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Position- and Shot-Adjusted Marginal Scoring (Part IV): Free Throw Shooting

So far in this series I've looked at inside, mid-range, and 3-pt scoring. In this post,  I will define the rating for foul shooting. The final post of the series will look at the total scoring rating, which is simply the sum of all four parts.

The logic for developing the foul shooting rating is essentially the same as for all the previous ratings. We compare the player's free throw rate (FTA per 100 possessions) and free throw efficiency to the league averages at his position.

As always, we demonstrate the rating calculation with a specific player. In this case, we'll use Kevin Martin who basically makes his living at the charity stripe:

PSAMS_{ft}=4.41*(0.891-0.801)+(12.2-4.41)*(0.891-1.08*0.44)+(0.856-0.333)=4.14

Kevin Martin averages 12.2 FTA per 100 possessions at 89.1%. The league averages for SG are 4.41 and 80.1%, respectively. The first term in the rating, therefore, represents Martin's marginal value for the FTA he is expected to take. The second term represents the marginal value attributed to his additional FTA above the average. The term 1.08*0.44 represents the value that those FTA would bring if they were average possessions. Here, 1.08 is the approximate point value of a possession and 0.44 is the conversion factor to determine how many possessions would have been used by a certain number of FTA. Finally, the third term represents the marginal value of the Martin's AND1 free throw rate (per 100 possessions). Clearly, Martin generates a tremendous amount of value from his free throws. In fact, as you will see in the next post, his free throw rating alone is enough to propel him into the overall top 5. Of course, if we knew more specifically where on the court Martin draws fouls, the value could be distributed into the other three ratings. But we don't have those data, so for now, we have to resort to this separate rating for free throws.

Here's the entire list of players with above average possessions and games started (overall rank (ORK) and position rank (PRK)):

