense instead of crashing the offensive board is even more helpful than over the whole sample from 1987/88 to 2011/12.

Last but not least: I apologize for all mistakes in grammar and orthography. 😉