Lance Thomas12,142+0.32 Jeff Teague2,695-0.07 David West17,671+1.40 PlayerPossessions playedDRAYMOND RATING Chris Bosh+1.14+1.25+0.12 Joel Embiid11,766+2.95 Manu Ginobili16,974+0.08 James Harden6,754+1.40 Serge Ibaka32,865+1.54 Jeremy Lamb4,710-0.93 JaMychal Green-0.39-0.32+0.07 Solomon Hill14,891+0.87 Roy Hibbert14,695+1.92 Jayson Tatum+1.44+1.34-0.10 Aron Baynes14,484+1.71 Elfrid Payton21,014-0.78 Maurice Harkless3,833+0.66 Mike Muscala2,889+0.64 Tyson Chandler18,693-0.09 Reggie Jackson-1.15-1.23-0.07 De’Aaron Fox5,626-0.17 Clint Capela18,110+1.39 Tim Duncan14,218+2.20 Willie Cauley-Stein+1.24+0.92-0.32 Lauri Markkanen3,496-0.81 George Hill26,013+0.64 Paul George6,639+0.09 Al Horford30,395+1.41 Maxi Kleber3,168+2.94 Ty Lawson17,022-1.31 Pau Gasol23,255+1.38 James Johnson17,746+1.33 Jon Leuer10,751-0.57 Jusuf Nurkic15,099+1.24 CJ McCollum-1.18-0.89+0.29 Goran Dragic2,134+0.11 Kent Bazemore22,184+0.16 Alex Len3,489+0.40 Nemanja Bjelica11,568+1.15 Manu Ginobili+0.71+0.61-0.10 Danny Green28,467+1.12 Vince Carter2,998-1.00 Patrick Beverley22,626+0.17 Jose Calderon-1.67-2.14-0.48 Steven Adams28,973+1.09 Jon Leuer+0.39+0.15-0.24 Luke Kennard3,218-1.21 Dwight Powell3,524+1.10 Jeremy Lamb-0.32-0.18+0.13 Tony Parker-1.44-1.50-0.06 PlayerPossessions playedDRAYMOND RATING Davis Bertans3,653+0.12 Mario Chalmers15,652+0.15 Iman Shumpert3,455-0.83 Tony Parker2,145-0.85 Jamal Murray15,101-0.79 Lance Stephenson20,349-0.52 Wayne Ellington-1.29-1.27+0.02 Russell Westbrook+1.16+0.02-1.14 Darren Collison-1.34-1.28+0.06 Jordan Hill10,087-0.45 Evan Turner27,518+0.61 Trey Lyles-0.46-0.16+0.30 Dion Waiters2,334-0.38 Eric Gordon5,347+0.45 Isaiah Canaan-2.13-1.79+0.34 Gordon Hayward26,388-0.23 Randy Foye13,985-0.32 Ian Clark10,859-0.39 PJ Tucker32,880+0.08 Marc Gasol30,496+0.71 Robert Covington21,084-0.07 Nik Stauskas2,164-2.23 Nerlens Noel+3.36+2.89-0.47 Amir Johnson20,436+0.75 Deron Williams17,520-0.31 Meyers Leonard-0.31-0.43-0.12 Dwight Powell+1.04+1.26+0.22 Tomas Satoransky4,634-1.07 Kyle Korver2,966-2.29 Dwight Powell12,343+0.59 PJ Tucker6,632+0.85 Jameer Nelson15,646-0.97 JJ Redick29,725+0.10 Jimmy Butler32,597+0.54 Gorgui Dieng21,118-0.82 Eric Bledsoe+0.81+0.98+0.17 Thabo Sefolosha+2.21+2.12-0.09 Jimmy Butler5,562+0.62 Shane Larkin-1.12-1.12-0.01 Mario Hezonja10,871-0.56 Boris Diaw15,683-0.04 Tim Frazier2,554-3.01 Domantas Sabonis4,021+0.22 Joakim Noah15,511+1.60 Luol Deng18,725+0.15 Shaquille Harrison3,032+0.88 Goran Dragic28,790+0.41 Kawhi Leonard6,178+0.25 Ben Simmons13,358+1.10 Dion Waiters-1.16-0.87+0.29 Kentavious Caldwell-Pope-0.38-0.80-0.42 Eric Bledsoe26,635+0.36 Taurean Prince3,462-1.14 Meyers Leonard10,837-0.10 Evan Turner3,896+2.23 Norman Powell3,207+0.71 Allen Crabbe18,711+0.33 Nikola Vucevic+1.83+1.71-0.12 Joe Ingles5,832-1.17 Tyler Johnson15,111+0.30 Anthony Tolliver-0.28+0.02+0.31 Danilo Gallinari4,818-0.65 Mason Plumlee+1.40+0.93-0.47 Norris Cole11,175-0.97 Enes Kanter4,397+0.01 Wesley Johnson+0.67+0.26-0.41 LeBron James39,997+0.19 Rudy Gay24,069+0.19 Amir