# The Value of Replacement Level in the NBA rev.2: Improving the Algorithm

Posted on 08/16/2010 by

“Sometimes when I talk to journalism students and they will ask how I get people to open up to me, and the answer is that I’m genuinely curious about what those people are saying. I honestly care about the stories they are telling. There’s a force that talks to the deepest part of us. There is something that happens during therapy when the therapy session is going well: If someone is talking to a therapist about something unresolved – something they don’t understand- and they suddenly start talking about it, it just flows out in this highly narrative,highly detailed form. Most people are not articulate about everything in their life, but they are articulate about the things they’re still figuring out” – Ira Glass, host of “This American Life” being interviewed by  Chuck Klosterman for his book “Eating the dinosaur”

I was on a plane to South Beach this morning when I read this passage and it struck a deep chord within me. Why do I write this blog? I write because I have something I don’t understand that I’m trying to work out. There is an intrinsic need for me to externalize these questions that are in my head. I want to lay my theories out there right or wrong and seek knowledgeable criticism that will guide on the path to truth.

When I first started reading Wages of Wins, It, like all good books, lead to a lot of questions within me. I love sports (and basketball in particular) and I love statistics (enough to make a career of it) so any exercise that tries to marry the two and create quantitative measurements (specially with a high degree of correlation is right up my alley). Wages of Wins did an excellent job at answering the question of value in the NBA but as with everything that answer a question new ones come. This is the genesis of this blog and this  is why we are talking about replacement value.

Refining the Replacement Value Algorithm or the Problem with tweeners

It is a mistake to suppose that people succeed through success; they often succeed through failures. ~Author Unknown

In the previous post on finding the Replacement Level for NBA Players I used the following algorithm to identify replacement level players:

Step #1 : Sort player by years and minutes played by position.

Step#2:  Calculate the productivity of the players that account for just over 20% of the minutes played at each position (or just about 10 minutes per game)

Step #3: Set that as the replacement level for each position.

There is a problem with that algorithm. Let me illustrate it. Here’s the list of replacement level centers for 2010:

Dwayne Jones,Paul Davis,Ryan Anderson,Kevin Garnett,Alexis Ajinca,Patrick O’Bryant,Byron Mullens,Chris Richard,Eddy Curry,Francisco Elson,Primoz Brezec,Jason Collins,Amare Stoudemire,Pops Mensah-Bonsu,Elton Brand,Tony Battie,Steven Hunter,Ian Mahinmi,Kosta Koufos,Zach Randolph,Earl Barron,Hamed Haddadi,Jeff Foster,Jarron Collins,DeSagana Diop,Ersan Ilyasova,Serge Ibaka,Aaron Gray,Dan Gadzuric,Etan Thomas,Hilton Armstrong,Didier Ilunga-Mbenga,Jamaal Magloire,Earl Clark,Mikki Moore,Kyrylo Fesenko,Rasho Nesterovic,Johan Petro,Chris Wilcox,Oleksiy Pecherov,Chris Hunter,Greg Oden,Al Harrington,Fabricio Oberto,Jon Brockman,Jason Smith,Kwame Brown

You’ll note that there are a couple of names that do not belong. What’s happening is that tweeners (multiple position players) who play a small percentage of their minutes at the Center are sneaking in and some are driving up the value of the replacement level pool.

But that’s ok, to paraphrase Herm Edwards, we can build on this. I’m going to work out take 2 of the algorithm and show my work:

Step #1 : Sort player by years and minutes played total for that season. This is the ultimate assertion of the perceived value of a player to a team. For example here’s the top 20 in minutes played for 2010:

 Y2010PJason Kidd Born 1974 Y2010PJoe Johnson Born 1982 Y2010PStephen Curry Born 1989 Y2010PBoris Diaw Born 1983 Y2010PAaron Brooks Born 1985 Y2010PLaMarcus Aldridge Born 1986 Y2010PDavid West Born 1981 Y2010PRajon Rondo Born 1987 Y2010PLeBron James Born 1985 Y2010PDavid Lee Born 1984 Y2010PBrook Lopez Born 1989 Y2010PDirk Nowitzki Born 1979 Y2010PJeff Green Born 1987 Y2010PZach Randolph Born 1982 Y2010PO.J. Mayo Born 1988 Y2010PGerald Wallace Born 1983 Y2010PStephen Jackson Born 1979 Y2010PRudy Gay Born 1987 Y2010PAndre Iguodala Born 1984 Y2010PKevin Durant Born 1989