ORK PRK NAME TEAM POS PSAMS-FT FTR FT% AND1_RATE
1 1 Kevin Martin HOU SG 4.14 12.2 89.1% 0.856
2 1 Kevin Durant OKC SF 3.22 10.8 88.0% 0.618
3 2 Carmelo Anthony DEN SF 2.81 11.0 81.3% 0.880
4 2 Kobe Bryant LAL SG 2.61 10.3 82.0% 0.831
5 1 Dirk Nowitzki DAL PF 2.51 8.6 90.0% 0.626
6 1 Russell Westbrook OKC PG 2.49 10.9 83.4% 0.683
7 3 Dwyane Wade MIA SG 2.22 11.0 73.4% 1.138
8 2 Rodney Stuckey DET PG 2.18 8.5 85.6% 1.028
9 3 Chauncey Billups DEN PG 2.16 8.4 93.0% 0.431
10 2 Kevin Love MIN PF 2.13 8.9 84.4% 0.610
11 1 Brook Lopez NJN C 2.10 8.1 76.3% 1.034
12 4 Derrick Rose CHI PG 2.09 9.1 85.2% 0.766
13 3 Danilo Gallinari NYK SF 2.07 8.4 89.4% 0.308
14 4 Manu Ginobili SAS SG 2.07 7.9 87.7% 0.656
15 4 LeBron James MIA SF 2.06 10.4 74.9% 0.981
16 3 Amare Stoudemire NYK PF 2.06 9.5 77.3% 0.997
17 5 Paul Pierce BOS SF 1.94 7.8 85.0% 0.786
18 5 Deron Williams UTA PG 1.92 8.6 85.5% 0.742
19 6 Ramon Sessions CLE PG 1.79 9.7 82.3% 0.506
20 7 Devin Harris NJN PG 1.77 9.0 83.6% 0.625
21 2 Andrea Bargnani TOR C 1.77 6.8 79.8% 0.830
22 6 Danny Granger IND SF 1.74 8.1 85.3% 0.459
23 5 Eric Gordon LAC SG 1.72 7.8 82.3% 0.788
24 4 Chris Bosh MIA PF 1.59 8.2 80.0% 0.662
25 3 Nene Hilario DEN C 1.36 7.9 67.2% 1.068
26 5 Pau Gasol LAL PF 1.24 6.8 80.7% 0.741
27 4 Dwight Howard ORL C 1.16 15.6 57.4% 0.878
28 6 Tyler Hansbrough IND PF 1.10 7.8 76.6% 0.596
29 8 Chris Paul NOH PG 1.10 6.7 87.7% 0.470
30 6 DeMar DeRozan TOR SG 1.02 6.6 79.4% 0.674
31 7 David West NOH PF 0.98 6.7 79.3% 0.624
32 8 LaMarcus Aldridge POR PF 0.96 6.9 77.0% 0.668
33 5 DeMarcus Cousins SAC C 0.94 8.2 66.0% 0.684
34 6 Tyson Chandler DAL C 0.92 7.0 71.2% 0.534
35 9 Blake Griffin LAC PF 0.90 10.5 62.3% 1.106
36 10 Zach Randolph MEM PF 0.84 7.0 73.7% 0.764
37 7 Wes Matthews POR SG 0.78 5.8 85.5% 0.335
38 8 Stephen Jackson CHA SG 0.77 6.4 81.3% 0.379
39 9 Richard Hamilton DET SG 0.71 6.0 84.9% 0.218
40 7 Roy Hibbert IND C 0.70 5.6 71.8% 0.609
41 8 Marc Gasol MEM C 0.70 5.4 71.9% 0.639
42 9 D.J. Augustin CHA PG 0.69 5.3 91.2% 0.467
43 9 Joakim Noah CHI C 0.64 5.9 71.8% 0.472
44 10 Monta Ellis GSW SG 0.63 6.4 78.4% 0.441
45 10 Al Jefferson UTA C 0.62 4.5 71.8% 0.802
46 7 Andrei Kirilenko UTA SF 0.62 6.7 76.0% 0.484
47 11 Randy Foye LAC SG 0.57 4.8 91.5% 0.235
48 8 Gerald Wallace CHA SF 0.57 7.7 72.6% 0.402
49 11 Brandon Bass ORL PF 0.57 6.0 80.0% 0.388
50 12 Paul Millsap UTA PF 0.55 6.0 72.5% 0.798
51 13 Andray Blatche WAS PF 0.55 6.2 75.7% 0.571
52 12 Brandon Roy POR SG 0.54 5.5 84.0% 0.295
53 13 Nick Young WAS SG 0.52 5.3 83.3% 0.383
54 10 Andre Miller POR PG 0.52 5.8 87.5% 0.272
55 11 John Wall WAS PG 0.44 7.4 75.3% 0.467
56 9 Rudy Gay MEM SF 0.43 5.5 79.8% 0.441
57 14 Tyreke Evans SAC SG 0.42 6.0 74.9% 0.564
58 12 Steve Nash PHX PG 0.39 4.8 92.8% 0.289
59 14 Kevin Garnett BOS PF 0.39 4.9 85.4% 0.287
60 10 Grant Hill PHX SF 0.36 5.0 81.4% 0.426
61 11 Tim Duncan SAS C 0.34 5.9 70.3% 0.263
62 11 Marvin Williams ATL SF 0.34 4.7 85.3% 0.320
63 13 Stephen Curry GSW PG 0.33 4.1 95.1% 0.445
64 14 Brandon Jennings MIL PG 0.29 5.8 84.3% 0.246
65 12 Michael Beasley MIN SF 0.29 5.4 72.4% 0.718
66 15 Jeff Green OKC PF 0.29 4.7 79.8% 0.521
67 15 Jodie Meeks PHI SG 0.27 4.1 92.0% 0.204
68 16 Joe Johnson ATL SG 0.24 4.8 81.9% 0.361
69 15 Darren Collison IND PG 0.24 4.4 88.8% 0.512
70 17 Tony Allen MEM SG 0.21 6.0 73.5% 0.423
71 18 Ray Allen BOS SG 0.17 3.8 91.7% 0.277
72 12 Andrew Bynum LAL C 0.15 6.9 63.2% 0.328
73 16 J.J. Hickson CLE PF 0.14 7.9 65.2% 0.503
74 13 Al Horford ATL C 0.14 3.4 78.0% 0.380
75 17 Carlos Boozer CHI PF 0.13 6.2 67.6% 0.650
76 18 Antawn Jamison CLE PF 0.13 6.0 71.2% 0.472
77 19 David Lee GSW PF 0.13 4.5 75.8% 0.596
78 20 Josh Smith ATL PF 0.10 6.0 71.2% 0.429
79 13 John Salmons MIL SF 0.09 4.8 80.5% 0.295
80 19 Kirk Hinrich WAS SG 0.07 3.3 90.3% 0.427
81 21 Amir Johnson TOR PF 0.06 3.8 78.3% 0.644
82 20 Gerald Henderson CHA SG 0.03 5.0 77.3% 0.295
