Tim Duncan is the Defensive Player of the Year: Blocks

I feel undeniably privileged to have carefully observed Tim Duncan's 2012-2013 season to date. In a season where the San Antonio Spurs have received numerous "bites" from the injury bug, Tim Duncan has been consistent, and dominant. He is a difference maker on the both sides of the court. While Duncan has remained effective offensively by retooling his game to include less 4-down post moves and more mid-range shooting, Tony Parker's emergence as the main offensive weapon for the Spurs has limited his offensive role in recent years.

His defense is a different story. The San Antonio Spurs have a refocused defense this year, and their return to the league's defensive elite has been anchored by a fresh Tim Duncan. He is having a career year in terms of defensive statistics. Read that again: Tim Duncan is having a career year. In terms of per minute numbers, a man who has made eight NBA All-Defensive 1st teams is posting career-bests in blocks, defensive rebounding, and steals. Are your eyebrows raised? They should be. Tim Duncan is the Defensive Player of the Year. I would like to show you why over a series of posts. In this first post, I'm going to focus on blocks.

Tim's blocking this year has been beyond exceptional. Did I mention that his per minute blocking numbers are the best of his career, a career lauded for its elite defense? How has he done this? It's a combination of footwork, positioning, overall awareness and basketball savvy. Keep an eye out for a future post from J Gomez which will break down how Duncan moves on the court to maximize his defensive efficiency. At 36, Duncan has schemed his way onto the shortlist of this year's blocks leaders. Currently he has 2.7 blocks per outing, good for 3rd in the league, behind Larry Sanders and Serge Ibaka, who are 24 and 23, respectively. Tim Duncan blocks more shots per game than Roy Hibbert, Dwight Howard, Joakim Noah, and Brook Lopez.

But the value of Tim's blocking isn't only defined by volume. Duncan achieves his blocking numbers while limiting personal fouls, ensuring blocked shots do not give opponents a second chance, and protecting near the rim. When combined, these three things make Duncan the best blocker in the league. You will never see his blocks on ESPN's Top Plays, but nonetheless Tim provides the most defensive value through blocking than any other blocker in the league.

Defining Defensive Value

Defensive value is measured simply: how many points did the other guy(s) score? When we look at blocking value, we want to assess how many points a blocker prevents per block.

According to Basketball-Reference.com, NBA teams average 1.046 points per possession. The immediate train of thought is, "Well a block turns that number into 0." This is true in a confined sense, but when analyzing the value of a block, we need to ask three questions:

1) How often do missed blocks result in personal fouls?

2) How often do blocked shots go out of bounds, resulting in a new possession for the opponent?

3) How often does a player block layups versus jumpers?

With these three questions in mind, let's break it down.

Personal Fouls

Players in the NBA make on average 75.3% of their free throws. This means that when a player is fouled on an attempted block, the opposing team will earn, on average, 1.506 points for that possession. This number increases for "and-1" situations. This is why players should, obviously, avoid fouling. Free throws earn the opponent a massive increase in points per possession over the expected average.

Tim Duncan excels at avoiding personal fouls, despite generating a high volume of blocks. Check out the table below comparing Duncan's blocks-to-fouls ratio to some of the league's elite blockers.

Player	BPG	PF/G	BLK/PF Ratio
Tim Duncan	2.7	1.8	1.50
Larry Sanders	3.1	3.5	0.89
Serge Ibaka	2.9	2.8	1.04
Roy Hibbert	2.7	3.5	0.77
Dwight Howard	2.4	3.8	0.63
Joakim Noah	2.3	2.9	0.79
Brook Lopez	2.1	2.0	1.05

Tim Duncan, the best in the league in this area, is the only player on this list with a block to foul ratio significantly greater than 1. Dwight Howard's value of 0.63 is downright terrible, and even the second best Brook Lopez barely blocks more than he fouls. It is incredible that the increase in BLK/PF ratio from the worst to second best on this list (Howard to Lopez), is still less than the increase from Lopez to Duncan! Tim Duncan puts the league's other blockers to shame in terms of avoiding fouls when attempting blocks.

Blocking Out of Bounds or to Opponents

Let's face it, out-of-bounds blocks are sexy. When an athletic player loads his spring-like legs and soars to confront an incoming scorer, swatting the ball into the stands at ludicrious speed, we love it. It is precisely this brand of athleticism for which most people enjoy watching the NBA. Statistically, though, these blocks, and blocks which are recovered by the opposing team, have the same value as an opponent offensive rebound. They allow the opponent a new possession, a new chance to score, and even the chance to set up a go-to inbound play. They are much less valuable than blocks which are recovered by the blocker or his teammates.