Johnson+2.46+2.38-0.08 And here’s the data for last season (2018-19), with a minimum of 2,000 possessions defended. The Jazz’s Derrick Favors was the top defender, followed by the Knicks’ Mitchell Robinson, while the Cavaliers’ Collin Sexton was the worst defender in the league. Alex Len17,616+0.71 Garrett Temple18,146-0.15 Damian Lillard38,628+0.16 Cory Joseph23,771+0.57 Matthew Dellavedova18,129+0.16 John Wall31,634+0.07 Justise Winslow14,191+0.97 Kevin Durant35,683+1.44 Jerami Grant6,093+0.70 Derrick Rose3,020+0.27 Andre Iguodala29,712+0.11 Tristan Thompson+0.17+0.19+0.02 Tony Allen14,520+1.04 Draymond Green6,260+1.76 Jonas Valanciunas+0.57+0.91+0.34 Stephen Curry6,852-0.42 David Lee12,774+0.67 Avery Bradley26,335-0.54 Josh Richardson17,276+1.28 Nick Young14,675-1.26 Taurean Prince-0.69-0.83-0.14 Tyler Zeller+0.62+1.19+0.57 Ian Clark2,165-1.95 Jeremy Lamb18,210+0.06 Andre Drummond31,709+0.00 Thaddeus Young+1.19+1.01-0.18 Ian Mahinmi+3.03+2.80-0.23 Paul George+1.30+1.32+0.03 Donovan Mitchell12,171+0.04 Isaiah Thomas23,565+0.04 JR Smith25,891-0.64 CJ Miles17,938+0.03 Spencer Hawes11,803+0.78 Clint Capela+2.18+2.54+0.36 Jusuf Nurkic+3.25+3.18-0.06 Reggie Bullock10,929+0.01 Mike Muscala10,947-0.07 Montrezl Harrell5,060+1.82 Tyler Johnson-0.24-0.31-0.07 Marcus Smart22,997+0.00 Norris Cole-1.61-1.83-0.21 Jodie Meeks12,673-0.47 Frank Kaminsky13,278-0.69 Courtney Lee25,321-0.02 Derrick Favors+2.03+2.63+0.61 Jarrett Jack14,572-0.05 Rajon Rondo2,992-1.79 Rudy Gay+0.31+0.42+0.11 Jeff Teague-0.75-0.53+0.22 Terrence Jones12,064+0.00 Jae Crowder4,940+0.34 Luis Scola+0.30-0.15-0.45 De’Anthony Melton2,112-0.41 Kyle Kuzma10,183-0.06 Mike Scott15,790-0.34 Hollis Thompson13,414-0.21 Cody Zeller17,321+0.72 Buddy Hield-1.61-1.59+0.02 Jerryd Bayless-1.88-1.86+0.02 Jared Sullinger11,886+0.35 Marreese Speights11,425+0.40 Nikola Jokic+2.62+2.08-0.53 Jeff Teague29,994-0.13 Danny Green6,093+0.08 Bradley Beal34,063-0.14 Yogi Ferrell2,330-0.92 Harrison Barnes5,415-0.42 Ed Davis3,157+0.23 Royce O’Neale3,884+0.75 Thaddeus Young31,870-0.22 Ersan Ilyasova21,881-0.41 Draymond Green+4.43+5.09+0.66 Bobby Portis10,791-0.20 Tyler Zeller11,412+1.09 DeMar DeRozan6,023-0.96 Jrue Holiday25,597+0.80 Ian Clark-1.99-2.10-0.11 Jeff Green28,433-0.23 Aaron Brooks11,764-0.17 Iman Shumpert+0.80+0.48-0.32 Stanley Johnson12,913-0.25 Khris Middleton30,940-0.03 Kyle O’Quinn11,843+1.52 Mitchell Robinson2,882+3.32 Damian Lillard7,338+0.40 Danilo Gallinari-0.44-0.40+0.05 Avery Bradley-0.62-0.80-0.18 Jaylen Brown13,507+1.25 Jrue Holiday+0.72+1.25+0.54 Shai Gilgeous-Alexander5,090+0.87 Gorgui Dieng+1.66+1.03-0.62 Myles Turner4,656+2.43 Jerryd Bayless13,461-0.32 DeAndre’ Bembry4,311-1.00 Mirza Teletovic11,261-0.22 Aaron Gordon20,045+0.40 Kentavious Caldwell-Pope29,067-0.88 T.J. Warren2,895-2.27 Lance Stephenson2,511-1.20 Trey Burke17,019-0.36 Ben McLemore-1.15-1.34-0.19 Joe Ingles22,212-0.37 JaMychal Green3,244-0.66 Chandler Parsons18,098-0.40 Mike Dunleavy12,931+1.08 Jason Terry13,194-0.32 Omri Casspi-0.11-0.15-0.05 Gordon