## Tuesday, August 10, 2010

### The Anatomy of a Block: By Shot Location (Part 2)

In case you missed it, check out Part 1 in this series, The Anatomy of a Block: Introduction.

In this post, I'll take a look at the value of a blocked shot based on the shot location. The conventional wisdom is that big men down low find plenty of shot-blocking opportunities in the painted area and that perhaps forwards and more athletic guards get blocks at the 3-point line and in the jump shot range. Each location on the grid of a basketball court can be assigned a point value based on the expected point value of a shot in that specific location. These assigned point values can then be totaled by the number of blocks in each location in order to come up with "points saved per block by shot location" for each player.

To do this, I looked at four seasons' worth of PbP data with over 750,000+ shots and their X,Y coordinates to indicate their locations. If you can imagine yourself standing behind the offense's basket, the X-axis runs from left to right along the baseline (the range of X values is 0 to 50, or 51 possible values) and the Y-axis runs from bottom to top toward and beyond the 3-point line (the range of Y values is 1 to 35, or 35 possible values). This forms the basis of a half court, where the center of the hoop is located at (25, 5.25).

For the 51*35 = 1785 shot location coordinates I looked at, I noted the total number of shots taken in each coordinate over the past four seasons and stored it in a matrix. Here's what the shot location frequency for the NBA in that time period looks like (excuse the color scheme and note that approximately 28% of the shots were taken at rim):

I then found the number of points scored in each coordinate over the past four seasons, and multiplied that by each element from the shot location frequency matrix. Basically, this shows me where the average NBA player was efficient with his shots, giving the expected point value for each shot location. Here's what the shot location efficiency for the NBA looks like (statistical noise shmatistical shmoise):
As you would expect, the high value shots (not necessarily high percentage) are either at rim or along the 3-point line, particular the corner 3s coming at 1.1 to 1.4 points per shot, or PPS. Jump shots just outside the key and near the baseline are low value shots, going down to 0.8 PPS. To give you a general idea of points per shot based on location, here's points per shot by distance from the basket in 2007-2010 according to Hoopdata.com:

Similar to the shot location efficiency heat map, at rim shots return the most points per shot at 1.208 PPS, with threes at 1.081 PPS and long twos at 0.801 PPS.

Taking the expected point values of each shot location coordinate multiplied by the number of blocks by a player in each coordinate, I found the total number of points saved by location and the points saved per block. Let's take a look at the top 25 shot-blockers in terms of total blocks since the 2007 season and see how they fared in points saved per block:

A quick glance at this table sorted by total blocks shows that although the top shot-blockers in block count nearly matches the number of points saved per block by location (notice how the column "Pts by loc" fades from green to yellow pretty consistently), the value of a player's blocks in terms of points saved per block varies. With the knowledge that the average is about 1.075 PPS, Andris Biedrins (0.982 PPS, or points saved per block if you prefer) and Brendan Haywood (0.987 PPS) clearly save the lowest in value per blocked shot on this top 25 list, while Andrew Bogut (1.152 PPS), Emeka Okafor (1.118 PPS), Tyrus Thomas (1.118 PPS), and Josh Smith (1.116 PPS) come out on top.

But do these shot-blockers, among the league leaders in most blocks, also lead the entire league in points saved per block? Let's take a look at the top 10 shot-blockers in value per blocked shot (minimum of 200 blocks since 2007):

Gerald Wallace comes out as the player with the most points saved per block at 1.163 PPS, despite averaging just under 1.00 block a game. Paul Millsap, Lamar Odom, and Shane Battier are other notable players that you wouldn't expect to get good value for each block, at least, according to shot location (perhaps this could be an extension to Battier's underappreciated defensive value to the Rockets). The most notable player on this list has got to be Chris Anderson. Not only has Anderson blocked 2.12 shots per game since being reinstated in 2008 from expulsion due to positive tests for abusive drugs, but he has also saved 1.130 PPS for each block. Whether this makes up for his relatively lacking presence on offense, that's for another study, but Anderson certainly may be one of the best shot-blockers in the NBA today. Bogut, Okafor, and Thomas are the only players on this list to also appear in the previous top 25 total blocks list.

What about the "overrated" shot-blockers in terms of points saved per blocked shot? Let's take a look at the bottom 10 (minimum of 200 blocks since 2007):

Andris Biedrins and Brendan Haywood appear again at the bottom with the least points saved per block, despite averaging 1.46 and 1.64 blocks per game since 2007. Dwyane Wade, Shawn Marion, and Kevin Durant are notable players who don't get as much value for each block they get, but this is likely due to their guard/forward position and the fact that they defend jump shots more often than the traditional shot-blocker. I lowered the minimum blocks to 100 and found there were other guards/forwards with low PPS saved by block as well, such as Baron Davis, Francisco Garcia, Grant Hill, and Stephen Jackson, the type of players you don't find in the high value points per block list.

