Golden State Of Mind

Got the lockout blues? I find that a soothing dose of new stats can help alleviate some of the symptoms. I've created a new stat for assigning value to inside scoring, so I wanted to share it with you guys, and see what you think. There are actually two versions of the stat, one that adjusts for position, and one that doesn't. Both could be useful or interesting depending on the context.

I happened to be looking at Hoopdata's shot location stats, and was trying to think about how to compare the efficiency of players at different positions. For example, how do we compare the inside efficiency of a point guard and a center? On average, Hoopdata says that centers shoot 66% at the rim compared to 59% for point guards. In absolute terms, then, centers are more efficient on average. However, in basketball as in other sports, measuring efficiency in "absolute" terms may not be the most valuable thing to do. To paraphrase Albert Einstein via James Carville, Everything is relative, stupid.

Here's what I came up with after a little bit of thought. I'm going to illustrate the calculation with a couple of examples. First up is Tony Parker. Tony Parker averaged 7.3 shot attempts (per 40 minutes) at the rim in 2011 according to Hoopdata. His FG% at the rim was 65.4%. The average number of shot attempts at the rim for point guards is 4.03. The average FG% at the rim for point guards is 60%. So, not only did Parker take more shot attempts than the average point guard, he shot them at a considerably better percentage. I propose that his "adjusted marginal scoring" adjusted for position and shot location (PSAMS) is as follows:

PSAMS = 2*(7.30-4.03)*(0.654-0.50)+2*4.03*(0.654-0.60) = 1.18

Let me explain this formula in steps. The first term on the right side accounts for the additional number of shots that Parker took compared to the average point guard at the rim and the marginal increase in efficiency that those shots had over the average efficiency of what those shots would have had if they were taken by an average player taking an average shot (i.e. league average efficiency). In other words, the assumption is that if Parker didn't take those 3.3 "extra" shots, an average player shooting with average efficiency would have. Of course, that isn't always or even mostly the case, but it's a common reference point that enables us to compare all players fairly. Ok, still with me? The second part of the equation represents the marginal value of the shots that Parker was "supposed" to take relative to other point guards. In the case of Parker, both terms are positive, and his total of 1.18 ranks him very high (#6) on the list of 152 players that I looked at (who qualified by playing 40+ games of 25+ minutes per game).

The second example is Steve Nash. Nash only attempted 2 shots at the rim per 40 minutes. His FG% was 72.8%, which is very high. The calculation for Nash goes as follows:

PSAMS = 2*(2-4.03)*(0.60-0.50)+2*2.0*(0.728-0.60) = 0.27

In Nash's case, the first term is actually negative, because Nash took fewer shots at the rim than the average PG, and those shots are normally more efficient than an average shot, thus costing his team a little bit (compared to average!). Now, the good news is that Nash's marginal value on the two shots he did take was positive, because his efficiency on those shots was above what an average point guard would do. In the end, Nash ranked #73 on the list. The values 4.03 and 0.60, which represent the shot attempts and FG% for PG at the rim, are replaced by their respective values at each of the other positions. In this post, I am just looking at shots at the rim (< 3ft from the basket according to Hoopdata). Here are the top 20 overall:

Top 20

Thaddeus Young comes out on top, which is not surprising, given his 7.9 attempts per 40 at 73.4% efficiency. Note that Monta Ellis comes in at #11 overall and #2 among shooting guards.

RANK	POS RANK	NAME	TEAM	POS	PSAMS
1	1	Thaddeus Young	PHI	3	2.92
2	2	LeBron James	MIA	3	1.92
3	1	Dwight Howard	ORL	5	1.74
4	1	Dwyane Wade	MIA	2	1.73
5	3	Shawn Marion	DAL	3	1.60
6	1	Tony Parker	SAS	1	1.44
7	4	Wilson Chandler	NYK	3	1.34
8	2	Nene Hilario	DEN	5	1.33
9	5	Kevin Durant	OKC	3	1.24
10	6	Tayshaun Prince	DET	3	1.15
11	2	Monta Ellis	GSW	2	1.15
12	7	Jeff Green	OKC	3	1.08
13	8	Paul Pierce	BOS	3	1.06
14	1	Blake Griffin	LAC	4	1.04
15	3	Marcin Gortat	PHO	5	0.85
16	2	Carlos Boozer	CHI	4	0.83
17	2	Russell Westbrook	OKC	1	0.82
18	3	Eric Gordon	LAC	2	0.77
19	4	Kevin Martin	HOU	2	0.76
20	5	Landry Fields	NYK	2	0.73

Here are the bottom 20 on the list:

Bottom 20  

No Warriors here. Phew.