83 14 Luol Deng CHI SF -0.00 5.2 74.4% 0.371
84 16 Tony Parker SAS PG -0.00 5.7 74.6% 0.554
85 22 Elton Brand PHI PF -0.01 4.8 76.4% 0.359
86 21 Ben Gordon DET SG -0.01 3.8 87.3% 0.252
87 23 Luis Scola HOU PF -0.03 5.8 72.6% 0.273
88 24 Ersan Ilyasova MIL PF -0.08 3.5 89.8% 0.212
89 14 Kwame Brown CHA C -0.10 6.7 54.3% 0.706
90 15 Samuel Dalembert SAC C -0.14 3.6 70.1% 0.320
91 17 Raymond Felton NYK PG -0.14 4.1 88.8% 0.245
92 18 Beno Udrih SAC PG -0.15 3.8 87.4% 0.409
93 15 Andre Iguodala PHI SF -0.23 6.2 67.9% 0.280
94 22 Anthony Morrow NJN SG -0.26 2.9 92.9% 0.205
95 23 Arron Afflalo DEN SG -0.28 3.3 84.8% 0.263
96 16 Greg Monroe DET C -0.29 5.3 59.5% 0.343
97 19 Ty Lawson DEN PG -0.31 4.8 73.9% 0.520
98 16 Nicolas Batum POR SF -0.34 3.2 82.7% 0.302
99 25 Serge Ibaka OKC PF -0.41 4.2 74.0% 0.241
100 17 Emeka Okafor NOH C -0.44 5.6 52.3% 0.550
101 26 Luc Mbah a Moute MIL PF -0.46 4.6 69.5% 0.287
102 27 Lamar Odom LAL PF -0.46 4.4 62.6% 0.635
103 18 JaVale McGee WAS C -0.47 5.1 55.3% 0.394
104 17 Richard Jefferson SAS SF -0.49 3.9 74.5% 0.234
105 18 Dorell Wright GSW SF -0.50 3.4 78.6% 0.208
106 19 Mike Dunleavy IND SF -0.50 3.6 79.2% 0.149
107 19 Chuck Hayes HOU C -0.51 3.3 64.2% 0.200
108 20 Sam Young MEM SF -0.51 3.4 73.8% 0.367
109 24 Marco Belinelli NOH SG -0.51 3.2 80.5% 0.192
110 20 Kyle Lowry HOU PG -0.51 4.7 75.1% 0.279
111 21 Jrue Holiday PHI PG -0.51 3.3 80.6% 0.492
112 21 Wilson Chandler NYK SF -0.52 3.0 79.6% 0.292
113 22 Shawn Marion DAL SF -0.52 3.6 76.1% 0.211
114 28 Josh McRoberts IND PF -0.53 3.4 73.1% 0.348
115 23 Travis Outlaw NJN SF -0.54 3.6 75.2% 0.231
116 20 Zydrunas Ilgauskas MIA C -0.54 2.0 76.7% 0.139
117 22 Baron Davis LAC PG -0.56 3.8 76.6% 0.409
118 24 Francisco Garcia SAC SF -0.58 2.6 85.7% 0.219
119 25 Vince Carter PHX SG -0.61 3.2 69.8% 0.446
120 29 Kris Humphries NJN PF -0.63 4.7 64.0% 0.346
121 26 Raja Bell UTA SG -0.63 2.6 91.1% 0.025
122 23 Jameer Nelson ORL PG -0.64 3.5 82.8% 0.210
123 24 Luke Ridnour MIN PG -0.66 3.0 89.1% 0.185
124 27 Sonny Weems TOR SG -0.68 3.2 76.7% 0.144
125 25 Trevor Ariza NOH SF -0.71 3.8 67.6% 0.312
126 28 Tracy McGrady DET SG -0.72 4.0 68.0% 0.230
127 25 Mike Conley MEM PG -0.78 4.4 73.5% 0.166
128 26 Tayshaun Prince DET SF -0.79 3.3 68.6% 0.282
129 21 Marcus Camby POR C -0.80 2.3 57.8% 0.219
130 29 Landry Fields NYK SG -0.81 2.7 75.2% 0.201
131 30 DeJuan Blair SAS PF -0.83 3.7 62.1% 0.389
132 31 Jason Thompson SAC PF -0.86 5.5 58.4% 0.292
133 22 Darko Milicic MIN C -0.86 3.1 52.8% 0.237
134 26 Eric Bledsoe LAC PG -0.88 3.4 73.1% 0.343
135 32 Channing Frye PHX PF -0.88 2.0 81.4% 0.204
136 30 Carlos Delfino MIL SG -0.93 2.5 79.7% 0.034
137 23 Spencer Hawes PHI C -0.94 2.5 51.9% 0.215
138 31 Anthony Parker CLE SG -0.95 2.1 76.2% 0.224
139 27 Jose Calderon TOR PG -0.99 2.4 89.8% 0.097
140 27 Hedo Turkoglu ORL SF -1.03 3.1 65.4% 0.200
141 28 Omri Casspi SAC SF -1.08 2.7 66.7% 0.176
142 32 DeShawn Stevenson DAL SG -1.13 1.8 75.0% 0.137
143 29 Ron Artest LAL SF -1.14 2.9 65.9% 0.111
144 33 Jason Richardson ORL SG -1.15 2.3 71.3% 0.085
145 34 Thabo Sefolosha OKC SG -1.16 1.9 73.0% 0.127
146 33 Boris Diaw CHA PF -1.17 2.2 65.5% 0.193
147 35 Wesley Johnson MIN SG -1.19 2.1 68.6% 0.143
148 30 Ryan Gomes LAC SF -1.23 2.0 70.7% 0.075
149 28 Derek Fisher LAL PG -1.23 2.2 79.6% 0.163
150 29 Mario Chalmers MIA PG -1.25 2.0 86.9% 0.034
151 24 DeAndre Jordan LAC C -1.29 5.3 43.8% 0.179
152 25 Andrew Bogut MIL C -1.32 4.9 41.5% 0.237
153 34 Kenyon Martin DEN PF -1.32 2.7 54.5% 0.246
154 31 Shane Battier HOU SF -1.38 2.0 63.0% 0.084
155 26 Andris Biedrins GSW C -1.42 1.1 30.0% 0.036
156 35 Kurt Thomas CHI PF -1.47 1.3 59.3% 0.141
157 30 Jason Kidd DAL PG -1.47 1.5 86.7% 0.039
158 36 Keith Bogans CHI SG -1.59 1.1 63.3% 0.000
159 27 Ben Wallace DET C -1.63 2.6 33.3% 0.000
160 31 Mike Bibby ATL PG -1.76 1.4 61.9% 0.130
161 32 Rajon Rondo BOS PG -1.78 2.7 55.1% 0.105

