Tim Duncan is the Defensive Player of the Year: Rebounds

With little more than an eighth of the NBA regular season remaining, the Spurs still maintain a firm hold on the top spot in the Western Conference. While the Heat's soon-to-end-on-March-31st winning streak has captured the collective attention of sports media, the Spurs have continued to play at an elite level, thanks in part to their team defensive rating of 101.1, an improvement of 2.1 over last season and good for 3rd in the league. Tim Duncan's play this year has been the catalyst for this defensive improvement, and his absolutely stellar performance has earned him serious consideration for the Defensive Player of the Year award.

In the second of a series of statistical analysis posts on Duncan's defensive dominance, I'm going to take a look at rebounding. In case you missed it, my first post looked at Duncan's contributions as a shot-blocker, breaking down why the Spurs' franchise player brings to his team the most defensive value of all the league's best blockers. Also, don't miss J Gomez's thorough take on Duncan's positioning and basketball IQ while defending the pick and roll, as it precisely describes the excellence of Duncan's defense in a way that numbers can't. No statistical analysis of defensive big men would be complete without considering rebounding and the defensive value it brings, however, so let's take some time to look at Tim Duncan's rebounding numbers.

I mentioned in my previous post that Duncan is having a career year. This is true not only in terms of blocks, but also in terms of defensive rebounding. Duncan, 36, holds a DRB% of 29.7, 3rd best in the NBA. The future Hall-of-Famer just passed Shaquille O'Neal for 13th on the NBA all time rebounds list, a list whose top 25 contains 4 other DPOY winners. Clearly, Tim Duncan is an elite rebounder, and his career-best performance this year is just one more reason why he is the Defensive Player of the Year.

Defining Rebounding Value

There may be no other area of statistical analysis in basketball more controversial than defining the value of rebounding. Many NBA statistical analysts have attempted to break it down, and the resulting conclusions have varied just about as wildly as Dennis Rodman's hairstyle. Attempts to assign point value to offensive and defensive rebounding are especially difficult due to the numerous confounding factors which can inflate or deflate rebounding numbers. For instance, a team may collect a higher number of defensive rebounds because they force opponents to shoot a lower field goal percentage. Or consider teams who employ the high-screen pick and roll/pop as a primary offensive set. This offensive philosophy draws the big man away from the rim in order to set screens, potentially limiting his ability to collect offensive boards.

In his book, Basketball on Paper, Dean Oliver illustrates that when no confounding variables are considered, defensive rebounds are the 3rd highest predictor of winning, behind only FG% and FGM (Field Goal Percentage and Field Goals Made, respectively), while offensive rebounds are the 15th highest predictor. For contests in which teams shoot roughly the same field goal percentage, however, defensive rebounds become the 2nd lowest predictor of winning, while offensive rebounds move up to 7th highest. Even still, when removing assist-to-turnover ratio as a confounding variable, offensive and defensive rebounding share almost equal value as predictors of winning. This analysis alone should demonstrate how much rebounding value depends on context, and why it is so difficult to assign a numerical value to rebounding statistics.

Since this post is primarily focused on the defensive value of rebounding, we can refine our analysis to try to answer a few questions:

1) How does the player's presence affect his team's rebounding rates?

2) How many opponent possessions does a player prevent due to defensive rebounding?

3) How does the player's rebounding affect the opponent's rebounding rates?

On/Off Rebounding Splits

In order to answer the first question, we will look at the on court/off court statistics for the big men who have a decent shot at earning DPOY: Tim Duncan, Joakim Noah, Marc Gasol, and Larry Sanders. I'll throw in Dwight Howard as well, mainly for reference, because though he does not stand much of a chance of earning the award considering the Lakers' poor defensive rating, he is an exceptional rebounder and a 3-time DPOY winner. Below is a chart with rebounding statistics for each player's team when he is on or off the court.

