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lakers4sho
09-27-2010, 10:55 PM
by lakers4sho

I. Introduction

In this thread, we explore rebound rate for both an individual player and a team. Rebound rate, or rebound percentage, simply stated, is the percentage of the total rebounds a player (or a team) obtains. Rebound rate can be evaluated as a whole, or divided into two sub-stats: offensive rebound rate and defensive rebound rate.

II. Individual Rebound Rate

Rebound rates by an individual player are usually determined in a per-minute basis. Therefore, such kinds of statistics can be and are affected by the pace at which the teams play, as well as their ability to make shots and force opponents to miss.

As a consequence, it is usually best that rebounding be evaluated by the percentage of all the missed shots a player rebounds while he is currently in the game. This is the total rebound rate (TRB%) for player X.

The formula is as follows:

TRB%(x) = [ TRB(x) / (TRB(a) + TRB(b)) ] / (Min(x)/Min(a))

where

TRB%(x) is the rebound rate for Player X
TRB(x) is total rebounds for Player X
TRB(a) is total rebounds for Team A (which Player X is a part of)
TRB(b) is total rebounds for Team B (the "opposing team")
Min(x) is total minutes played by Player X
Min(a) is total minutes by Team A

The formula clearly shows us the definition of rebound rate, which is the fraction of the total rebounds Player X grabs, divided by the fraction of the total minutes Player X is on the court.

Therefore, we can see that player X can increase his TRB% in 3 ways:

(a) getting more rebounds, while playing the same number of minutes
(b) player less(er) minutes, while obtaining the same number of rebounds
(c) both (getting more rebounds AND playing less(er) minutes at the same time)

As stated in I, rebound rate can be split off into two categories: offensive rebound rate and defensive rebound rate. The formulas for both are similar to each other and to the formula for TRB%.

ORB%(x) = [ ORB(x) / (ORB(a) + DRB(b)) ] / (Min(x)/Min(a))
DRB%(x) = [ DRB(x) / (DRB(a) + ORB(b)) ] / (Min(x)/Min(a))

The analyses for both ORB% and DRB% would be the mirror images of each other. ORB% quantifies the percentage of the total offensive rebounds possible that Player X grabs, while DRB% shows the percentage of the total defensive rebounds possible that Player X grabs. Both, as in TRB%, are divided by the fraction of the minutes Player X plays, because all three are per-minute rebound rates.

III. Team Rebound Rate

At the team level, rebound rate is determined slightly differently than individual rate. An important thing to take note is that rebound percentage (TRB%) is a more accurate measure of ability than mere rebounds per game (RPG). Good teams tend to rebound the ball at a higher rate than their opponents because they usually miss fewer shots, and missed shots are usually rebounded by the defending team. Therefore, good teams allow a lesser chance for opposing teams to rebound the ball than they are allowed.

Team TRB% is the average of its ORB% and DRB%, shown by the formulas:

OREB%(a) = OREB(a) / [ OREB(a) + DREB(b) ]

OREB% shows the percentage of offensive rebounds possible that Team A grabs. Offensive rebounds possible is the sum of the offensive rebounds of Team A and defensive rebounds of Team B (defensive rebounds of B can be stated as missed opportunities for A for additional offensive rebounds).

DREB%(a) = DREB(a) / [ DREB(a) + OREB(b) ]

DREB% shows the percentage of defensive rebounds possible that Team A grabs. Defensive rebounds possible is the sum of the defensive rebounds of Team A and offensive rebounds of Team B (offensive rebounds of B can be stated as missed opportunities for A for additional defensive rebounds).

TRB%(a) = [ ORB%(a) + DRB%(a) ] / 2

IV. Putting it All Together

Using data collected from league sources, it can be shown that there is an inverse relationship between ORB% and DRB%. For example, from the 1996-1997 season to the 2005-2006 season, the relationship correlation is -0.31. One of the proposed reasoning behind this is that offensive rebounds depend mostly on whether the coach favors crashing the boards or rushing back in order to prevent fast breaks.