RANK	POS RANK	NAME	TEAM	POS	PSAMS
152	34	Marcus Camby	POR	4	-1.56
151	19	Andrea Bargnani	TOR	5	-1.42
150	33	Channing Frye	PHO	4	-1.35
149	33	Daniel Gibson	CLE	1	-1.28
148	32	Ersan Ilyasova	MIL	4	-1.08
147	32	Carlos Delfino	MIL	3	-0.90
146	34	Anthony Morrow	NJN	2	-0.87
145	33	Sasha Vujacic	NJN	2	-0.85
144	32	Derek Fisher	LAL	1	-0.82
143	18	Chuck Hayes	HOU	5	-0.80
142	31	Luke Ridnour	MIN	1	-0.75
141	32	Anthony Parker	CLE	2	-0.69
140	17	Roy Hibbert	IND	5	-0.68
139	30	Brandon Jennings	MIL	1	-0.67
138	16	Kwame Brown	CHA	5	-0.65
137	29	Jason Kidd	DAL	1	-0.65
136	31	Elton Brand	PHI	4	-0.64
135	15	Brook Lopez	NJN	5	-0.63
134	30	Antawn Jamison	CLE	4	-0.60
133	31	John Salmons	MIL	2	-0.60

Here is the full list of players by position, with their overall rank and positional rank:

Point Guards 

Curry ranks 19th among PG and #90 overall.

RANK	POS RANK	NAME	TEAM	PSAMS
6	1	Tony Parker	SAS	1.44
17	2	Russell Westbrook	OKC	0.82
22	3	Ty Lawson	DEN	0.73
32	4	Derrick Rose	CHI	0.55
38	5	Andre Miller	POR	0.51
39	6	Tyreke Evans	SAC	0.51
44	7	Rajon Rondo	BOS	0.43
46	8	Beno Udrih	SAC	0.42
55	9	John Wall	WAS	0.30
56	10	Deron Williams	UTH	0.30
58	11	Darren Collison	IND	0.27
59	12	Ramon Sessions	CLE	0.27
73	13	Steve Nash	PHO	0.11
76	14	Kyle Lowry	HOU	0.08
77	15	Jrue Holiday	PHI	0.07
79	16	Mike Conley	MEM	0.06
81	17	Baron Davis	LAC	0.01
84	18	Rodney Stuckey	DET	-0.04
90	19	Stephen Curry	GSW	-0.12
93	20	Jameer Nelson	ORL	-0.16
96	21	George Hill	SAS	-0.18
99	22	Raymond Felton	NYK	-0.24
103	23	Chris Paul	NOR	-0.27
110	24	Jose Calderon	TOR	-0.32
115	25	Chauncey Billups	DEN	-0.39
119	26	Devin Harris	NJN	-0.44
121	27	D.J. Augustin	CHA	-0.46
130	28	Mike Bibby	ATL	-0.56
137	29	Jason Kidd	DAL	-0.65
139	30	Brandon Jennings	MIL	-0.67
142	31	Luke Ridnour	MIN	-0.75
144	32	Derek Fisher	LAL	-0.82
149	33	Daniel Gibson	CLE	-1.28

Shooting Guards

Monta getting some love at #2 among SG.

RANK	POS RANK	NAME	TEAM	PSAMS
4	1	Dwyane Wade	MIA	1.73
11	2	Monta Ellis	GSW	1.15
18	3	Eric Gordon	LAC	0.77
19	4	Kevin Martin	HOU	0.76
20	5	Landry Fields	NYK	0.73
24	6	Andre Iguodala	PHI	0.71
43	7	Kobe Bryant	LAL	0.43
50	8	Wesley Matthews	POR	0.37
53	9	Manu Ginobili	SAS	0.31
54	10	Joe Johnson	ATL	0.30
66	11	Vince Carter	PHO	0.22
67	12	DeMar DeRozan	TOR	0.20
72	13	Jason Richardson	ORL	0.11
74	14	Arron Afflalo	DEN	0.10
75	15	James Harden	OKC	0.09
82	16	Thabo Sefolosha	OKC	-0.00
83	17	Jason Terry	DAL	-0.02
86	18	Richard Hamilton	DET	-0.07
87	19	Ray Allen	BOS	-0.08
95	20	Brandon Roy	POR	-0.18
100	21	Kirk Hinrich	WAS	-0.24
101	22	Brandon Rush	IND	-0.25
104	23	Stephen Jackson	CHA	-0.29
106	24	Nick Young	WAS	-0.30
113	25	O.J. Mayo	MEM	-0.37
114	26	Jamal Crawford	ATL	-0.38
116	27	Raja Bell	UTH	-0.39
117	28	Jodie Meeks	PHI	-0.41
120	29	Ben Gordon	DET	-0.46
124	30	J.J. Redick	ORL	-0.49
133	31	John Salmons	MIL	-0.60
141	32	Anthony Parker	CLE	-0.69
145	33	Sasha Vujacic	NJN	-0.85
146	34	Anthony Morrow	NJN	-0.87

Small Forwards

As other Warriors starters, except for Monta, Dorell is an average inside scorer.