Player	ORB% On	ORB% Off	Diff	DRB% On	DRB% Off	Diff
Tim Duncan	21.6	19.1	+2.5	76.4	72.6	+3.8
Joakim Noah	30.1	30.4	-0.3	72.9	72.4	+0.5
Marc Gasol	32.0	31.1	+0.9	74.7	72.7	+2.0
Larry Sanders	27.4	28.4	-1.0	72.0	70.3	+1.7
Dwight Howard	26.3	27.9	-1.6	75.2	72.4	+2.8

Earlier this month I wrote a piece about the Spurs' rebounding trends. In it, I demonstrated how they have almost perfectly mirrored the rebounding numbers of Tim Duncan. If Duncan is rebounding at a high clip, so are the Spurs. If Duncan is out, the Spurs suffer on the boards. The numbers above confirm the impact of Duncan's rebounding. Among the candidates for DPOY, Duncan far and away brings the biggest rebounding boost to his team.

"Wait a second," you may say, "suppose this is due to the presence of other good rebounders who play with Duncan." Well, no other Spur even sniffs Tim's differential in terms of contribution to TRB% (Total Rebounding Percentage). Duncan has an on/off TRB% differential of +4.0%. The second best contributor on the boards, Kawhi Leonard, has a +1.9%. Tiago Splitter, who shares a fair amount of floor time with Duncan, has a +0.9%.

Possessions prevented due to defensive rebounding

The On/Off differential can also be used to provide an estimate of the number of possessions saved by a player due to defensive rebounding. To develop this idea, I'm going to borrow a train of thought from Andrew Lynch of Hardwood Paroxysm. According to this article, Lynch suggests that the number of rebounding opportunities per 100 possessions is:

DReb Opp/100 = (Missed FG%*FGA/100) + 0.44 * (Missed FT%*FTA/100)

For the Spurs, whose opponents Missed FG% is 55.9%, FGA/100 is 88.2, Missed FT% is 23.8%, and FTA/100 is 20.1, there are 51.5 defensive rebound opportunities per 100 possessions. Since the Spurs grab 3.8% more of the available rebounds with Duncan on the court, he provides a boost of about 2 defensive rebounds per 100 possessions, meaning he essentially saves 1.85 possessions per game when adjusted for league pace. Here are the same numbers for all the players:

Player	DReb Opp/100	%Boost	Boost/100	Adj Boost/Game
Tim Duncan	51.5	3.8	1.96	1.85
Joakim Noah	51.8	0.5	0.26	0.24
Marc Gasol	49.6	2.0	0.99	0.94
Larry Sanders	50.1	1.7	0.85	0.80
Dwight Howard	51.8	2.8	1.45	1.37

This is admittedly a rough estimate of possessions saved. It doesn't take into account that offensive rebounds reduce the possessions available to the opponent. (Either way, Tim Duncan provides the biggest boost to his team among the candidates in terms of offensive rebounding). But what you can see is that, relative to the other candidates, Duncan does the most on his team to prevent opponent possessions through defensive rebounding.

This is not an absolute measure of defensive rebounding value. It measures how a player's presence on the defensive glass affects his team's ability to reduce opponent possessions. Different teams take different approaches to rebounding, and different systems place more or less value on offensive or defensive rebounding. This measure is admittedly biased towards teams who value defensive rebounding, and the Spurs are a very good defensive rebounding team who place little weight on offensive rebounds. Certainly, offensive rebounding provides defensive value within the appropriate system, but the Spurs, like the Heat and Thunder, appear to avoid offensive rebounding by design.

Opponent Rebounding Rates

On/off statistics provide a good description of which player is most important to his own team, but they don't really tell us anything about how a player's absolute rebounding prowess. Likewise, defensive rebounding boosts don't give a complete picture of absolute ability because they fail to demonstrate a player's rebounding effect relative to opposing teams and players. What we need is some way to measure how a player effectively earns possessions for his team, and prevents possessions for the other team, through total rebounding.