Finally, here's a look at 15 notable players we haven't seen yet, sorted by blocks per game. I selected 15 of the younger and up-and-coming shot-blockers in the NBA from my spreadsheet. Let's see if we can spot any value in their shot-blocking ability by location:

So I lied, sue me. Alonzo Mourning and Dikembe Mutombo aren't exactly young and up-and-coming, currently aged 40 and 44 respectively. But for the years that this data was available for, Mourning (1.080 PPS) and Mutombo (1.124 PPS) weren't too shabby at blocking high value shots while approaching retirement when compared to the NBA average of 1.075 PPS. Hasheem Thabeet (1.119 PPS), Taj Gibson (1.115 PPS), and Serge Ibaka (1.084 PPS) are notable rookies from the past season with high value blocks based on location as well.

Looking at Greg Oden's 1.077 PPS and 1.43 BLK/G being above average, there is little doubt that his shot-blocking ability along with Camby (1.103 PPS, 2.79 BLK/G) and Przybilla (1.141 PPS, 1.29 BLK/G) will give the Portland Trail Blazers multiple defensive weapons to frustrate opposing offenses in the paint. If the Blazers ever need to go big, they could conceivably have two of three of these shot-blockers on the court at any given time along with LaMarcus Aldridge. They will take away minutes and block opportunities from one another, but no matter which way you slice it, it will be a force that could lead to many defensive stops if they spread out the defense effectively. The Camby/Przybilla/Oden combination does sound enticing, but the Blazers must allocate minutes and usage rate to their shot-blockers efficiently in order for the three-headed tandem to be effective.

That's it for part 2 of this series. If there is something you like (or didn't like), please feel free to leave a comment! In my next post, I will take a look at blocks based on shot type, with an interesting look at which players blocked the most dunks, jump shots, layups, etc.

1. I'd be curious to see how back court blocks (jumpers) compare to front court blocks (layups and dunks) in terms of points generated off the turnover. I'd imagine that despite the low points saved per block by guys like Wade and Durant, a blocked jumper probably turns into a transition basket on the other end more frequently.

2. Great thinking/writing.

I wonder how a player's mobility is factored into this. It seems that if a player (like Dwight Howard) was able to roam away from the rim and meet the offensive player in the <10ft range or even in the 10-15 range for a shot block, then their overall contribution to defense would be higher, but their Pts/BLK score would be lower. Is it not more valuable to force a lower percentage shot /and/ get the block?

Should there be a factor for keeping players from getting into a position to take a high percentage shot? Hard to find data points for this to add it to the calculation. How would you factor that in?

(yes, I'm a fan of the Magic, so Howard came to mind)

3. @JB, by intuition, there is definitely a reason to think that blocks off jumpers could turn into transition fastbreak points more frequently than do blocked layups for instance (Dwight Howard swatting the ball out of bounds and "Russells" plays as described by Bill Simmons certainly comes to mind). The study I am doing is limited to points saved, however. John Huizinga's work did take "points created" into account, and he found that there indeed is a difference in the ability of shot-blockers to turn blocks into easy buckets on the other end.

@magicfaninTN, that certainly is another interesting perspective to add into this. The prerequisite for an opportunity to be blocked in the <10ft range is to penetrate the defense (or a good bounce pass) past the 10-15ft range, if that makes sense. It is more valuable to force a lower percentage shot and get the block rather than allow the opportunity to take a higher percentage shot. Again, this study is limited to just the value of the blocks themselves, not the interaction effects of a cohesive defense and a "presence" in the front court.

The values I find here are best to be taken with a grain of salt. The point is that not all blocks are created equal, and that there are objective measures in order to ascertain which are more valuable than others based on context. However, blocks capture but a fraction of the complete defensive ability of a player and as a contributor to a 5-man unit defense.

Good thoughts, and thanks for commenting.

4. Do you take into account likelihood of fouling the shooter? How about shooting fouls per blocked shot?

5. @porkbarbecueman, I did read your comment in another post, and I haven't looked into the numbers just yet, but it would seem to me that you are on to something in considering that there are risks of shooting fouls based on all sorts of factors such as number of block attempts, type of shot, skill of defender in blocking vs. committing a shooting foul, etc. The data I've looked at only filtered out all of the recorded blocks.

The difficult part is trying to recall all of the events that, say, Dwight Howard had a block opportunity, where the results were either block, shooting foul, or missed block attempt. If that makes sense.

Another interesting issue to look at would be legal blocks vs. goaltending as well. The value of a blocked shot is strictly not just confined to shot type and shot location, as there's definitely a lot of interesting extensions to consider.

6. Albert,

I guess missed block attempt would be kinda hard to get, but shooting fouls (and, you're right, goal tends too) should be pretty easy to get. Then your population set becomes blocks + shooting fouls committed + goal tends committed + other, where "other" would seem to be every other shot attempted against Howard's team in the game. I guess you can't really tell how many of "other" were shot attempts against Howard himself, but you might could approximate it based on shot location and/or the person who attempted the shot (e.g. the opposing center).

But even if you didn't, I'd be interested to see blocked shots somehow juxtaposed with shooting fouls and goal tending charges. Maybe I'll take a look at it myself and just see if there's a "story" there. There may not even be one at all!

7. @porkbarbecueman, do you have a site out there where you share your own research? If you do, let me know, I can't seem to find it based on your OpenID.

8. Hi Albert,

I don't often post my research, but when I do, you can find it here: nrfhl.tumblr.com

If I reach any conclusions about comparing your findings with shooting foul tendencies, I'll post them there and let you know to look.