RANK	POS RANK	NAME	TEAM	PSAMS
1	1	Thaddeus Young	PHI	2.92
2	2	LeBron James	MIA	1.92
5	3	Shawn Marion	DAL	1.60
7	4	Wilson Chandler	NYK	1.34
9	5	Kevin Durant	OKC	1.24
10	6	Tayshaun Prince	DET	1.15
12	7	Jeff Green	OKC	1.08
13	8	Paul Pierce	BOS	1.06
23	9	Grant Hill	PHO	0.72
27	10	Nicolas Batum	POR	0.62
29	11	C.J. Miles	UTH	0.59
31	12	Luol Deng	CHI	0.59
35	13	Rudy Gay	MEM	0.54
47	14	Andrei Kirilenko	UTH	0.42
49	15	Trevor Ariza	NOR	0.38
51	16	Danilo Gallinari	NYK	0.35
57	17	Dorell Wright	GSW	0.28
63	18	Jared Dudley	PHO	0.24
68	19	Marvin Williams	ATL	0.18
69	20	Danny Granger	IND	0.18
70	21	Carmelo Anthony	DEN	0.14
78	22	Mike Dunleavy	IND	0.07
85	23	Richard Jefferson	SAS	-0.04
88	24	Gerald Wallace	CHA	-0.08
89	25	Luc Mbah a Moute	MIL	-0.11
105	26	Wesley Johnson	MIN	-0.30
107	27	Ron Artest	LAL	-0.31
108	28	Shane Battier	HOU	-0.31
123	29	Ryan Gomes	LAC	-0.48
128	30	Travis Outlaw	NJN	-0.52
129	31	Hedo Turkoglu	ORL	-0.53
147	32	Carlos Delfino	MIL	-0.90

Power Forwards

David Lee is also average among PFs.

RANK	POS RANK	NAME	TEAM	PSAMS
14	1	Blake Griffin	LAC	1.04
16	2	Carlos Boozer	CHI	0.83
25	3	Lamar Odom	LAL	0.65
28	4	Kenyon Martin	DEN	0.61
30	5	Greg Monroe	DET	0.59
33	6	Andray Blatche	WAS	0.55
36	7	Amir Johnson	TOR	0.53
37	8	Carl Landry	SAC	0.53
40	9	LaMarcus Aldridge	POR	0.51
41	10	Serge Ibaka	OKC	0.48
42	11	Paul Millsap	UTH	0.48
48	12	Kevin Garnett	BOS	0.40
52	13	Zach Randolph	MEM	0.34
60	14	Kris Humphries	NJN	0.26
61	15	Josh Smith	ATL	0.24
64	16	David Lee	GSW	0.23
65	17	Pau Gasol	LAL	0.22
71	18	Amare Stoudemire	NYK	0.13
80	19	J.J. Hickson	CLE	0.04
94	20	Chris Bosh	MIA	-0.18
97	21	Luis Scola	HOU	-0.21
98	22	Michael Beasley	MIN	-0.23
102	23	DeMarcus Cousins	SAC	-0.25
109	24	David West	NOR	-0.32
112	25	Brandon Bass	ORL	-0.34
126	26	Dirk Nowitzki	DAL	-0.50
127	27	Kevin Love	MIN	-0.52
131	28	Glen Davis	BOS	-0.59
132	29	Boris Diaw	CHA	-0.59
134	30	Antawn Jamison	CLE	-0.60
136	31	Elton Brand	PHI	-0.64
148	32	Ersan Ilyasova	MIL	-1.08
150	33	Channing Frye	PHO	-1.35
152	34	Marcus Camby	POR	-1.56

Centers

Udoh didn't have enough minutes to qualify, but his PSAMS was -1.90, which  would have placed him dead last.