Hayward-0.11-0.25-0.15 Justin Holiday16,591+0.38 Trevor Booker+0.47+0.57+0.10 Taj Gibson+1.23+1.45+0.22 Al-Farouq Aminu5,689-0.92 Shelvin Mack2,577-1.69 Danilo Gallinari17,302-0.57 Kyle Kuzma5,063-0.25 Ben McLemore17,957-0.94 Kenrich Williams2,390+0.09 Avery Bradley4,044+0.42 Jerian Grant-0.75-0.57+0.18 DeMarcus Cousins+2.58+2.68+0.10 Kyle Singler11,355-0.53 Zaza Pachulia17,765-0.33 Larry Nance Jr.12,949-0.49 Brandon Ingram-1.01-0.95+0.06 Goran Dragic-0.92-0.61+0.32 Richard Jefferson-0.76-0.77-0.01 Patrick Beverley5,029+1.25 Brandon Ingram12,815-0.07 Bradley Beal6,505-0.80 Isaiah Thomas-2.62-1.99+0.63 Jaren Jackson Jr.3,076+1.51 Dennis Smith Jr.3,200+1.15 Malik Monk2,703-1.98 Joe Harris-1.57-1.56+0.01 Kevin Durant6,753+0.94 Paul Pierce12,678+0.59 Brandon Bass-0.13-0.08+0.04 Tony Snell-0.85-0.97-0.11 Gary Harris19,416-0.64 Jordan Hill-0.25-0.52-0.27 Vince Carter+0.26+0.44+0.17 Corey Brewer21,400-0.67 Al-Farouq Aminu26,956+0.03 Ryan Anderson18,873-0.52 Tobias Harris6,998-0.24 Miles Plumlee11,556+1.04 Channing Frye16,675-0.65 Taj Gibson3,607-0.47 Dennis Schroder-2.10-1.91+0.19 Shaun Livingston2,710+0.08 Patrick Beverley+0.93+0.83-0.09 Allen Crabbe2,444+1.09 Brandon Knight16,757-0.80 Frank Kaminsky-0.74-1.00-0.25 Dion Waiters21,066+0.45 James Harden40,828+0.52 Tyus Jones3,348-1.79 Derrick Williams11,367-0.83 * Defensive Rating Accounting for Yielding Minimal Openness by Nearest Defender Kyle Singler-0.50-0.64-0.14 T.J. McConnell-0.40-0.55-0.15 Jeremy Lin18,390+0.46 T.J. McConnell15,302-0.03 Robert Covington+2.35+2.08-0.26 Landry Shamet4,303-0.05 Rodions Kurucs3,041+0.28 Garrett Temple4,386-0.31 Kyrie Irving31,938-0.99 Josh Richardson5,296+0.16 Paul Pierce+0.83+1.08+0.25 Otto Porter Jr.24,148-1.03 Michael Carter-Williams17,756-0.03 Jakob Poeltl3,061+0.64 Kelly Oubre Jr.14,377-1.08 Tim Hardaway Jr.-2.23-2.07+0.16 Myles Turner17,509+1.73 Anthony Morrow10,184-1.18 Kyle Lowry+0.89+0.88-0.01 David Lee+1.29+1.19-0.10 Jabari Parker15,480-1.24 Evan Fournier5,642-0.56 J.J. Barea16,230-1.25 Blake Griffin29,325+0.16 Pascal Siakam7,195+1.65 Luka Doncic4,912-0.81 Zach LaVine17,990-1.36 Derrick Rose17,293+0.47 Paul Millsap30,217+0.39 Buddy Hield13,734-0.78 Paul Millsap+2.64+2.32-0.32 Jerami Grant20,433+1.10 Ryan Arcidiacono4,105-0.25 PlayerPossessions playedDRAYMOND RATING Nemanja Bjelica3,950+1.76 Emmanuel Mudiay3,418+0.48 Marvin Williams+0.59+0.52-0.07 Jaylen Brown4,698+1.18 Nerlens Noel2,437+2.15 Bojan Bogdanovic5,659-0.32 Omer Asik+1.87+1.67-0.20 Wilson Chandler21,126+0.76 Ed Davis+1.71+1.46-0.25 Shelvin Mack-1.28-1.34-0.06 Kenneth Faried17,635-0.82 Enes Kanter-1.59-1.55+0.03 Jason Terry-0.54-0.42+0.12 Ivica Zubac2,365+2.43 Nikola Mirotic18,138+0.57 James Harden-0.33-0.02+0.31 Devin Booker-2.76-2.51+0.25 Derrick Favors24,324+1.86 Raymond Felton16,949+0.97 Jordan Clarkson-2.79-2.68+0.11 Danuel House Jr.2,369+0.40 Jalen Brunson3,346-0.94 Larry Nance Jr.