Step#2:  For each position, find the players with the least perceived value (i.e total minutes played and add them up until you reach just over 20% of the minutes played at each position (or just about 10 minutes per game). These are our Replacement Level players (By the way this is a hateful build which I have not found how to automate as of yet but hey I got to work out those issues ;-))

For 2010 at center the list of Replacement players now looks like this:

 Player Sum of Minutes C MP Rank Percent of Minutes Dwayne Jones Born 1984 7 2 0.0% Paul Davis Born 1985 8 4 0.0% Alexis Ajinca Born 1989 30 9 0.0% Patrick O’Bryant Born 1987 51 19 0.0% Byron Mullens Born 1990 54 21 0.0% Eddy Curry Born 1983 62 24 0.0% Francisco Elson Born 1977 66 25 0.0% Primoz Brezec Born 1980 95 31 0.0% Jason Collins Born 1979 115 39 0.0% Pops Mensah-Bonsu Born 1984 120 41 0.0% Tony Battie Born 1977 134 48 0.0% Steven Hunter Born 1982 158 51 0.0% Ian Mahinmi Born 1987 165 52 0.0% Kosta Koufos Born 1990 172 53 1.0% Chris Richard Born 1985 57 58 1.0% Earl Barron Born 1982 232 61 1.0% Hamed Haddadi Born 1986 240 65 1.0% Jeff Foster Born 1977 255 68 1.0% Jarron Collins Born 1979 260 69 1.0% DeSagana Diop Born 1982 262 70 2.0% Aaron Gray Born 1985 311 78 2.0% Dan Gadzuric Born 1979 314 81 2.0% Etan Thomas Born 1979 321 83 2.0% Hilton Armstrong Born 1985 335 87 3.0% Didier Ilunga-Mbenga Born 1981 355 89 3.0% Jamaal Magloire Born 1979 359 90 3.0% Earl Clark Born 1988 383 92 4.0% Mikki Moore Born 1976 406 97 4.0% Kyrylo Fesenko Born 1987 408 99 4.0% Rasho Nesterovic Born 1977 413 101 5.0% Johan Petro Born 1986 435 102 5.0% Chris Wilcox Born 1983 441 103 5.0% Oleksiy Pecherov Born 1986 447 104 6.0% Greg Oden Born 1988 502 111 6.0% Fabricio Oberto Born 1976 650 127 7.0% Jon Brockman Born 1988 654 128 7.0% Jason Smith Born 1987 658 129 8.0% Kwame Brown Born 1983 660 131 8.0% Solomon Jones Born 1985 675 133 9.0% Joel Przybilla Born 1980 681 134 9.0% Darko Milicic Born 1986 685 136 10.0% Andris Biedrins Born 1987 763 149 11.0% Chris Hunter Born 1985 483 152 11.0% Theo Ratliff Born 1974 807 158 12.0% Ronny Turiaf Born 1983 872 167 12.0% Hasheem Thabeet Born 1988 883 171 13.0% David Andersen Born 1981 891 174 14.0% Ryan Anderson Born 1989 15 175 14.0% JaVale McGee Born 1988 968 183 15.0% Nazr Mohammed Born 1978 984 188 16.0% Robin Lopez Born 1989 986 189 16.0% Marreese Speights Born 1988 1016 190 17.0% Josh Boone Born 1985 796 192 18.0% Kurt Thomas Born 1973 1049 194 19.0% Marcin Gortat Born 1985 1088 199 20.0%

Here’s PF:

 Player Sum of Minutes PF MP Rank Percent of Minutes Othello Hunter Born 1987 33 11 0.0% Brian Cook Born 1981 44 14 0.0% Marcus Haislip Born 1981 44 16 0.0% Shavlik Randolph Born 1984 53 20 0.0% Sean Marks Born 1976 75 29 0.0% D.J. White Born 1987 102 35 0.0% Joey Dorsey Born 1984 106 36 0.0% Darnell Jackson Born 1986 122 44 0.0% Brian Skinner Born 1977 123 45 0.0% Randolph Morris Born 1986 124 46 0.0% Chris Richard Born 1985 167 58 0.0% Sean Williams Born 1987 227 59 1.0% Leon Powe Born 1984 236 63 1.0% Brian Cardinal Born 1978 267 72 1.0% Tim Thomas Born 1978 285 74 1.0% Jonathan Bender Born 1981 292 75 1.0% Reggie Evans Born 1981 311 79 2.0% Kenny Thomas Born 1978 313 80 2.0% Sean May Born 1985 331 85 2.0% Steve Novak Born 1984 362 91 3.0% Bobby Simmons Born 1981 395 94 3.0% DaJuan Summers Born 1988 405 95 3.0% Jeff Pendergraph Born 1988 405 96 4.0% Nathan Jawai Born 1987 412 100 4.0% Malik Allen Born 1979 456 105 4.0% Darrell Arthur Born 1989 457 106 5.0% Brian Scalabrine Born 1979 388 108 5.0% Ricky Davis Born 1980 461 110 5.0% Tyler Hansbrough Born 1986 511 113 6.0% Josh McRoberts Born 1988 524 115 6.0% Derrick Brown Born 1988 535 116 7.0% Josh Powell Born 1983 581 120 7.0% Joe Smith Born 1976 592 122 8.0% Shelden Williams Born 1984 597 123 8.0% Jordan Hill Born 1988 624 124 9.0% Brandon Bass Born 1986 648 126 9.0% Eduardo Najera Born 1977 685 135 10.0% Dante Cunningham Born 1988 707 139 10.0% Travis Outlaw Born 1985 231 143 11.0% Jawad Williams Born 1984 742 144 11.0% Anthony Randolph Born 1990 749 145 12.0% James Johnson Born 1988 399 146 12.0% Devean George Born 1978 58 148 12.0% Chris Hunter Born 1985 300 152 13.0% Julian Wright Born 1988 629 166 13.0% Vladimir Radmanovic Born 1981 891 173 14.0% Ryan Anderson Born 1989 895 175 15.0% Glen Davis Born 1986 933 179 15.0% James Singleton Born 1982 766 187 16.0% Josh Boone Born 1985 249 192 16.0% Matt Bonner Born 1981 1161 207 17.0% Louis Amundson Born 1983 1168 209 18.0% Tyrus Thomas Born 1987 1220 213 19.0% Kris Humphries Born 1986 1221 214 20.0%

Here’s SF:

 Player Sum of MinutesSF MP Rank Percent of Minutes Trey Gilder Born 1985 5 1 0.0% Ryan Bowen Born 1976 8 3 0.0% Joe Alexander Born 1987 29 8 0.0% Taylor Griffin Born 1987 32 10 0.0% Yakhouba Diawara Born 1983 44 15 0.0% Desmond Mason Born 1978 66 26 0.0% Renaldo Balkman Born 1985 91 30 0.0% Mike Harris Born 1984 96 32 0.0% Alando Tucker Born 1985 96 33 0.0% Marcus Landry Born 1986 111 37 0.0% Danny Green Born 1988 115 40 0.0% Matt Carroll Born 1981 121 42 0.0% Kelenna Azubuike Born 1984 231 60 0.0% Adam Morrison Born 1985 241 66 1.0% Luke Walton Born 1981 272 73 1.0% Dominic McGuire Born 1986 240 77 1.0% Cartier Martin Born 1985 390 93 1.0% Brian Scalabrine Born 1979 84 108 1.0% Ricky Davis Born 1980 38 110 1.0% James Jones Born 1981 503 112 2.0% Quinton Ross Born 1982 301 117 2.0% Tracy McGrady Born 1980 673 132 3.0% Michael Finley Born 1974 709 140 3.0% Travis Outlaw Born 1985 499 143 4.0% James Johnson Born 1988 358 146 4.0% Joey Graham Born 1983 759 147 5.0% Devean George Born 1978 703 148 5.0% Bill Walker Born 1988 768 150 6.0% Reggie Williams Born 1987 782 151 7.0% DeMarre Carroll Born 1987 795 154 7.0% Rodney Carney Born 1985 857 162 8.0% Julian Wright Born 1988 242 166 8.0% Austin Daye Born 1989 915 176 9.0% Josh Howard Born 1981 918 177 10.0% Nicolas Batum Born 1989 918 178 11.0% Marquis Daniels Born 1981 937 180 11.0% Ime Udoka Born 1978 103 181 11.0% Kyle Korver Born 1982 952 182 12.0% Morris Peterson Born 1978 973 185 13.0% Jason Kapono Born 1982 976 186 14.0% James Singleton Born 1982 211 187 14.0% Jamario Moon Born 1981 448 195 14.0% Trenton Hassell Born 1980 782 201 15.0% Maurice Evans Born 1979 1317 222 16.0% Sam Young Born 1986 710 223 17.0% Antoine Wright Born 1985 1392 229 18.0% Andres Nocioni Born 1980 246 239 18.0% Mike Dunleavy Born 1981 1486 240 19.0%