RANK	POS RANK	NAME	TEAM	PSAMS
3	1	Dwight Howard	ORL	1.74
8	2	Nene Hilario	DEN	1.33
15	3	Marcin Gortat	PHO	0.85
21	4	Andrew Bynum	LAL	0.73
26	5	Tyson Chandler	DAL	0.62
34	6	DeAndre Jordan	LAC	0.54
45	7	JaVale McGee	WAS	0.42
62	8	Emeka Okafor	NOR	0.24
91	9	Al Jefferson	UTH	-0.12
92	10	Tim Duncan	SAS	-0.15
111	11	Al Horford	ATL	-0.33
118	12	Marc Gasol	MEM	-0.42
122	13	Andrew Bogut	MIL	-0.46
125	14	Joakim Noah	CHI	-0.50
135	15	Brook Lopez	NJN	-0.63
138	16	Kwame Brown	CHA	-0.65
140	17	Roy Hibbert	IND	-0.68
143	18	Chuck Hayes	HOU	-0.80
151	19	Andrea Bargnani	TOR	-1.42

You might disagree with the notion of adjusting for position. For those who do, I've calculated SAMS, which simply uses the league average shot attempts per 40 (3.4) and FG% at the rim (65%), thus, ignoring any position dependency. 

SAMS

As you can see, Dwight Howard is now on top, but Thaddeus Young is (perhaps, surprisingly) still #2 and very close behind. Note that Monta Ellis still ranks ahead of David Lee even though position is not taken into account.