+2.01+1.54-0.46 Anthony Tolliver17,263+0.08 Kelly Olynyk20,609-0.01 John Wall2,404-0.91 Jamal Crawford25,169-1.28 Chris Bosh12,709+0.06 Shane Larkin10,117-0.49 LaMarcus Aldridge6,012+1.82 Jahlil Okafor2,039+1.52 Dorian Finney-Smith4,200+1.31 Derrick White3,964+1.74 Ricky Rubio+1.32+0.89-0.42 Zach Collins3,419+0.49 Ish Smith2,763+0.39 Norman Powell10,579-0.53 DeMarre Carroll3,942-0.54 Ish Smith-0.57-0.35+0.22 John Wall+0.10+0.27+0.17 Shelvin Mack15,274-0.49 Giannis Antetokounmpo6,339+2.13 Jameer Nelson-1.84-1.93-0.10 Jrue Holiday5,233+0.24 Dwyane Wade25,627+0.08 Jayson Tatum5,809+1.26 Collin Sexton5,374-3.59 Jonas Valanciunas23,901+0.85 Al Horford4,834+1.18 Nene16,100-0.03 Ty Lawson-1.62-1.98-0.36 Montrezl Harrell-0.05+0.56+0.61 Alec Burks-1.50-2.08-0.58 Brandon Ingram3,850+1.15 Nikola Vucevic5,515+0.94 Ante Zizic2,259-0.44 Nikola Mirotic+0.79+0.93+0.14 Juancho Hernangomez2,863+0.83 Seth Curry3,615+1.03 Tony Snell20,715-0.13 Kyle O’Quinn+2.12+2.20+0.08 Lou Williams4,812-1.67 Which players’ defense had been underrated or overrated?Change in CARMELO defensive ratings since 2013-14 after incorporating DRAYMOND*, for players with a minimum of 10,000 possessions Jabari Parker-1.46-1.99-0.53 Markieff Morris2,863+0.94 Cory Joseph4,489+1.13 Terrence Ross4,804-1.14 Kosta Koufos+1.57+1.99+0.42 Domantas Sabonis11,443+0.44 Luc Mbah a Moute16,502+1.56 Miles Bridges3,625-1.35 Chris Paul+1.46+1.03-0.43 Marreese Speights-0.54-0.31+0.23 Tyreke Evans18,965-0.40 Steven Adams6,187+0.78 Monte Morris4,561-0.62 Courtney Lee-0.71-0.75-0.03 Randy Foye-1.05-1.04+0.02 Chris Paul31,344-0.58 Iman Shumpert20,064-0.17 Evan Turner-0.14-0.04+0.10 Pascal Siakam+1.64+1.55-0.09 Garrett Temple+0.35+0.28-0.07 James Johnson+1.49+1.78+0.29 CJ McCollum6,340+0.70 Marcin Gortat28,529+0.84 Rodney Hood4,642+0.12 Myles Turner+2.35+2.72+0.37 Noah Vonleh+0.95+0.91-0.04 Solomon Hill+0.29+0.42+0.13 Kyle Korver+0.20+0.19-0.02 DeMarre Carroll+0.58+0.63+0.05 Ian Mahinmi14,184+0.88 Blake Griffin+0.97+0.80-0.17 Jordan Clarkson22,324-1.03 Noah Vonleh11,214+0.47 Andre Roberson15,147+2.06 Roy Hibbert+2.34+2.71+0.36 Dennis Schroder5,385-0.42 Michael Kidd-Gilchrist2,511+1.92 Jonathan Isaac4,456+0.61 Omri Casspi13,641-0.25 Shabazz Napier2,193+1.92 Vince Carter18,232-0.09 Jeff Green-0.99-0.81+0.18 Karl-Anthony Towns5,392+0.53 Victor Oladipo+0.85+0.75-0.10 Monta Ellis22,806-0.32 Bismack Biyombo+1.46+1.40-0.06 Lonzo Ball3,122+1.00 Devin Booker4,792-0.93 Greg Monroe+0.81+0.32-0.50 Robin Lopez+1.24+1.68+0.44 Boris Diaw+0.73+0.35-0.37 Aron Baynes+1.82+2.49+0.66 Al Jefferson+0.90+0.45-0.46 Terrance Ferguson4,504-0.33 Ed Davis17,428+0.43 Brandon Knight-2.13-2.01+0.12 LaMarcus Aldridge33,382+1.27 Mario Hezonja-1.07-1.23-0.16 Matt Barnes18,283-0.10 Daniel Theis2,061+0.34 Tim Hardaway Jr.4,345-1.16 Thomas Bryant3,241+0.17 Terry Rozier4,133+0.30 Patty Mills-1.01-1.08-0.07 Richaun Holmes2,558+2.54 Steven Adams+1.61+1.81+0.19 Tyreke Evans3,134+0.35 Carmelo Anthony24,805-0.59 Nicolas Batum4,923+0.62 Elfrid Payton2,778+0.23 Derrick Rose-2.11-1.68+0.43 Malcolm Brogdon4,463+0.88 Will Barton3,155-1.00 Kawhi Leonard27,674+0.88 Kent Bazemore3,658-1.07 Josh Smith13,122+1.90 