Here is the list of players with above average possessions but below average games started:

ORK PRK NAME TEAM POS PSAMS-FT FTR FT% AND1_RATE
1 1 Corey Maggette MIL SF 3.21 11.5 83.4% 0.873
2 1 Louis Williams PHI PG 1.92 10.1 81.8% 0.541
3 1 James Harden OKC SG 1.52 7.8 83.7% 0.465
4 1 Hakim Warrick PHX PF 1.13 10.2 70.7% 0.512
5 1 Zaza Pachulia ATL C 1.10 7.4 74.1% 0.392
6 2 Jamal Crawford ATL SG 0.87 5.7 87.7% 0.371
7 2 George Hill SAS PG 0.78 6.0 85.8% 0.561
8 3 Jerryd Bayless TOR PG 0.72 6.9 80.7% 0.512
9 4 Jarrett Jack NOH PG 0.67 6.3 84.1% 0.444
10 2 Carl Landry SAC PF 0.61 7.0 68.6% 0.883
11 2 Ryan Hollins CLE C 0.41 6.7 65.3% 0.488
12 3 C.J. Miles UTA SG 0.39 4.8 81.7% 0.520
13 5 Will Bynum DET PG 0.38 5.2 85.5% 0.477
14 3 Marcin Gortat PHX C 0.34 5.3 71.3% 0.353
15 4 J.J. Redick ORL SG 0.30 4.2 91.5% 0.246
16 6 Shaun Livingston CHA PG 0.26 4.9 85.0% 0.518
17 7 Jose Barea DAL PG 0.13 4.3 83.1% 0.671
18 5 Rudy Fernandez POR SG 0.11 4.0 86.8% 0.297
19 6 Jason Terry DAL SG 0.11 4.1 86.5% 0.286
20 7 Daniel Gibson CLE SG 0.06 4.3 83.1% 0.306
21 3 Anthony Tolliver MIN PF 0.06 4.3 78.4% 0.482
22 4 Glen Davis BOS PF 0.04 5.9 72.1% 0.332
23 8 Leandro Barbosa TOR SG 0.02 4.5 77.2% 0.443
24 2 Martell Webster MIN SF 0.02 5.3 75.9% 0.277
25 9 J.R. Smith DEN SG -0.04 5.2 73.3% 0.381
26 3 Chase Budinger HOU SF -0.05 3.7 84.0% 0.382
27 10 Shannon Brown LAL SG -0.11 3.0 91.0% 0.341
28 5 Darrell Arthur MEM PF -0.11 3.9 80.7% 0.359
29 11 Corey Brewer MIN SG -0.14 5.8 68.8% 0.399
30 6 Ryan Anderson ORL PF -0.15 4.0 80.4% 0.298
31 4 Jared Dudley PHX SF -0.18 4.9 72.4% 0.366
32 5 Al-Farouq Aminu LAC SF -0.29 3.9 75.9% 0.392
33 12 Evan Turner PHI SG -0.35 3.4 79.8% 0.326
34 13 Reggie Williams GSW SG -0.38 3.8 72.5% 0.442
35 4 Ronny Turiaf NYK C -0.45 4.0 58.9% 0.357
36 5 Nick Collison OKC C -0.46 2.1 70.7% 0.321
37 14 Courtney Lee HOU SG -0.49 3.4 78.8% 0.212
38 15 Sasha Vujacic NJN SG -0.50 3.1 85.7% 0.101
39 16 Paul George IND SG -0.50 3.6 73.6% 0.319
40 7 Thaddeus Young PHI PF -0.51 3.8 66.9% 0.500
41 6 Austin Daye DET SF -0.53 3.8 74.5% 0.222
42 17 O.J. Mayo MEM SG -0.54 3.5 78.6% 0.140
43 18 Gary Neal SAS SG -0.54 2.8 77.5% 0.403
44 8 Jordan Hill HOU PF -0.57 3.3 65.3% 0.600
45 9 Charlie Villanueva DET PF -0.57 3.5 75.5% 0.193
46 7 Kyle Korver CHI SF -0.60 2.5 92.1% 0.066
47 8 Gordon Hayward UTA SF -0.64 3.9 69.7% 0.266
48 19 Willie Green NOH SG -0.64 3.0 75.8% 0.293
49 10 Al Harrington DEN PF -0.67 3.2 70.5% 0.360
50 6 Joel Anthony MIA C -0.68 2.6 65.7% 0.111
51 9 James Jones MIA SF -0.74 2.4 87.0% 0.103
52 11 Taj Gibson CHI PF -0.75 4.5 66.7% 0.158
53 20 Brandon Rush IND SG -0.86 3.0 75.2% 0.088
54 8 Jordan Farmar NJN PG -0.86 2.8 83.9% 0.211
55 9 Keyon Dooling MIL PG -0.93 2.7 84.3% 0.154
56 21 Ronnie Brewer CHI SG -0.94 3.7 63.9% 0.214
57 22 Wayne Ellington MIN SG -0.96 2.0 77.1% 0.211
58 10 Donte Greene SAC SF -1.10 2.7 62.7% 0.271
59 12 Vladimir Radmanovic GSW PF -1.10 1.4 87.5% 0.088
60 13 Antonio McDyess SAS PF -1.11 2.8 67.6% 0.077
61 10 Toney Douglas NYK PG -1.17 2.6 78.4% 0.103
62 14 Ed Davis TOR PF -1.27 3.8 51.7% 0.326
63 15 Matt Bonner SAS PF -1.28 1.5 72.5% 0.109
64 11 Eric Maynor OKC PG -1.35 2.5 71.4% 0.135
65 12 Earl Watson UTA PG -1.50 2.7 67.9% 0.035
66 13 Steve Blake LAL PG -1.72 1.0 85.7% 0.000
67 7 Brendan Haywood DAL C -1.91 6.7 33.1% 0.319

Position- and Shot-Location-Adjusted Marginal Scoring (Part II): Mid-Range Shooting

No surprises. Dirk is the king of mid-range shooting.

