# Position- and Shot-Adjusted Marginal Defense (Part I): Analysis of Interior Defense

Andrew Bynum and Dwight Howard are two of the best interior defenders.

Now that I've written a series of posts introducing and applying my new offensive scoring metric Position- and Shot-Adjusted Marginal Scoring (PSAMS), I'm going to turn my attention to the defensive side of the ball. It turns out that with a little modification PSAMS can be turned into PSAMD (where the "D" is for defense). Here, I'll give some explanation of the defensive version of this metric, and apply it to the center position.

In general, we should be quite a bit more skeptical of defensive statistics that utilize box score or play-by-play (PBP) data. That certainly applies here. In a nutshell, the main issue is that when a basket is scored, we definitely know who scored. Unfortunately, we don't know for sure by looking at the box score or PBP who was responsible for defending the play (i.e. who got scored on). Moreover, the entire team bears some responsibility for defense, not just one defender. (Of course, it should be obvious that the latter point is also true for offense to some extent.)

At any rate, we can make some simple assumptions and check whether the model makes some sense. Before getting into the model, itself, let me explain how I gathered the data. I use a programming language (Ruby) to parse and collect data from PBP files made available by Aaron Barzalai who runs the website BasketballValue.com. In addition to providing the PBP data, Aaron also provides "matchup" files, which enables one to determine for every single play who was on the court for both teams. Although the matchup data doesn't tell us who actually defended each play, it does allow us to determine who was the position-counterpart. When a player scores, we can assign "fault" to the position-counterpart, with the underlying assumption being that over the long run, the assignment of blame to the position-counterpart will capture the bulk of the individual defensive responsibility for that player. TO BE CLEAR, IT'S NOT A PERFECT MEASUREMENT. Just wanted to make sure everyone gets the disclaimer.

Just like in the PSAMS metric, I go through the PBP data programmatically looking for made and missed baskets. In addition, each shot is placed into one of the following categories: DUNK, LAYUP, TIP, HOOK, MID-RANGE, 3PT, FT. For this post, we are going to look at inside shots, which include the first four categories.

Here's how the calculation works using Dwight Howard as an example:

`PSAMD = 2*[8.1*(0.621-0.584)+(9.77-8.1)*(0.621-0.500)]=1.01`

The first term represents the marginal value that Howard's defense creates against his counterpart. The opposing centers averaged 8.1 shots (per 100 non-turnover possessions) against Howard. On those shots, they averaged 58.4% compared to the league average for centers of 62.1%. Therefore, this term is positive, because Howard kept opposing centers below the average efficiency on those shots. The second term in the formula represents the marginal value of the shots that weren't taken against Howard, and instead, became mid-range or 3-pt shots. Recall that on the offensive side, players were penalized for "undershooting". On the defensive side, we reverse things. Howard is actually credited for not allowing opposing centers to take those efficient inside shots. The difference in efficiency (62.1%-50%) is quite large. If a player allows more shots by his counterpart than the average, we penalize the player for the difference between his allowed efficiency and the 50% league average.

In addition to compiling the counterpart data, I also keep track of all the shots by the non-counterpart opponents. In the following table, I rank centers by PSAMD calculated on the counterpart data, but I also list the PSAMD calculated on the non-counterparts. The idea is that a good center not only has an effect on his counterpart but on the rest of defense as well. I'll show how we can use this metric to test that assumption.

### PSAMD Ratings for Centers

Here, PSAMD_5 is the counterpart rating. PSAMD_1_4 is the rating calculated on the other four positions. RATE_5 is the number of shots (per 100 non-turnover possessions) by the counterpart. RATE_1_4 is the rate for the other four non-counterpart positions. EFF_5 is the FG% for the counterpart, and EFF_1_4 is the FG% for the other four positions. Remember these are all calculated for inside shots only (dunks, layups, tips, and hooks).