Nene+2.73+2.44-0.29 Ersan Ilyasova-0.23-0.40-0.17 Devin Harris15,894-0.29 Carmelo Anthony-1.31-1.43-0.11 Matthew Dellavedova-1.16-0.60+0.56 Dario Saric4,371+0.11 Kyle Kuzma-1.15-1.07+0.08 Clint Capela5,313+1.13 Noah Vonleh3,662+0.08 Basketball, in some sense, is fundamentally a shooting game. Shooting isn’t the only important action that takes place on a basketball court, obviously. But if no one kept track of who was taking shots and making buckets, we’d have, at best, an extremely fuzzy impression of which players were actually any good, even if we had access to all their other statistics.But believe it or not, this had long been the situation when it came to measuring player defense. There are individual defensive statistics such as rebounds and steals, of course. But there’s no direct measure of shooting defense (other than blocks, which account for a relatively small fraction of missed shots). If an opponent gets hot against your team and shoots 53 for 91 en route to scoring 130 points, we know your team defended poorly in the aggregate, but we don’t know which players to blame.That is, until a few years ago, when the NBA started publishing data on opponents’ shooting. Last regular season, for example, NBA Defensive Player of the Year Rudy Gobert defended a league-high 1,426 shots, according to motion tracking data by Second Spectrum, which identifies the nearest defender on every field goal attempt. Opponents made only 45 percent of those field goal attempts, well below the roughly 49 percent that Second Spectrum estimates “should” have gone in against average defense for a given distance to the basket.We’ve been obsessed with this opponents’ shooting data for a while, in part because it sometimes seemed to track closely with players who had stronger or weaker defensive reputations than you would infer from other advanced statistics such as Real Plus-Minus. Boston’s Kyrie Irving was regarded as a slightly above-average defender by RPM last year, for instance. But his opponents’ shooting data suggests he’s a big liability instead. On the other hand, Toronto’s Serge Ibaka was an excellent defender based on opponents’ shooting, whereas RPM regards him as just average.So this year, we decided to evaluate the opponents’ shooting data in a more comprehensive way and incorporate it into our projection system, CARMELO. Just as CARMELO is a goofy backronym (Career-Arc Regression Model Estimator with Local Optimization) that honors one of our favorite players, Carmelo Anthony, we decided to give our new defensive rating a player-centric name, this time in honor of the Golden State Warriors’ Draymond Green, who has long been one of the best players in basketball by opponent shooting. So our new rating is called DRAYMOND, which stands for….DefensiveRatingAccounting forYieldingMinimalOpenness byNearestDefender🙄All right, so the acronym may or may not catch on. But it does get at one essential discovery we made in playing around with the opponents’ shooting data: the