In my last post, I introduced a new marginal scoring stat (PSAMS) and posted the formulas and ratings for inside scoring. Here, I will introduce the metric for evaluating mid-range shooting, which I define as any shot in between 3 ft from the rim and the 3-pt line. I lump all these shots together because, according to Hoopdata, the averages for 3-9 ft (39%), 10-15 ft (39.3%), and 16-23 ft (39.4%), are very similar (especially compared to the averages for inside scoring, 64.1%, and 3-pt shooting, 53.8%).

Recall (or learn for the first time) that the league-average effective FG% (eFG%) is about 50% (to be exact, it's 49.8%). The fact that the average mid-range shot is actually worse than the, uh, average average shot(?), makes evaluation somewhat trickier, and likely somewhat more open to challenge. Here's why. In theory, players hurt their teams when they take mid-range shots. Unless you're Dirk Nowitzki, that is. Among the 150 or so players in my database (>40+ games, >25+ mpg), Dirk is the only one who shot better than 50% from mid-range. As I've written previously (here and here), I believe that mid-range shots are an important and inevitable part of the game, and that, because somebody has to take those shots, you just want to make sure your best shooter is the one doing it. If you think about it this way, you begin to realize that the players who are given the responsibility risk hurting their overall averages. To be sure, some players may force too many of those shots, but it's very difficult to know which shots are necessary (after all, they don't tell us!).

Therefore, what I've come up with for the metric actually is a bit of a hedge, because it averages the two philosophies. In both philosophies, players who shoot less than their "fair share" of mid-range shots (defined by the average mid-range FGA for their position) are penalized for their "undershooting". How this is done will be explained a bit later. Where the philosophies differ is their handling of players who shoot more than the average number of mid-range shots for their position. How do we handle those extra shots?

  • Philosophy I: All "extra" mid-range FGA are shots taken away from teammates who would have taken average ("better") shots, i.e. shots that should be compared to the league-average 50%.
  • Philosophy II: All "extra" mid-range FGA are not really extra at all, and would have still been taken by a teammate. Therefore, these shots should also be compared to the average mid-range shot efficiency of ~39%.

You can see how these are two very different viewpoints, right? In fact, I would argue it's one of the central debates of basketball fandom, one that separates Kobe Bryant (and Monta Ellis) fans from their detractors, for example. There's really no good way right now to resolve the debate, so for now, I'm going to calculate the rating using both philosophies, and then take the simple average between them. Having said that, I think the final results will seem reasonable to folks on both sides of the argument.

As in my last post, I will use a couple of players to illustrate the actual calculation. First up is a no-brainer, Dirk Nowitzki. Dirk averaged 13.8 mid-range FGA per 40 minutes with 50.4% efficiency. Here's how I calculate his rating according to Philosophy I:

PSAMS_{MR}^I = 2*(13.3 - 8.6)*(50.4-49.8) + 2*8.6*(50.4-40.2)=1.81

The first term on the right represents the "extra" mid-range shots, which according to Philosophy I, are compared to the league-average average shot efficiency (I know, try saying that 10 times fast). The second term represents the average number of mid-range shots (for the PF position), which are being compared to the average mid-range shot efficiency for PF. Follow all that? Here's how Dirk rates according to Philosophy II:

PSAMS_{MR}^{II} = 2*13.3*(50.4-40.2)=2.71

That one is simple, right? Just compare all his shots to the average mid-range efficiency for PF. Dirk's final rating is then simply the average of the two (2.26).

Now we need to look at a player that shoots fewer than the average mid-range FGA. Arron Afflalo is one such "undershooter", taking only 3.8 mid-range FGA per 40 compared to the average 6.7 for the SG position. Here's how I calculate the rating for Afflalo (there is no need to distinguish between the two philosophies):

PSAMS_{MR}=2*3.8*(44.7-39.4)-2*(6.7-3.8)*(49.8-39.4)=-0.20

The first term here represents the shots that Afflalo did take compared to the average mid-range efficiency for SG. The second term represents a "penalty" for undershooting. The idea is that the shots that he didn't take would be shifted to teammates who otherwise would have taken better shots. Therefore, the efficiency differential (49.8-39.4) represents the difference between an average shot and an average mid-range shot. The reason I believe we need such a penalty is that if players simply "opt out" of these types of shots, their PSAMS would be 0, which would make them appear to be better shooters than about half the players at their position. Any system that rewards a player for not shooting at all doesn't make sense to me. You can't win games by opting out of shooting.

With the groundwork laid out, let's get to the ratings. Here are the top and bottom 25, respectively.

Top 25 Mid-Range Shooters

The FGA and FG% are for mid-range shots.

