Predicting Team Rebounding Rates
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As we saw in my post on ranking net efficiency ratings, we don’t gain a lot of information by ranking NBA efficiency ratings at the team level. In other words, finding each team’s rating does not affect their overall ranking very much. The same holds true for offensive and defensive rebounding rates, and I suspect it will hold true for the other team statistics that I rate.
That said, these methods give us a framework for understanding the statistics with respect to the entire league. It also allows us to measure the affects of things like home court advantage. This is important, since this information is valuable when making predictions.
So by rating team stats I hope to gain a framework for rating unit stats, which in turn I hope to apply to player stats. Adjusted plus/minus is the current standard for rating players contributions not gathered by traditional statistics, but my goal is to understand how coaching strategy (and other factors) affect these ratings, since the ideal goal is to measure players independent of teammates, opponents, coaching strategy, player usage, etc.
The Method
I have chosen to use a logistic regression to calculate team ratings for offensive and defensive rebounding rates. I chose to use a logistic regression over the Colley Matrix Method because the logistic regression allows me to measure the affect of home court advantage, where as Colley’s method does not allow us to quantify these external factors.
Therefore, to use the ratings listed in the table below you will need to apply the inverse logit function: logit^{1}(x) = e^{x} / ( 1 + e^{x} )
The Model
Let me first note that this model is with respect to offensive rebounding. So the predicted rates are always in terms of the offensive team.
That said, the intercept for this model is 0.905, and the home court advantage is 0.096.
The team ratings are as follows:
Team  Offensive Rating  Defensive Rating 
ATL  0.117  0.008 
BOS  0.016  0.249 
CHA 
0.043  0.027 
CHI  0.035  0.011 
CLE  0.029  0.146 
DAL 
0.064  0.141 
DEN  0.059  0.036 
DET  0.091  0.141 
GSW  0.052  0.165 
HOU  0.089  0.185 
IND  0.150  0.177 
LAC  0.061  0.009 
LAL  0.066  0.059 
MEM  0.188  0.139 
MIA  0.159  0.047 
MIL  0.057  0.149 
MIN  0.064  0.143 
NJN  0.061  0.174 
NOH  0.180  0.166 
NYK  0.201  0.083 
OKC  0.041  0.123 
ORL  0.193  0.221 
PHI  0.170  0.039 
PHX  0.105  0.067 
POR  0.210  0.182 
SAC  0.134  0.073 
SAS  0.334  0.335 
TOR  0.287  0.098 
UTA  0.095  0.035 
WAS  0  0 
Interpreting These Numbers
In a nutshell, teams with higher the offensive ratings are the best offensive rebounding teams, and teams with lower defensive ratings are the better defensive rebounding teams.
Also, you might be asking yourself the following question: “Why is the Wizard’s offensive and defensive ratings zero?” The answer is because of the way the model is fit. Basically one of the offensive and defensive team’s ratings is “extra information”. In statistical terms, this happens because of singularity.
Since Washington is last alphabetically, they’re the lucky winners of the 0 rating. If the teams were mixed around such that someone else got the 0 ratings, the intercept and ratings for all of the other teams would be different than those listed above. But the interpretations (and predictions) you make would still be the same.
Making Predictions
So the whole point of this is to get an idea of how we might expect one team to rebound against another team. Let’s suppose the Kings are going to Dallas to face the Mavs. The Kings expected offensive rebounding rate would be:
logit^{1}(0.905 0.134 0.141) = 23.5%
The Mavs expected offensive rebounding rate would be:
logit^{1}(0.905 +0.096 0.064 +0.073) = 31%
In other words, the Mavs and Kings expected defensive rebounding rates would be 76.5% and 69%, respectively.
Summary
Although I did not list the standard errors above, I will say that there is some uncertainty in roughly half the teams ratings. What I mean by that is, their ratings are not statistically signifigant from 0 at traditional levels of signifigance.
Because teams are made up of many 5player unit combinations and playing situations, there could be many possible explanations for this. So these results have inspired me to fit ratings for last year’s starting 5player units to see if we can get more confident measures of each 5player unit’s rebounding rates than we can at the team level.
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Mountain said:
Yeah 5 man lineup level analysis would be good. That is how teams play. Marry this up to your player location study taken to adjusted and get it all tuned up, integrated (maybe use calculus) and you’ve got it mapped at all levels.
March 17th, 2009 at 1:47 am