idea of minimizing openness. The main goal of shooting defense, especially in today’s spacing-centric, ball-movement-forward offensive era, is really to minimize the chance of an open shot.So when I cited Gobert’s numbers earlier in this article, for instance, the most impressive part was not that opponents shot poorly against him, although that helped the Jazz, of course. Rather, it was that he was the nearest defender on so many shots: about 26 shots per 100 possessions that he was on the floor last year1Between the playoffs and regular season combined. as compared with a league average of about 17 shots defended per 100 possessions. By contrast, Oklahoma City’s Russell Westbrook — whom DRAYMOND regards as being vastly overrated by other defensive metrics — was the nearest defender on only 12 shots per 100 possessions. Some of this has to do with Westbrook’s and Gobert’s respective positions — centers naturally defend more shots than guards do, a factor that DRAYMOND corrects for (see below). But even accounting for that, it’s clear that some players are much more impactful defenders than others.I’m sure you’re curious to see some data, but first, an explanation of how DRAYMOND is calculated. We’ll keep it pretty brief.As I mentioned above, what we’re really interested in is how much value a defender provides relative to an open shot. That is to say, we generally don’t want to punish a player for happening to be the nearest defender according to the Second Spectrum data. Some defense is generally better than none; if Player X hadn’t defended the shot, it’s possible that no one else would have.2A more advanced version of DRAYMOND might identify which player was supposed to have defended a shot (e.g., Westbrook was originally assigned to Damian Lillard) and compare it against which player was actually the nearest defender (e.g., Stephen Adams picked up the shot after Lillard blew by Westbrook). But that requires more detailed data than is currently available publicly, so we’re sticking with the simpler version for the time being.Through trial and error, we found that DRAYMOND performs best3By regressing against five-year Regularized Adjusted Plus-Minus (RAPM); see the discussion later in this article for more detail. if you assume that shooting percentages on open shots are about 8 percentage points higher than against average defense. For instance, if a certain type of above-the-break 3-pointer is made 34 percent of the time against average defense, we’d expect it to go in about 42 percent of the time if it was truly open.This allows us to calculate an initial score that we call RAW_DRAYMOND. For example, if a player faced 100 2-point shots and allowed 46 of them to go in when you’d expect 56 percent of them to be converted if wide open, that player prevented …(.56-.46) x 100 x 2 = 20… about 20 points from being scored with his defense. (Obviously, this player could have provided additional value based on his defense against 3-point shots. Indeed, since 3-point