Tim Duncan also excels at blocking the ball to himself or his teammates. Below is a table with how each players blocks are recovered, courtesy of Evan Zamir of nbawowy.com. %Own is the percentage the player himself rebounds his block, %Team is the percentage a teammate rebounds his block, and %Opp is the percentage the other team recovers the block.

Player	%Own	%Team	%Opp
Tim Duncan	29.6	34.5	35.9
Larry Sanders	19.3	36.0	44.7
Serge Ibaka	10.1	54.7	35.2
Roy Hibbert	17.8	48.5	33.7
Dwight Howard	16.7	42.7	40.6
Joakim Noah	15.0	47.4	37.6
Brook Lopez	11.6	47.1	41.3

Duncan's Opp% is 3rd lowest in this list, and his %Own is tremendous. Duncan recovers nearly a third of his blocks. When you consider how talented he is as an outlet passer, this is no insignificant feat.

Layups vs. Jumpers

Tom Haberstroh wrote a shining article about Duncan's defensive prowess earlier this year. In it he discusses the value of blocking layups versus jumpers. According to Hoopdata, NBA players make 64.4% of their shots at the rim, while converting only 39.0% on all other two point attempts. In terms of points per possession, possessions which end in layups gain more than 0.5 points over other two point shots. As a shot blocker, therefore, it is more important to block layups than jumpers. The chart below indicates the percentage of shots blocked which are layup attempts, defined as a shot less than 3 feet from the rim.

Player	%Layups
Tim Duncan	72
Larry Sanders	61
Serge Ibaka	58
Roy Hibbert	50
Dwight Howard	45
Joakim Noah	54
Brook Lopez	53

When it comes to cleaning up shop near the rim, Tim Duncan is, again, best among the league's elite blockers. Haberstroh also mentions that Tim Duncan's average blocked shot distance is 2.9 ft while the average of the top blockers is 4.8 ft. By staying close to home, Duncan chooses to engage shots which have a higher chance of falling and get set to rebound on those which don't. Brilliant.

Marginal Blocking Value

So how much value does Tim Duncan add through his blocking as compared to the rest of the league's best blockers? Lets define a statistic, Marginal Blocking Value (MBV), which will tell us on a per game basis how many points a player's block attempts add or subtract. We will define this by looking at expected point values from our different outcomes.

At its most basic form, the block has an expected point outcome of 0, however we have to consider recovery, the possibility of a personal foul, and the expected point value of a shot not blocked.

The formula I derived for MBV is as follows:

MBV = BPG*[(1.288*%LU)+(0.78*%2P)]-[0.460*0.67*PFG+0.523*%Opp]

BPG is blocks/game; 1.288 signifies the expected point value of a layup attempt (league layup FG% * 2 pts); %LU is the percentage of blocked shots that are layup attempts; 0.78 is the expected point value of a non-layup 2pt shot; %2P is the percentage of blocked shots that are layup attempts, 0.460 is the expected point value of two free throw attempts over a regular possession; 0.67 is a weighting which assumes that 2/3rds of a big's foul attempts come when contesting shots; PFG is personal fouls per game; 0.523 is the expected point value of a recovered block (equal to one half of the league average expected points per possession; 1.046, since a possession is added); and %Opp is the percent of block shots recovered by the opponent.

It's a little complicated, but it roughly indicates the added point value per game that a player's shot blocking contributes. Here are the MBV numbers for the 7 top shot-blockers in the league.

Player	BPG	%LU	%2P	PFG	%Opp	MBV
Tim Duncan	2.7	72	28	1.8	35.9	2.35
Larry Sanders	3.1	61	39	3.5	44.7	2.07
Serge Ibaka	2.9	58	42	2.8	35.2	2.07
Roy Hibbert	2.7	50	50	3.5	33.7	1.54
Dwight Howard	2.4	45	55	3.8	40.6	1.04
Joakim Noah	2.3	54	46	2.9	37.6	1.33
Brook Lopez	2.1	53	47	2.0	41.3	1.37

Tim Duncan, far and away, adds the most value to his defense, almost two and a half points per game due to his blocking. For those of you keeping track, that is the difference between 3rd and 9th in DRtg. He has proven himself to be the best blocker in the NBA in terms of value added to the defense, and his defensive presence in the post this season has significantly impacted the Spurs defensive rating.

Conclusions

Blocking is but one of several ways in which Duncan displays his sharp defensive acuity. In a year where the Spurs have rekindled the defensive fires which once fueled them, the future Hall-of-Famer has continually fanned the flame with his fundamentals and brilliant floor knowledge. Parker may now be the go-to offensive weapon for the Spurs, but Duncan is, and will always be, the backbone of the Spurs defense. Cool, calm, and masterful, Tim Duncan keeps reminding us why he is the greatest power forward of all time, and this year's Defensive Player of the Year.

#DuncanDPOY

*Keep an eye out for the next article on Tim's rebounding prowess.