Analysis of Interior Defense using PSAMD

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%