Basketash
09-28-2010, 09:04 AM
Great post!

Patman
09-28-2010, 09:30 AM
Nice wantet to do Rebound Rate over the Weekend so i will have to find something else, but there are enough stats out there that can use explaining.

Rebound Rate is so much better then RPG, and it's pretty easy to understand why, it's just more interesting to know how many rebounds a guy grabs in relation to the total rebounds aviable.

bholly
09-28-2010, 09:33 AM
Thanks! Great post.

I'm very surprised by the negative correlation between ORB% and DRB%. That has to be for team rebound rate, right? I definitely would've thought the general quality of your rebounders more than offset the losses from crashing the boards and not getting back (or whatever the other proposed reasons are). Weird.

Also why is TRB% calculated as a simple mean of DRB% and ORB% for the team stats? Shouldn't it be [ DREB(a) + OREB(a) ] / [ DREB(a) + OREB(b) + OREB(a) + DREB(b) ]?
As far as I can figure it (and I may be wrong, because it's very late) the method given only works if there're the same number of rebounds at each end, ie the denominators of ORB% and DRB% are the same.

bholly
09-28-2010, 09:42 AM
In case I wasn't clear in what I meant about the formula, say Philly plays the Knicks. Philly miss 50 shots, 10 of which they recover as OREBs, and 40 of which the Knicks get as DREBs. The Knicks only miss 30 shots - 10 OREBs for the Knicks and 20 DREBs for the Sixers.
This means Philly's OREB% = 10 / [10 + 40] = 20%
And their DREB% = 20 / [10 + 20] = 66.66%

So by the formula above, their TRB% = [20% + 66.66%] / 2 = 43.33%

Actually, though, they took down 30 total rebounds, while the Knicks took down 50. So their percentage of the total rebounds is actually 30 / [ 30 + 50] = 37.5%

Why is the first formula used, and not the second? I would've thought the second more accurately shows what it's meant to?

Edit: One more question. Are there any rebounding stats that take into account the added difficulty of getting offensive rebounds on (non-tech) free-throws, rather than regular shots? Otherwise an individual's stats would be similarly skewed by whether you happen to be on a team that shoots a lot of (or not very many) free throws, or gives up a lot (or not very many), as well as how well the teams shoot them.

arkanian215
10-05-2010, 12:01 PM
In case I wasn't clear in what I meant about the formula, say Philly plays the Knicks. Philly miss 50 shots, 10 of which they recover as OREBs, and 40 of which the Knicks get as DREBs. The Knicks only miss 30 shots - 10 OREBs for the Knicks and 20 DREBs for the Sixers.
This means Philly's OREB% = 10 / [10 + 40] = 20%
And their DREB% = 20 / [10 + 20] = 66.66%

So by the formula above, their TRB% = [20% + 66.66%] / 2 = 43.33%

Actually, though, they took down 30 total rebounds, while the Knicks took down 50. So their percentage of the total rebounds is actually 30 / [ 30 + 50] = 37.5%

Why is the first formula used, and not the second? I would've thought the second more accurately shows what it's meant to?

Edit: One more question. Are there any rebounding stats that take into account the added difficulty of getting offensive rebounds on (non-tech) free-throws, rather than regular shots? Otherwise an individual's stats would be similarly skewed by whether you happen to be on a team that shoots a lot of (or not very many) free throws, or gives up a lot (or not very many), as well as how well the teams shoot them.

Yeah I think you got it right
TRB%(a) = 100*TRB(a)/[TRB(a) + TRB(b)]

B-R doesnt list TRB% for teams but hoopdata does. Hoopdata's uses that formula. http://hoopdata.com/teamadvancedstats.aspx

@lakers4sho JW, how did you derive team TRB%?

lakers4sho
10-07-2010, 12:03 AM
I used the equation Dean Oliver uses in his book.

I'm still trying to find an equal ground between the two equations. I think bholly brings up a wonderful and truly valid point (I realized that too while typing the formulas). In any case, once I find a common link, I'll surely update.