RANK	NAME	TEAM	POS	SAMS
1	Dwight Howard	ORL	5	2.74
2	Thaddeus Young	PHI	3	2.68
3	Nene Hilario	DEN	5	2.33
4	Marcin Gortat	PHO	5	1.85
5	Andrew Bynum	LAL	5	1.73
6	Blake Griffin	LAC	4	1.71
7	LeBron James	MIA	3	1.68
8	Tyson Chandler	DAL	5	1.62
9	DeAndre Jordan	LAC	5	1.54
10	Dwyane Wade	MIA	2	1.54
11	Carlos Boozer	CHI	4	1.50
12	JaVale McGee	WAS	5	1.42
13	Shawn Marion	DAL	3	1.35
14	Lamar Odom	LAL	4	1.32
15	Kenyon Martin	DEN	4	1.28
16	Greg Monroe	DET	4	1.26
17	Emeka Okafor	NOR	5	1.24
18	Tony Parker	SAS	1	1.23
19	Andray Blatche	WAS	4	1.22
20	Amir Johnson	TOR	4	1.20
21	Carl Landry	SAC	4	1.20
22	LaMarcus Aldridge	POR	4	1.17
23	Serge Ibaka	OKC	4	1.15
24	Paul Millsap	UTH	4	1.15
25	Wilson Chandler	NYK	3	1.09
26	Kevin Garnett	BOS	4	1.07
27	Zach Randolph	MEM	4	1.01
28	Kevin Durant	OKC	3	0.99
29	Monta Ellis	GSW	2	0.96
30	Kris Humphries	NJN	4	0.93
31	Josh Smith	ATL	4	0.91
32	Tayshaun Prince	DET	3	0.91
33	David Lee	GSW	4	0.90
34	Pau Gasol	LAL	4	0.89
35	Al Jefferson	UTH	5	0.88
36	Tim Duncan	SAS	5	0.85
37	Jeff Green	OKC	3	0.83
38	Paul Pierce	BOS	3	0.82
39	Amare Stoudemire	NYK	4	0.80
40	J.J. Hickson	CLE	4	0.70
41	Al Horford	ATL	5	0.67
42	Russell Westbrook	OKC	1	0.60
43	Marc Gasol	MEM	5	0.58
44	Eric Gordon	LAC	2	0.58
45	Kevin Martin	HOU	2	0.57
46	Andrew Bogut	MIL	5	0.54
47	Landry Fields	NYK	2	0.54
48	Andre Iguodala	PHI	2	0.52
49	Ty Lawson	DEN	1	0.51
50	Joakim Noah	CHI	5	0.50
51	Chris Bosh	MIA	4	0.49
52	Grant Hill	PHO	3	0.47
53	Luis Scola	HOU	4	0.45
54	Michael Beasley	MIN	4	0.44
55	DeMarcus Cousins	SAC	4	0.42
56	Nicolas Batum	POR	3	0.38
57	Brook Lopez	NJN	5	0.37
58	Kwame Brown	CHA	5	0.35
59	C.J. Miles	UTH	3	0.35
60	David West	NOR	4	0.35
61	Luol Deng	CHI	3	0.34
62	Derrick Rose	CHI	1	0.34
63	Brandon Bass	ORL	4	0.33
64	Roy Hibbert	IND	5	0.32
65	Andre Miller	POR	1	0.30
66	Tyreke Evans	SAC	1	0.29
67	Rudy Gay	MEM	3	0.29
68	Kobe Bryant	LAL	2	0.23
69	Rajon Rondo	BOS	1	0.21
70	Beno Udrih	SAC	1	0.21
71	Chuck Hayes	HOU	5	0.20
72	Wesley Matthews	POR	2	0.18
73	Andrei Kirilenko	UTH	3	0.17
74	Dirk Nowitzki	DAL	4	0.17
75	Kevin Love	MIN	4	0.15
76	Trevor Ariza	NOR	3	0.13
77	Manu Ginobili	SAS	2	0.12
78	Joe Johnson	ATL	2	0.11
79	Danilo Gallinari	NYK	3	0.11
80	John Wall	WAS	1	0.09
81	Deron Williams	UTH	1	0.09
82	Glen Davis	BOS	4	0.08
83	Boris Diaw	CHA	4	0.07
84	Antawn Jamison	CLE	4	0.07
85	Darren Collison	IND	1	0.05
86	Ramon Sessions	CLE	1	0.05
87	Dorell Wright	GSW	3	0.04
88	Elton Brand	PHI	4	0.03
89	Vince Carter	PHO	2	0.03
90	DeMar DeRozan	TOR	2	0.01
91	Jared Dudley	PHO	3	-0.01
92	Marvin Williams	ATL	3	-0.06
93	Danny Granger	IND	3	-0.07
94	Jason Richardson	ORL	2	-0.08
95	Arron Afflalo	DEN	2	-0.10
96	James Harden	OKC	2	-0.10
97	Carmelo Anthony	DEN	3	-0.10
98	Steve Nash	PHO	1	-0.11
99	Kyle Lowry	HOU	1	-0.14
100	Jrue Holiday	PHI	1	-0.14
101	Mike Conley	MEM	1	-0.15
102	Mike Dunleavy	IND	3	-0.18
103	Thabo Sefolosha	OKC	2	-0.19
104	Baron Davis	LAC	1	-0.20
105	Jason Terry	DAL	2	-0.21
106	Rodney Stuckey	DET	1	-0.25
107	Richard Hamilton	DET	2	-0.26
108	Ray Allen	BOS	2	-0.27
109	Richard Jefferson	SAS	3	-0.28
110	Gerald Wallace	CHA	3	-0.33
111	Stephen Curry	GSW	1	-0.34
112	Luc Mbah a Moute	MIL	3	-0.36
113	Brandon Roy	POR	2	-0.37
114	Jameer Nelson	ORL	1	-0.38
115	George Hill	SAS	1	-0.40
116	Ersan Ilyasova	MIL	4	-0.42
117	Andrea Bargnani	TOR	5	-0.42
118	Kirk Hinrich	WAS	2	-0.43
119	Brandon Rush	IND	2	-0.44
120	Raymond Felton	NYK	1	-0.45
121	Stephen Jackson	CHA	2	-0.48
122	Chris Paul	NOR	1	-0.49
123	Nick Young	WAS	2	-0.50
124	Jose Calderon	TOR	1	-0.54
125	Wesley Johnson	MIN	3	-0.54
126	Ron Artest	LAL	3	-0.55
127	Shane Battier	HOU	3	-0.56
128	O.J. Mayo	MEM	2	-0.57
129	Jamal Crawford	ATL	2	-0.57
130	Raja Bell	UTH	2	-0.58
131	Chauncey Billups	DEN	1	-0.60
132	Jodie Meeks	PHI	2	-0.60
133	Ben Gordon	DET	2	-0.65
134	Devin Harris	NJN	1	-0.65
135	D.J. Augustin	CHA	1	-0.67
136	J.J. Redick	ORL	2	-0.68
137	Channing Frye	PHO	4	-0.68
138	Ryan Gomes	LAC	3	-0.72
139	Travis Outlaw	NJN	3	-0.76
140	Mike Bibby	ATL	1	-0.77
141	Hedo Turkoglu	ORL	3	-0.77
142	John Salmons	MIL	2	-0.79
143	Jason Kidd	DAL	1	-0.86
144	Anthony Parker	CLE	2	-0.89
145	Brandon Jennings	MIL	1	-0.89
146	Marcus Camby	POR	4	-0.89
147	Luke Ridnour	MIN	1	-0.96
148	Derek Fisher	LAL	1	-1.04
149	Sasha Vujacic	NJN	2	-1.05
150	Anthony Morrow	NJN	2	-1.06
151	Carlos Delfino	MIL	3	-1.15
152	Daniel Gibson	CLE	1	-1.50