 RANK NAME TEAM GS PSAMD_5 RATE_5 EFF_5 PSAMD_1_4 RATE_1_4 EFF_1_4 1 Andrew Bynum LAL 47 2.28 8.5 50.5% 0.87 24.2 60.7% 2 Joel Anthony MIA 11 1.45 8.8 55.2% 4.18 25.7 53.7% 3 Andrew Bogut MIL 65 1.30 8.5 56.3% 2.59 26.1 56.6% 4 Tim Duncan SAS 76 1.14 9.7 56.3% 2.35 21.8 58.5% 5 Dwight Howard ORL 78 1.01 8.1 58.4% 2.37 18.7 59.8% 6 Marc Gasol MEM 81 0.99 9.6 57.1% -2.06 24.1 66.8% 7 Zydrunas Ilgauskas MIA 51 0.97 10.7 56.5% 0.63 24.1 61.2% 8 Marcus Camby POR 51 0.68 8.9 59.5% 0.37 26.5 60.7% 9 Al Jefferson UTA 82 0.58 11.0 58.1% -0.96 23.6 64.9% 10 Samuel Dalembert SAC 46 0.49 8.4 61.2% -3.64 25.3 69.2% 11 Nene Hilario DEN 75 0.41 8.8 61.2% 0.41 23.2 62.2% 12 Ronny Turiaf NYK 21 0.39 8.5 61.6% 1.88 24.9 58.4% 13 Roy Hibbert IND 80 0.32 10.7 59.5% 1.37 23.7 59.9% 14 Spencer Hawes PHI 81 0.09 11.3 60.1% 1.37 23.0 60.2% 15 Kwame Brown CHA 50 0.02 9.1 62.8% -1.13 26.1 63.8% 16 Ryan Hollins CLE 16 -0.19 9.4 63.5% 2.51 21.7 58.1% 17 Marcin Gortat PHX 12 -0.25 8.5 65.3% -0.39 19.6 66.4% 18 Chuck Hayes HOU 63 -0.26 10.3 62.8% -2.06 24.2 66.8% 19 Joakim Noah CHI 48 -0.35 9.0 65.0% -0.09 25.4 62.1% 20 Darko Milicic MIN 69 -0.36 9.3 64.7% -0.79 24.2 64.1% 21 Tyson Chandler DAL 74 -0.45 9.4 65.0% 1.32 23.2 60.2% 22 Brook Lopez NJN 82 -0.53 11.7 62.4% 0.10 25.8 61.5% 23 Zaza Pachulia ATL 7 -0.66 9.7 65.6% -1.06 23.7 65.0% 24 Andris Biedrins GSW 55 -0.70 10.3 64.9% -2.72 24.8 67.7% 25 DeAndre Jordan LAC 66 -0.94 10.0 66.6% -0.25 23.3 63.6% 26 Emeka Okafor NOH 72 -0.98 8.4 70.0% 0.03 22.9 63.1% 27 Brendan Haywood DAL 8 -1.23 10.4 67.3% -0.06 23.4 63.0% 28 Greg Monroe DET 48 -1.25 11.3 66.0% -3.00 28.2 66.1% 29 Andrea Bargnani TOR 66 -2.03 13.3 66.5% -0.89 29.6 61.7% 30 JaVale McGee WAS 75 -2.76 11.6 72.2% -3.26 25.3 68.4%

Here's a look at the correlation between the counterpart and non-counterpart PSAMD rating.

It turns out that there is a pretty good correlation (and it's statistically significant). The R^2=0.26 means that roughly 26% of the (team) defense against positions 1-4 is explained by the (individual) defense against the center counterpart. In plain English, this means that the counterpart metric is doing a fairly good job of telling us who the best interior defenders are. There are some interesting outliers, though. For example, Joel Anthony has a very good counterpart rating, but his non-counterpart rating is much higher than would be predicted by the regression. One explanation for this is that his teammates are exceptionally good at interior defense. I imagine few of you would argue with this logic. Another interesting outlier is Samuel Dalembert. He actually had a slightly above average counterpart rating, but the non-counterpart rating when he is on the floor is the worst among all centers. If Joel Anthony plays with above average interior defenders, it is probably safe to say that Dalembert plays with well-below-average interior defenders.

