# 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.