RANK NAME TEAM POS FGA FG% PSAMS-MR
1 Dirk Nowitzki DAL 4 13.3 50.4% 2.25
2 Al Horford ATL 5 10.0 49.0% 1.39
3 Elton Brand PHI 4 10.7 46.7% 1.19
4 Luke Ridnour MIN 1 7.0 47.1% 1.10
5 Beno Udrih SAC 1 6.8 47.1% 1.08
6 Steve Nash PHO 1 7.7 46.8% 1.08
7 LeBron James MIA 3 9.5 45.3% 1.08
8 David West NOR 4 12.7 45.7% 0.99
9 Stephen Curry GSW 1 8.1 45.7% 0.92
10 Anthony Morrow NJN 2 6.4 46.9% 0.87
11 Kevin Garnett BOS 4 10.3 44.7% 0.75
12 Luis Scola HOU 4 13.2 44.7% 0.73
13 Chris Paul NOR 1 8.1 44.4% 0.72
14 Jason Terry DAL 2 9.4 44.7% 0.71
15 Pau Gasol LAL 4 9.9 44.4% 0.71
16 Brandon Bass ORL 4 8.8 44.3% 0.70
17 Ray Allen BOS 2 5.7 47.4% 0.67
18 Sasha Vujacic NJN 2 6.8 44.1% 0.63
19 Paul Millsap UTH 4 9.1 44.0% 0.63
20 Chris Bosh MIA 4 10.8 43.5% 0.50
21 Jamal Crawford ATL 2 6.7 43.3% 0.49
22 Tony Parker SAS 1 8.6 43.0% 0.48
23 Amare Stoudemire NYK 4 13.5 43.7% 0.46
24 Deron Williams UTH 1 6.3 42.9% 0.46
25 Joe Johnson ATL 2 9.7 43.3% 0.44

Bottom 25 Mid-Range Shooters

Some of the names on this list may surprise you, but before bugging out, make sure to look at their FGA and FG%, and compare those to the players on the Top 25 list, and keep the two philosophies in mind.

RANK NAME TEAM POS FGA FG% PSAMS-MR
152 Andray Blatche WAS 4 10.6 31.1% -2.12
151 Greg Monroe DET 4 2.4 25.0% -1.94
150 Marcus Camby POR 4 3.8 28.9% -1.80
149 DeMarcus Cousins SAC 4 11.3 33.6% -1.75
148 Tyreke Evans SAC 1 8.1 29.6% -1.68
147 Trevor Ariza NOR 3 3.8 23.7% -1.59
146 John Wall WAS 1 7.5 29.3% -1.54
145 Russell Westbrook OKC 1 10.2 34.3% -1.34
144 Ron Artest LAL 3 3.7 27.0% -1.34
143 J.J. Hickson CLE 4 8.8 33.0% -1.30
142 Brandon Rush IND 2 4.5 31.1% -1.24
141 Landry Fields NYK 2 2.4 33.3% -1.22
140 Wesley Matthews POR 2 4.4 31.8% -1.18
139 Jodie Meeks PHI 2 2.3 34.8% -1.17
138 Kenyon Martin DEN 4 6.0 35.0% -1.13
137 Chuck Hayes HOU 5 2.7 33.3% -1.13
136 Jason Kidd DAL 1 2.3 34.8% -1.12
135 Danilo Gallinari NYK 3 3.6 30.6% -1.09
134 DeAndre Jordan LAC 5 1.0 40.0% -1.09
133 Kwame Brown CHA 5 3.5 34.3% -1.03
132 Brandon Roy POR 2 9.1 35.2% -1.02
131 Kyle Lowry HOU 1 3.9 33.3% -1.01
130 James Harden OKC 2 2.7 37.0% -1.00
129 Thabo Sefolosha OKC 2 2.0 40.0% -0.99
128 Jason Richardson ORL 2 4.3 34.9% -0.92

Here are the ratings broken down by position (ORNK is overall ranking and PRNK is ranking by position):

PG

ORNK PRNK NAME TEAM POS FGA FG% PSAMS-MR
4 1 Luke Ridnour MIN 1 7.0 47.1% 1.10
5 2 Beno Udrih SAC 1 6.8 47.1% 1.08
6 3 Steve Nash PHO 1 7.7 46.8% 1.08
9 4 Stephen Curry GSW 1 8.1 45.7% 0.92
13 5 Chris Paul NOR 1 8.1 44.4% 0.72
22 6 Tony Parker SAS 1 8.6 43.0% 0.48
24 7 Deron Williams UTH 1 6.3 42.9% 0.46
32 8 Raymond Felton NYK 1 6.5 41.5% 0.34
48 9 Jose Calderon TOR 1 5.8 41.4% 0.13
49 10 George Hill SAS 1 5.2 42.3% 0.07
52 11 Jameer Nelson ORL 1 5.7 40.4% -0.01
54 12 Devin Harris NJN 1 6.7 38.8% -0.03
55 13 Jrue Holiday PHI 1 6.7 38.8% -0.03
56 14 Darren Collison IND 1 8.3 39.8% -0.06
59 15 Daniel Gibson CLE 1 5.5 40.0% -0.10
64 16 Mike Conley MEM 1 6.0 38.3% -0.18
68 17 Baron Davis LAC 1 6.7 37.3% -0.23
69 18 Andre Miller POR 1 8.3 38.6% -0.26
70 19 Derrick Rose CHI 1 9.2 39.1% -0.26
76 20 Ty Lawson DEN 1 4.1 41.5% -0.32
83 21 Rodney Stuckey DET 1 7.1 36.6% -0.39
92 22 Brandon Jennings MIL 1 6.8 35.3% -0.52
93 23 Ramon Sessions CLE 1 7.7 36.4% -0.52
98 24 Rajon Rondo BOS 1 5.2 36.5% -0.53
97 25 Chauncey Billups DEN 1 5.2 36.5% -0.53
111 26 Derek Fisher LAL 1 5.1 35.3% -0.68
115 27 D.J. Augustin CHA 1 4.5 35.6% -0.74
125 28 Mike Bibby ATL 1 3.7 35.1% -0.90
131 29 Kyle Lowry HOU 1 3.9 33.3% -1.01
136 30 Jason Kidd DAL 1 2.3 34.8% -1.12
145 31 Russell Westbrook OKC 1 10.2 34.3% -1.34
146 32 John Wall WAS 1 7.5 29.3% -1.54
148 33 Tyreke Evans SAC 1 8.1 29.6% -1.68