If we add the counterpart rating to the non-counterpart rating, we get the total rating for interior defense:

### PSAMD Total Rating for Centers

One name that caught my eye is Ryan Hollins. Might be an interesting name to watch out for next off-season. He's in the last year of his contract (~\$3M).

 RANK NAME TEAM GS TOT RATE EFF 1 Joel Anthony MIA 11 5.62 34.52 54.0% 2 Andrew Bogut MIL 65 3.89 34.56 56.6% 3 Tim Duncan SAS 76 3.49 31.53 57.8% 4 Dwight Howard ORL 78 3.38 26.79 59.4% 5 Andrew Bynum LAL 47 3.15 32.68 58.1% 6 Ryan Hollins CLE 16 2.33 31.17 59.8% 7 Ronny Turiaf NYK 21 2.26 33.42 59.2% 8 Roy Hibbert IND 80 1.69 34.44 59.8% 9 Zydrunas Ilgauskas MIA 51 1.60 34.82 59.8% 10 Spencer Hawes PHI 81 1.46 34.27 60.1% 11 Marcus Camby POR 51 1.05 35.33 60.4% 12 Tyson Chandler DAL 74 0.87 32.56 61.6% 13 Nene Hilario DEN 75 0.81 31.98 61.9% 14 Al Jefferson UTA 82 -0.38 34.57 62.7% 15 Brook Lopez NJN 82 -0.43 37.56 61.8% 16 Joakim Noah CHI 48 -0.44 34.45 62.8% 17 Marcin Gortat PHX 12 -0.64 28.13 66.1% 18 Emeka Okafor NOH 72 -0.95 31.26 65.0% 19 Marc Gasol MEM 81 -1.07 33.76 64.0% 20 Kwame Brown CHA 50 -1.11 35.21 63.5% 21 Darko Milicic MIN 69 -1.15 33.47 64.3% 22 DeAndre Jordan LAC 66 -1.19 33.21 64.5% 23 Brendan Haywood DAL 8 -1.29 33.84 64.3% 24 Zaza Pachulia ATL 7 -1.73 33.35 65.2% 25 Chuck Hayes HOU 63 -2.32 34.45 65.6% 26 Andrea Bargnani TOR 66 -2.92 42.84 63.2% 27 Samuel Dalembert SAC 46 -3.15 33.63 67.2% 28 Andris Biedrins GSW 55 -3.42 35.15 66.8% 29 Greg Monroe DET 48 -4.25 39.45 66.1% 30 JaVale McGee WAS 75 -6.03 36.90 69.6%

## 2 thoughts on “Position- and Shot-Adjusted Marginal Defense (Part I): Analysis of Interior Defense”

1. Crow says:

Interesting data. Thanks as always for the extensive & nimble work.

If you had similar data for all positions and main rotation or all players then it would possible to compare the individual data with lineup data for biggest minutes lineups composed of 5 players and see how consistently the sum of the average individual performance data by shot distance compares with the aggregate data for the lineup. It would also be technically feasible to see what each opposing offense did in terms of shot distribution against that lineup and how well they did and whether they took more or less advantage of the defense's weaknesses.

It might also be possible to search for the optimal average weights for counterpart and non-counterpart marginal defense (probably league-wide but maybe team by team) and use that to update the 50 / 50 rating blend you've offered initially.

It would also be interesting to compare the ratings for players for all shot distances to the Adjusted Scoring RAPM Factor.

Defensive EZPM - PSAMD would be worth breaking out as well to isolate how much of a player's defensive value is coming from gaining more possessions (from turnovers and defensive rebounds) / preventing continued possessions for the offense compared to shot defense.

2. JZ says:

It's interesting that after all these years Tim Duncan can still be such a defensive force. Thanks for putting all this together.