Predicting Team Rebounding Rates

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 5-player 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 5-player units to see if we can get more confident measures of each 5-player unit’s rebounding rates than we can at the team level.