SG

ORNK PRNK NAME TEAM POS FGA FG% PSAMS-MR
10 1 Anthony Morrow NJN 2 6.4 46.9% 0.87
14 2 Jason Terry DAL 2 9.4 44.7% 0.71
17 3 Ray Allen BOS 2 5.7 47.4% 0.67
18 4 Sasha Vujacic NJN 2 6.8 44.1% 0.63
21 5 Jamal Crawford ATL 2 6.7 43.3% 0.49
25 6 Joe Johnson ATL 2 9.7 43.3% 0.44
28 7 DeMar DeRozan TOR 2 10.4 43.3% 0.42
30 8 Ben Gordon DET 2 7.1 42.3% 0.37
31 9 Dwyane Wade MIA 2 8.9 42.7% 0.36
33 10 Kobe Bryant LAL 2 14.3 43.4% 0.33
36 11 Kirk Hinrich WAS 2 7.2 41.7% 0.28
39 12 Nick Young WAS 2 10.8 42.6% 0.26
66 13 Manu Ginobili SAS 2 5.5 40.0% -0.22
67 14 Arron Afflalo DEN 2 3.8 44.7% -0.23
71 15 J.J. Redick ORL 2 4.2 42.9% -0.26
79 16 John Salmons MIL 2 7.9 38.0% -0.35
80 17 Stephen Jackson CHA 2 6.8 36.8% -0.37
81 18 O.J. Mayo MEM 2 7.7 37.7% -0.37
82 19 Raja Bell UTH 2 4.4 40.9% -0.38
84 20 Richard Hamilton DET 2 12.2 40.2% -0.39
86 21 Anthony Parker CLE 2 5.5 38.2% -0.42
87 22 Vince Carter PHO 2 7.1 36.6% -0.43
101 23 Eric Gordon LAC 2 6.8 35.3% -0.57
118 24 Kevin Martin HOU 2 8.4 35.7% -0.79
119 25 Monta Ellis GSW 2 10.0 37.0% -0.82
126 26 Andre Iguodala PHI 2 6.0 33.3% -0.90
128 27 Jason Richardson ORL 2 4.3 34.9% -0.92
129 28 Thabo Sefolosha OKC 2 2.0 40.0% -0.99
130 29 James Harden OKC 2 2.7 37.0% -1.00
132 30 Brandon Roy POR 2 9.1 35.2% -1.02
139 31 Jodie Meeks PHI 2 2.3 34.8% -1.17
140 32 Wesley Matthews POR 2 4.4 31.8% -1.18
141 33 Landry Fields NYK 2 2.4 33.3% -1.22
142 34 Brandon Rush IND 2 4.5 31.1% -1.24

SF

ORNK PRNK NAME TEAM POS FGA FG% PSAMS-MR
7 1 LeBron James MIA 3 9.5 45.3% 1.08
26 2 Shawn Marion DAL 3 8.4 41.7% 0.44
27 3 Paul Pierce BOS 3 5.8 41.4% 0.43
35 4 Kevin Durant OKC 3 11.1 41.4% 0.28
38 5 Hedo Turkoglu ORL 3 4.9 42.9% 0.27
40 6 Luol Deng CHI 3 6.1 39.3% 0.24
41 7 Grant Hill PHO 3 8.4 40.5% 0.24
43 8 Marvin Williams ATL 3 5.9 39.0% 0.18
46 9 Rudy Gay MEM 3 9.4 40.4% 0.16
50 10 Mike Dunleavy IND 3 4.1 43.9% 0.06
53 11 Wesley Johnson MIN 3 5.9 37.3% -0.02
57 12 Carmelo Anthony DEN 3 10.8 39.8% -0.06
60 13 Travis Outlaw NJN 3 6.3 36.5% -0.13
65 14 Ryan Gomes LAC 3 4.2 40.5% -0.19
72 15 Wilson Chandler NYK 3 6.7 35.8% -0.28
73 16 Tayshaun Prince DET 3 10.6 38.7% -0.28
88 17 Jared Dudley PHO 3 3.9 38.5% -0.44
89 18 Carlos Delfino MIL 3 3.5 40.0% -0.45
90 19 Nicolas Batum POR 3 3.6 38.9% -0.49
102 20 Jeff Green OKC 3 5.8 32.8% -0.57
104 21 C.J. Miles UTH 3 7.3 34.2% -0.60
105 22 Danny Granger IND 3 8.0 35.0% -0.62
108 23 Gerald Wallace CHA 3 5.1 33.3% -0.63
110 24 Richard Jefferson SAS 3 3.1 38.7% -0.65
114 25 Shane Battier HOU 3 2.4 41.7% -0.71
117 26 Luc Mbah a Moute MIL 3 3.8 34.2% -0.79
123 27 Dorell Wright GSW 3 4.8 31.3% -0.88
124 28 Andrei Kirilenko UTH 3 4.0 32.5% -0.89
135 29 Danilo Gallinari NYK 3 3.6 30.6% -1.09
144 30 Ron Artest LAL 3 3.7 27.0% -1.34
147 31 Trevor Ariza NOR 3 3.8 23.7% -1.59