shots are worth more than 2-pointers — hashtag #math — players who are effective at defending threes are especially rewarded by DRAYMOND.)However, there are several adjustments we need to make in getting from RAW_DRAYMOND to regular DRAYMOND:Since DRAYMOND is based on both regular-season and playoff data, we adjust for the fact that defenders face slightly tougher shooters on average in the playoffs.We divide RAW_DRAYMOND by the number of possessions that the player was on the floor, so that DRAYMOND (like RPM and most other NBA stats) is a rate statistic rather than a counting statistic.We adjust the number of shots defended based on a player’s position. The average point guard and shooting guard defends about 15 shots per 100 possessions, the average small forward defends about 16 shots, the average power forward 19 shots, and the average center 22 shots.4The adjustment works by multiplying the number of shots faced by 17 then dividing it by the number of shots faced on average at the position. For instance, for a power forward, the number of shots defended is multiplied by 17/19ths. This somewhat equalizes defensive value over the five positions. Even so, bigs are generally the most valuable defenders in basketball according to DRAYMOND, as they are under most other advanced statistics.Finally, we subtract the value of league-average shooting defense per possession from each player’s score. Thus, like RPM and Box Plus/Minus (BPM), the statistics that CARMELO has traditionally used to make its projections, DRAYMOND is a plus-minus statistic measured per 100 possessions, where a score of 0 represents average defense.Among players who have played at least 10,000 possessions over the past six seasons (the NBA’s opponents’ shooting data goes back to 2013-14), the top defender according to DRAYMOND is … Draymond Green, who has provided the Warriors with +3.2 points per 100 possessions of defensive value based on his scoring defense alone, not counting all of the other ways (e.g., steals) that he produces defensive value. Green is followed on the list by a fairly star-studded cast of defenders: Joel Embiid, Kristaps Porzingis (!), Rudy Gobert, Tim Duncan, Andre Roberson and Anthony Davis. Meanwhile, the worst-rated defender over the past six seasons according to DRAYMOND is Rajon Rondo. Trevor Ariza+0.78+0.03-0.75 Marc Gasol6,448+0.74 Darren Collison25,990-0.46 Derrick Favors4,036+3.74 Tobias Harris31,349-0.31 Tim Duncan+4.86+5.14+0.28 Marcus Smart4,760-0.01 Jayson Tatum12,138+0.53 Nemanja Bjelica+0.86+1.68+0.82 OG Anunoby2,920-0.05 Aaron Gordon5,817-0.06 Dwyane Wade-0.55-0.60-0.05 Brandon Bass12,616-0.02 Justin Jackson3,505-0.16 Tyler Johnson3,241-0.17 Meyers Leonard2,212-2.31 Khris Middleton6,334-0.19 Paul George32,598+0.33 Kelly Olynyk3,795-0.21 JaMychal Green14,173+0.18 Jaylen Brown+0.11+0.71+0.60 Lou Williams-2.83-2.64+0.18 Michael Kidd-Gilchrist+1.66+1.91+0.25 Ramon Sessions13,288-0.62 Jake Layman2,861-0.25 James Ennis III12,375-0.59 Jerami Grant+0.27+0.82+0.55 