Here’s SG:

 Player Sum of Minutes SG MP Rank Percent of Minutes Antonio Anderson Born 1986 15 5 0.0% Travis Diener Born 1983 26 18 0.0% Kareem Rush Born 1981 58 22 0.0% Othyus Jeffers Born 1986 72 27 0.0% Cedric Jackson Born 1987 74 28 0.0% Roko Ukic Born 1985 97 34 0.0% Coby Karl Born 1984 113 38 0.0% Mario West Born 1985 142 49 0.0% Kyle Weaver Born 1987 144 50 0.0% Raja Bell Born 1977 180 54 0.0% Alonzo Gee Born 1988 182 55 0.0% J.R. Giddens Born 1986 239 64 1.0% Kevin Ollie Born 1973 211 71 1.0% Jermaine Taylor Born 1987 303 76 1.0% Dominic McGuire Born 1986 67 77 1.0% Malik Hairston Born 1988 317 82 1.0% Garrett Temple Born 1987 334 86 2.0% Gerald Henderson Born 1988 355 88 2.0% Anthony Johnson Born 1975 24 98 2.0% Mardy Collins Born 1985 470 107 2.0% Michael Redd Born 1980 492 109 3.0% Bobby Brown Born 1985 200 114 3.0% Quinton Ross Born 1982 261 117 3.0% Sasha Vujacic Born 1985 575 118 4.0% Francisco Garcia Born 1982 575 119 4.0% Daequan Cook Born 1988 691 137 5.0% Rodrigue Beaubois Born 1989 700 138 5.0% Jodie Meeks Born 1988 719 142 6.0% Leandro Barbosa Born 1983 786 153 7.0% Stephen Graham Born 1983 804 156 7.0% Ronnie Price Born 1984 237 157 7.0% Luther Head Born 1983 813 159 8.0% Jannero Pargo Born 1980 828 160 9.0% Jerry Stackhouse Born 1975 855 161 10.0% Anthony Carter Born 1976 710 163 10.0% Allen Iverson Born 1976 820 165 11.0% Marcus Williams Born 1986 110 168 11.0% Sasha Pavlovic Born 1984 877 169 12.0% DeShawn Stevenson Born 1982 883 170 12.0% Tony Allen Born 1982 889 172 13.0% Ime Udoka Born 1978 841 181 14.0% Keyon Dooling Born 1981 225 184 14.0% Jarvis Hayes Born 1982 1032 191 15.0% Jamario Moon Born 1981 604 195 15.0% Devin Brown Born 1979 1060 196 16.0% Toney Douglas Born 1987 818 198 17.0% Trenton Hassell Born 1980 324 201 17.0% Larry Hughes Born 1979 1115 203 18.0% Marco Belinelli Born 1987 1121 205 19.0% Eddie House Born 1979 327 212 20.0% Sam Young Born 1986 611 223 20.0%

And here’s PG:

 Player Sum of Minutes PG MP Rank Percent of Minutes Oliver Lafayette Born 1985 22 6 0.0% Jason Hart Born 1979 22 7 0.0% Will Conroy Born 1983 36 12 0.0% Patrick Mills Born 1989 38 13 0.0% Mike James Born 1976 46 17 0.0% Travis Diener Born 1983 25 18 0.0% Mike Wilks Born 1980 59 23 0.0% Lindsey Hunter Born 1971 122 43 0.0% Lester Hudson Born 1985 131 47 0.0% Sundiata Gaines Born 1987 217 56 0.0% Chris Quinn Born 1984 223 57 0.0% Acie Law Born 1985 234 62 0.0% Marcus Banks Born 1982 244 67 1.0% Kevin Ollie Born 1973 52 71 1.0% Royal Ivey Born 1982 326 84 1.0% Anthony Johnson Born 1975 382 98 1.0% Bobby Brown Born 1985 319 114 2.0% Jamaal Tinsley Born 1979 589 121 2.0% Chucky Atkins Born 1975 644 125 3.0% Sebastian Telfair Born 1986 659 130 3.0% Jeff Teague Born 1989 719 141 4.0% Shaun Livingston Born 1986 796 155 4.0% Ronnie Price Born 1984 569 157 5.0% Anthony Carter Born 1976 149 163 5.0% A.J. Price Born 1987 865 164 6.0% Allen Iverson Born 1976 45 165 6.0% Marcus Williams Born 1986 762 168 6.0% Keyon Dooling Born 1981 746 184 7.0% Sergio Rodriguez Born 1987 1048 193 8.0% Daniel Gibson Born 1987 1068 197 9.0% Toney Douglas Born 1987 269 198 9.0% Nate Robinson Born 1985 1115 202 10.0% Earl Boykins Born 1977 1117 204 11.0% Gilbert Arenas Born 1982 1169 210 12.0% T.J. Ford Born 1984 1189 211 13.0% Eddie House Born 1979 890 212 14.0% Eric Maynor Born 1988 1269 218 15.0% Jerryd Bayless Born 1989 1304 220 16.0% Ty Lawson Born 1988 1316 221 17.0% Rafer Alston Born 1977 1421 231 18.0% Goran Dragic Born 1987 1285 235 19.0% D.J. Augustin Born 1988 1472 237 20.0%

You’ll note that near 20% the names start to get a little iffy. But the majority of these players could be had so for now that’s we’re the line stays.

Step#3:  Calculate the productivity of the players that account for just over 20% of the minutes played at each position (or just about 10 minutes per game)

Step #4: Set that as the replacement level for each position.

If we now modeled the projected wins for a team composed entirely of our refined replacement level  for both  the 10% and 20 % scenarios (See graph below):

So if we use 20% of the minutes played at each position,  a win total for a team composed solely of replacement level players now fluctuates between o and 15 wins. At 10% , the team looks like guys who really shouldn’t be in the NBA. Given that no team in the NBA has won less than 11 games, the results at 20% seem now even more in line with reality.  So we will  continue to calculate replacement level for NBA players based on the bottom tier of players based on overall minutes played and our revised algorithm per position up to the point where 20% of all player minutes at the position for the season are accounted for.

Replacement Level by position take #2

So now let’s see how everything else changes based on our re-build. The table & graph below illustrates the results for our replacement level by position:

The chart is below:

I improve the second chart significantly. You’ll note that the conclusion from the previous article hold. Tall People (Centers) and Point Guards have  more value over replacement than anyone else. As before the next step is to look at win difference by position of an average player vs. a replacement level  player. This is Basketball Wins over replacement by position (well call this WOR).

The gidyness still holds from before. Average Center and Point Guards have over time been much more valuable to teams than any of the other positions. Over the last 5 years the difference between an average center and a replacement level one  is 4 more wins than the same at shooting guard (and 2 at Point Guard). The short supply of tall people is really not a surprise however the short supply of ball handlers is.

The next steps are still (barring any other rebuilds to the baseline ) to start talking about WORP for individual players but you’ll have to wait to a future post for that.