PF

ORNK PRNK NAME TEAM POS FGA FG% PSAMS-MR
1 1 Dirk Nowitzki DAL 4 13.3 50.4% 2.25
3 2 Elton Brand PHI 4 10.7 46.7% 1.19
8 3 David West NOR 4 12.7 45.7% 0.99
11 4 Kevin Garnett BOS 4 10.3 44.7% 0.75
12 5 Luis Scola HOU 4 13.2 44.7% 0.73
15 6 Pau Gasol LAL 4 9.9 44.4% 0.71
16 7 Brandon Bass ORL 4 8.8 44.3% 0.70
19 8 Paul Millsap UTH 4 9.1 44.0% 0.63
20 9 Chris Bosh MIA 4 10.8 43.5% 0.50
23 10 Amare Stoudemire NYK 4 13.5 43.7% 0.46
37 11 Zach Randolph MEM 4 9.5 42.1% 0.27
42 12 David Lee GSW 4 9.1 41.8% 0.23
51 13 LaMarcus Aldridge POR 4 11.1 41.4% 0.03
61 14 Josh Smith ATL 4 8.3 39.8% -0.13
62 15 Boris Diaw CHA 4 4.4 47.7% -0.16
75 16 Ersan Ilyasova MIL 4 6.6 40.9% -0.30
74 17 Serge Ibaka OKC 4 6.6 40.9% -0.30
78 18 Carlos Boozer CHI 4 10.4 39.4% -0.34
85 19 Antawn Jamison CLE 4 9.8 38.8% -0.40
91 20 Michael Beasley MIN 4 13.7 40.1% -0.52
95 21 Channing Frye PHO 4 5.0 42.0% -0.53
96 22 Glen Davis BOS 4 9.5 37.9% -0.53
99 23 Carl Landry SAC 4 9.3 37.6% -0.55
103 24 Lamar Odom LAL 4 5.1 41.2% -0.59
106 25 Amir Johnson TOR 4 4.5 42.2% -0.62
109 26 Blake Griffin LAC 4 9.4 37.2% -0.64
112 27 Kris Humphries NJN 4 5.6 39.3% -0.69
113 28 Kevin Love MIN 4 6.6 37.9% -0.70
127 29 Thaddeus Young PHI 4 7.6 35.5% -0.91
138 30 Kenyon Martin DEN 4 6.0 35.0% -1.13
143 31 J.J. Hickson CLE 4 8.8 33.0% -1.30
149 32 DeMarcus Cousins SAC 4 11.3 33.6% -1.75
150 33 Marcus Camby POR 4 3.8 28.9% -1.80
151 34 Greg Monroe DET 4 2.4 25.0% -1.94
152 35 Andray Blatche WAS 4 10.6 31.1% -2.12

C

Hey, Andrea Bargnani fans, this might be the one stat you can hang on your hat.

ORNK PRNK NAME TEAM POS FGA FG% PSAMS-MR
2 1 Al Horford ATL 5 10.0 49.0% 1.39
29 2 Andrea Bargnani TOR 5 12.0 44.2% 0.39
34 3 Marcin Gortat PHO 5 6.8 42.6% 0.29
44 4 Marc Gasol MEM 5 6.7 41.8% 0.18
45 5 Dwight Howard ORL 5 6.7 41.8% 0.18
47 6 Brook Lopez NJN 5 12.7 43.3% 0.15
58 7 Tim Duncan SAS 5 11.2 42.0% -0.09
63 8 Andrew Bogut MIL 5 7.3 39.7% -0.16
77 9 Andrew Bynum LAL 5 5.3 39.6% -0.33
94 10 Al Jefferson UTH 5 11.9 40.3% -0.52
100 11 Tyson Chandler DAL 5 2.1 47.6% -0.56
107 12 Nene Hilario DEN 5 3.5 40.0% -0.63
116 13 Joakim Noah CHI 5 3.7 37.8% -0.75
120 14 Emeka Okafor NOR 5 3.5 37.1% -0.83
121 15 JaVale McGee WAS 5 4.5 35.6% -0.84
122 16 Roy Hibbert IND 5 10.5 38.1% -0.86
133 17 Kwame Brown CHA 5 3.5 34.3% -1.03
134 18 DeAndre Jordan LAC 5 1.0 40.0% -1.09
137 19 Chuck Hayes HOU 5 2.7 33.3% -1.13

Next post will wrap up with 3-pt shooting and overall rankings combining all three shot distances into a single metric.