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EvanZ
Joined: 22 Nov 2010
Posts: 303
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 Posted: Tue Jan 25, 2011 10:05 am Post subject: Rebounding correlation with other factors |
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I took team level data from 2004-2010 and ran multiple regressions for offensive and defensive rebounding on all the other "four factors" and pace. Let me give the summaries (from R) and my comments.
Defensive rebounding
| Code: |
Call:
lm(formula = DRB ~ eFG + TOV + ORB + FTR + OeFG + OTOV + OFTR +
Pace, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.054003 -0.009793 0.001288 0.013179 0.031671
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.0112741 0.0759232 13.320 < 2e-16 ***
eFG 0.1816257 0.0860123 2.112 0.03617 *
TOV -0.0289197 0.1549450 -0.187 0.85216
ORB -0.1506858 0.0634746 -2.374 0.01871 *
FTR -0.0768623 0.0629658 -1.221 0.22388
OeFG -0.2466962 0.0855494 -2.884 0.00444 **
OTOV -0.3119686 0.1516462 -2.057 0.04118 *
OFTR 0.1000762 0.0601562 1.664 0.09802 .
Pace -0.0018406 0.0005889 -3.126 0.00209 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.01796 on 171 degrees of freedom
Multiple R-squared: 0.2208, Adjusted R-squared: 0.1843
F-statistic: 6.057 on 8 and 171 DF, p-value: 7.413e-07 |
You can see that eFG%, ORB%, opponent eFG% (OeFG), opponent TOV%, and pace are statistically significant. Of these, I think it's conventional wisdom that there is some correlation between OeFG and DRB, whether it puts the defense in better position for rebounds or simply reflects greater talent level (size?). The talent effect probably explains the result for eFG. Pace and DRB are negatively correlated, but I think this is also conventional wisdom. ORB and DRB are found to have negative correlation, which I was not expecting. From reading some old threads, I gather this is not a new finding, but it is curious to me, nonetheless.
Offensive rebounding
| Code: |
Call:
lm(formula = ORB ~ eFG + TOV + DRB + FTR + OeFG + OTOV + OFTR +
Pace, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.056045 -0.015878 0.002585 0.013995 0.051631
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7436483 0.1151926 6.456 1.07e-09 ***
eFG -0.2730334 0.1011463 -2.699 0.007644 **
TOV -0.0406658 0.1836626 -0.221 0.825033
DRB -0.2117359 0.0891912 -2.374 0.018708 *
FTR 0.1808382 0.0736769 2.454 0.015111 *
OeFG 0.0089334 0.1038436 0.086 0.931545
OTOV 0.0127062 0.1819681 0.070 0.944413
OFTR 0.0724809 0.0716693 1.011 0.313290
Pace -0.0026649 0.0006882 -3.872 0.000153 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.02129 on 171 degrees of freedom
Multiple R-squared: 0.2674, Adjusted R-squared: 0.2331
F-statistic: 7.801 on 8 and 171 DF, p-value: 6.575e-09 |
For offensive rebounding, I am surprised that there is a negative correlation for eFG. One thought I have is that better 3-point shooting teams may tend to be smaller. This may also explain why FTR is significant on offense. Fouls tend to come on inside shots rather than jumpers, so higher foul rates suggest better post scorers, who are then in better position to get offensive rebounds. It also doesn't surprise me that Pace is negatively correlated for some of the same reasons. Of course, here you see the negative correlation between ORB/DRB again.
So, I have a feeling I have probably summed up what has been done before...I did some searching through the forum, but couldn't find specific threads on this topic. I'd appreciate if anyone can point me to previous work here or elsewhere on the web. Also, I would be interested to hear alternative explanations for some of these findings.
_________________
http://www.thecity2.com
http://www.ibb.gatech.edu/evan-zamir |
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Crow
Joined: 20 Jan 2009
Posts: 825
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| Posted: Tue Jan 25, 2011 12:17 pm Post subject: |
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| I wonder if any of the findings for just the first 8-10-12 seconds of the shot clock are much different from the remainder of the shot clock. Particularly on the ORB - DRB issue. |
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gabefarkas
Joined: 31 Dec 2004
Posts: 1313
Location: Durham, NC
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| Posted: Tue Jan 25, 2011 12:17 pm Post subject: Re: Rebounding correlation with other factors |
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| EvanZ wrote: | | You can see that eFG%, ORB%, opponent eFG% (OeFG), opponent TOV%, and pace are statistically significant. Of these, I think it's conventional wisdom that there is some correlation between OeFG and DRB, whether it puts the defense in better position for rebounds or simply reflects greater talent level (size?). The talent effect probably explains the result for eFG. Pace and DRB are negatively correlated, but I think this is also conventional wisdom. ORB and DRB are found to have negative correlation, which I was not expecting. From reading some old threads, I gather this is not a new finding, but it is curious to me, nonetheless. |
I'm not sure it's that straightforward. The correlation between eFG and DRB exists only within the framework of the model you created. In other words, there is a correlation between eFG and DRB when considering the other variables in your model. Can you generate the correlation matrix in R? I'd recommend taking a look at that.
| EvanZ wrote: | | For offensive rebounding, I am surprised that there is a negative correlation for eFG. One thought I have is that better 3-point shooting teams may tend to be smaller. This may also explain why FTR is significant on offense. Fouls tend to come on inside shots rather than jumpers, so higher foul rates suggest better post scorers, who are then in better position to get offensive rebounds. It also doesn't surprise me that Pace is negatively correlated for some of the same reasons. Of course, here you see the negative correlation between ORB/DRB again |
Again, I'd caution against a simple (ie, direct) interpretation, such as what you wrote. The negative correlation exists between OR and eFG only when taking into consideration the other independent variables in your model. But what are the correlations between each of these? Have you tried any sort of model selection procedure, or reviewed model fitting, to see if you might be better off removing some of the independent variables? |
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EvanZ
Joined: 22 Nov 2010
Posts: 303
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| Posted: Tue Jan 25, 2011 4:53 pm Post subject: |
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DRB regressed on eFG alone:
| Code: |
Call:
lm(formula = DRB ~ eFG, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.053448 -0.012722 0.001900 0.013400 0.047607
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.63333 0.03867 16.378 <2e-16 ***
eFG 0.19311 0.07816 2.471 0.0144 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.01961 on 178 degrees of freedom
Multiple R-squared: 0.03316, Adjusted R-squared: 0.02773
F-statistic: 6.105 on 1 and 178 DF, p-value: 0.01442
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ORB regressed on eFG alone:
| Code: |
Call:
lm(formula = ORB ~ eFG, data = data)
Residuals:
Min 1Q Median 3Q Max
-0.0568674 -0.0160022 -0.0008958 0.0152078 0.0625642
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.50441 0.04478 11.26 < 2e-16 ***
eFG -0.47158 0.09052 -5.21 5.19e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.02271 on 178 degrees of freedom
Multiple R-squared: 0.1323, Adjusted R-squared: 0.1274
F-statistic: 27.14 on 1 and 178 DF, p-value: 5.187e-07
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Both are statistically significant. There is still a negative correlation between ORB and eFG.
_________________
http://www.thecity2.com
http://www.ibb.gatech.edu/evan-zamir |
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bbstats
Joined: 25 Apr 2010
Posts: 46
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DJE09
Joined: 05 May 2009
Posts: 148
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| Posted: Tue Jan 25, 2011 11:09 pm Post subject: |
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Is it as simple as you miss more shots, there are more rebound opportunities, you go looking for them more?
You (expect to) make more shots, you hussle back on D more ... |
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