Consider this: A missed field goal leads to three different rebounding scenarios for a defensive player. Either he rebounds it, his teammates rebound it, or the opponents get an offensive rebound. If a player can grab a higher percentage of available rebounds, or direct them to teammates, he effectively prevents the opponent from gaining possessions. Since the entire purpose of rebounding is to prevent the other team from gaining possession, perhaps the best way to objectively assess true rebounding value is to consider how well a player prevents other players from rebounding. To do this, we will look at the matchups of each candidate with the top 10 rebounders in the league (excluding themselves or teammates), and see which player does the best job of limiting other great rebounders.

The top 10 rebounders in the league in terms of TRB% are Reggie Evans, Omer Asik, JJ Hickson, Nikola Vucevic, Zach Randolph, Dwight Howard, Tyson Chandler, Tim Duncan, Larry Sanders and Emeka Okafor.

In order the analyze these matchups, I calculated the differential between the season average and the weighted matchup average of each top rebounder's TRB/36. The weighting was based on minutes played in each matchup, so that the numbers were not skewed by results from matchups where a player had limited minutes. For instance, Tim Duncan has played 91 minutes against Zach Randolph and only 15 against Nikola Vucevic (about 6 times more minutes). Therefore his effect on Randolph will be considered about 6 times as heavily as his effect on Vucevic. The formula I used is:

AVG Net Change = OATR36 - [SUM(MUTR36*MMP)/TMPMU]

OATR36 is the specific opponent season average TRB/36 minutes, MUTR36 is the specific opponent matchup average TRB/36, MMP is specific matchup minutes played, and TMPMU is total minutes played for all matchups.

The results indicate the average net change each player had on the TRB/36 of the top 10 rebounders. In the event that a player or teammate was in the top 10, the list was expanded to include the #11 rebounder (DeMarcus Cousins), so that each player had 10 matchups. The final results are below:

Player	AVG Opp TRB/36	Weighted AVG Opp MU TRB/36	Total MP	AVG Net Change/36
Tim Duncan	12.76	11.43	460	-1.32
Joakim Noah	12.79	13.60	508	+0.81
Marc Gasol	12.75	12.02	524	-0.73
Larry Sanders*	12.75	14.59	296	+1.84
Dwight Howard	12.68	11.39	367	-1.29

*Sanders and Cousins have not had any matchups this season due to injury, so Kenneth Faried (#12 TRB) was included in Sanders' matchups.

Tim Duncan is, once again, the best. He is tops on this list at limiting his opponents from grabbing rebounds, stealing 1.32 rebounds from his opponents per 36 minutes. Gasol and Howard are the only other players who effect a negative change in opponent rebounding numbers. Sanders' and Noah's presence actually lead to an increase in opponent rebounding. Considering that Duncan leads the candidates in terms of On/Off differential, we can also postulate that his limiting effect is mostly due to his own rebounding. While these results are not immune to bias due to lineup circumstances and relatively small sample size, they give a pretty good view as to how the DPOY candidates fare at preventing the league's top rebounders from securing possessions.

Conclusions

Rebounding is a tricky subject. Depending on who you ask, it can carry considerable, or very little, defensive value. What can be assuredly said for both offensive and defensive rebounds, however, is that they prevent opponent possessions. The only way the ball can change possession is through a turnover or a rebound. In a hypothetical game where opponents have equal effective field goal percentage and turnovers, the only way to win is to have more possessions. Snagging rebounds, and preventing opponents from doing the same, is the best way to accomplish this. In this analysis I have demonstrated that Tim Duncan is elite in this area.

Though rebounds may take a back seat on the Defense Bus to things like blocks, steals, and situational defensive prowess, (Pick and roll, low-block iso, etc.), it still plays a part in earning the victory. Pat Riley once said, "No rebounds, no rings." Little things which make you just better than your opponent earn championships down the stretch, and Tim Duncan realizes this. Always the perfectionist, Timmy is without a doubt intent on squeezing every last drop of defensive efficiency out of his 36-year-old body to earn championships for himself and his teammates. His rebounding is as good a testament to that as any.

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