# Inside The Numbers - How To Measure Rebounding Success

Kendrick Perkins is among the NBA leaders in rebounds per 48 minutes.

By Mike Zarren
Celtics.com

January 19, 2006

## A. Team Rebounding

Everyone knows that rebounding is an important part of basketball - a team that doesn't get a lot of defensive rebounds allows easy put backs for its opponents, and a team that gets a lot of offensive rebounds doesn't need to worry as much about hitting every outside shot. But how do you know which team did a better job rebounding on a given night, or over the course of a season? Before you say, "Just look at who got more total rebounds," consider this case:

On January 4th, the Celtics played the Bobcats. Both teams hit 40 shots, but Boston took 70 (a 57% field goal percentage, continuing the Celtics' league-leading FG% pace), while Charlotte took 100. As a result, Charlotte had 60 misses, from which the Celtics grabbed 40 defensive rebounds. The Celtics had 30 misses, from which Charlotte grabbed 22 defensive rebounds. Who did the better job rebounding?

Celtic coaches, along with most basketball fans, know that it's usually easier to get a defensive rebound than it is to get an offensive rebound, since a defender is often located between each offensive player and the basket. As a result, if a Celtics opponent missed far more shots than did the Celtics, the Celtics are likely to have more total rebounds not because we did a better job rebounding, but simply because there were more rebounds available on our defensive end.

Paul Pierce is often underrated as a rebounder, but the numbers tell a different story.

So how do we figure out which team did the better job rebounding?

Celtic coaches use the defensive rebounding percentage stat. This stat effectively says: "Out of all possible defensive rebounds each team could have gotten, how many did they actually get?" Though the answer doesn't appear in the boxscore, it's not hard to calculate: just divide the Celtics' defensive rebounds by the sum of the Celtics' defensive rebounds plus the opponent's offensive rebounds.

DefReb% = DefReb / (DefReb + OppOffReb)

Then, to see which team did a better job rebounding, you just compare the two teams' defensive rebounding percentages. If the Celtics have a good night on the offensive glass, it will lower the opponent's defensive rebounding percentage. If the Celtics have a good night on the defensive glass, it will raise our defensive rebounding percentage. Either way, you'll know which team did the better job, even if that team had fewer chances to get a rebound than did its opponents. The league average defensive rebounding percentage is just over 73%.

Turning back to the Bobcats game on January 4th, the Celtics grabbed 40 of the possible 60 rebounds on the defensive end, for 66.7%. The Bobcats grabbed 22 of the possible 30 rebounds on the defensive end, for 73.3%. So though each of the major Boston newspapers claimed that a big part of the Celtics' win was out-rebounding the Bobcats, in fact the Celtics won this game despite being out-rebounded. In fact, this (along with turnovers) was one reason this game was close even though the Celtics shot 57% to the Bobcats' 40%.

## B. Individual Players' Rebounding

So now you know how to determine which team has had the better rebounding night. What about individual players? How do you know if someone did a good job rebounding in a particular game or over the course of the season? Before you say "Just look at his average rebounds per game," consider the following:

First, we have the same problem for individuals as we do for teams, above. Consider these two players: imagine Kendrick Perkins enters the game for five minutes. During those five minutes, the Celtics make 4-of-5 shots, and the Sixers make 3-of-5 shots. Perkins gets two rebounds during those five minutes. Al Jefferson also plays for five minutes, later in the game. During the second five minutes, the Celtics make 1-of-5 shots, and the Sixers make 0-of-5. Jefferson gets three rebounds during his five minutes. Who did the better job rebounding, assuming each rebound was equally difficult to grab?

Al Jefferson is one of the best young rebounding power forwards in the NBA according to his rebounding percentage numbers.

Despite the fact that the two players played the same amount of time, and that Jefferson grabbed three rebounds to Perkins's two (and assuming that all the rebounds were equally difficult to grab), many basketball-savvy people would agree that the Perkins did the better job rebounding. During the five minutes when he was in the game, there were only three rebounds available to anyone, and he got two of them - a rate of 66%. While Jefferson was in the game, there were 9 available rebounds, but he only grabbed three - a rate of 33%.

Next, there is the problem of unequal minutes. While two teams always play the same total minutes against each other, two players of course do not. If Paul Pierce plays twenty minutes and grabs four rebounds, and Ricky Davis plays forty minutes, and gets five rebounds, who did the better job rebounding? Most people agree that Pierce, who got a rebound every five minutes while he was in the game, did a better job than Davis, who only got one rebound every 8 minutes.

So then you might agree that the way to determine who had the best rebounding night would be to look at the misses of both teams while each player was in the game. This is what Celtic coaches do, using the "Percentage of Available Rebounds" (or "Reb%," for short) statistic.

This stat uses scorers' table data to determine how many total rebounds were available while a player was in the game. This is easy to calculate; you just add up all the missed shots that didn't go out of bounds or result in a foul. Then, you simply see what percentage of those shots a particular player captured, ignoring rebounds from foul shots (which are usually easy "gimmies" for the inside defender). For example, on November 30, Kendrick Perkins was in the game for 28 minutes. During this time, there were 54 missed shots that didn't go out of bounds or result in a foul. Perkins grabbed 19 rebounds, none of which were off of missed free throws. This represented 35% of available rebounds, which, along with Perkins's season average, is far above the league average for centers, as you can see from the table below.

Boston Celtics Rebounding Percentages vs. League Averages, By Position
As of December 31, 2005
Position NBA Average, Rebounding % Celtics' Leader by Position Rebouding %
Center 15.0% Kendrick Perkins 20.9%
Power Forward 13.8% Al Jefferson 16.0%
SF/SG 8.9% Paul Pierce 12.2%
Point Guard 5.9% Delonte West 7.2%

As you can see, the 2005-06 Celtics feature players at every position who significantly exceed the league average rebounding percentage; especially Perkins and Pierce, who are two of the best rebounders in the league at their respective positions. This is one reason why the current Celtics team has drastically improved at rebounding since two years ago, when we had the worst team rebounding differential in the league.

Michael Zarren is the Celtics' Basketball Operations Analyst, responsible for assisting team decision making via quantitative analyses. Check our archive for more Inside the Numbers columns.