Who Are The NBA's Most Valuable Inside Scorers?

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
 

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