Lance Stephenson-0.53-1.13-0.59 Kevin Durant+0.57+1.03+0.46 Mike Muscala+0.58+0.40-0.18 Spencer Dinwiddie13,248+0.07 Marcus Morris28,223+0.02 Kawhi Leonard+2.28+2.25-0.03 Derrick Jones Jr.2,389+3.10 Langston Galloway3,888+0.24 Josh Hart3,796+1.72 Patty Mills23,097-0.51 Tobias Harris-0.40-0.47-0.07 Will Barton-0.98-1.15-0.17 Andrew Bogut+5.17+4.92-0.25 Donovan Mitchell5,923-1.08 Devin Booker19,065-0.80 Anthony Davis+2.85+3.56+0.71 Elie Okobo2,040-0.85 Terrence Jones-0.56-0.93-0.37 Dirk Nowitzki24,696-0.37 Michael Carter-Williams+0.23+0.12-0.11 Marcin Gortat+2.26+2.42+0.16 James Ennis III-0.28-0.62-0.34 David Nwaba2,034-0.32 Dwyane Wade4,006+0.34 Spencer Dinwiddie-1.30-1.07+0.23 Josh Okogie3,830-1.45 Jarrett Jack-1.23-0.98+0.25 Michael Kidd-Gilchrist17,801+0.99 Sterling Brown2,651-0.29 Mario Hezonja2,549-1.22 PJ Tucker+1.23+0.98-0.25 Stanley Johnson+0.55+0.25-0.31 Gorgui Dieng2,247-0.59 Buddy Hield5,744-0.22 DeMar DeRozan-1.15-1.55-0.39 Rondae Hollis-Jefferson2,847+0.11 Gerald Green18,429+0.00 Jeff Green4,501-0.67 E’Twaun Moore19,870-0.48 Nick Young-2.61-2.56+0.05 Dewayne Dedmon+2.04+2.62+0.59 Zach Randolph+0.12-0.34-0.46 Wes Iwundu2,757+1.69 Wesley Matthews4,656-1.01 Russell Westbrook6,193-0.84 E’Twaun Moore3,187-1.44 Joe Johnson25,036-0.52 T.J. McConnell3,358+0.62 Reggie Bullock3,974-0.86 Timofey Mozgov14,696+1.57 Nik Stauskas-2.08-2.07+0.01 Josh Smith+1.60+2.39+0.80 Andrew Wiggins5,400+0.14 Luc Mbah a Moute+1.59+2.21+0.62 Allonzo Trier3,104-0.90 Allen Crabbe-1.50-1.34+0.16 Brook Lopez+1.22+2.00+0.78 Mike Scott-1.18-1.15+0.03 Patty Mills4,431-0.96 Tristan Thompson2,445-0.25 Mikal Bridges5,176-0.98 Jerian Grant2,016-0.99 Josh Jackson4,267+0.56 Nik Stauskas13,971-0.56 Caris LeVert2,593-0.97 Enes Kanter24,020-0.18 Kyrie Irving5,434-1.01 Dante Cunningham-0.05-0.85-0.80 Mike Conley-0.38+0.06+0.44 Ersan Ilyasova3,315-0.20 Mike Conley4,816+0.38 Cedi Osman5,021-1.10 Otto Porter Jr.3,634-1.14 Jamal Murray6,100-0.53 Kyle Lowry35,784+0.02 Stanley Johnson2,607-0.54 T.J. Warren15,353-0.55 Rudy Gobert24,889+2.40 Austin Rivers4,753+0.11 DeAndre Jordan+3.11+2.87-0.24 Jonas Jerebko+0.23+0.24+0.02 Jamal Murray-1.66-1.72-0.07 Serge Ibaka+1.53+1.92+0.39 Ryan Anderson-1.85-1.57+0.28 Zach LaVine4,547-0.83 Al-Farouq Aminu+1.91+1.49-0.43 DeMarcus Cousins24,075+1.00 Ricky Rubio4,414-1.44 Mason Plumlee4,086+1.33 Kyle Anderson12,802+0.05 Emmanuel Mudiay-2.25-2.41-0.17 Mike Scott3,520-0.32 Terry Rozier+0.09-0.17-0.26 Jerian Grant10,248-0.03 Ben Simmons6,761+0.97 Channing Frye+0.26+0.10-0.16 Reggie Jackson4,971-1.82 Bryn Forbes5,200-1.82 Trae Young5,570-1.83 Joe Johnson-0.91-1.02-0.11 Jae Crowder27,620+0.16 DeAndre Jordan34,072+0.96 Nikola Jokic6,263+0.87 Lance Thomas-1.01-0.75+0.26 Ricky Rubio26,045-0.99 Quinn Cook2,649-2.11 JJ Redick-1.66-1.25+0.41 Reggie Bullock-0.91-0.69+0.22 George Hill+0.38+0.53+0.15 Kevin Love+1.16+1.15-0.01 Jared Dudley18,767+0.42 Kris Dunn2,898-0.42 Matt Barnes+0.57+0.34-0.23 James Ennis III3,105-2.68 Brandon Jennings14,286-1.16 Trevor Ariza4,997-3.25 Wilson Chandler-0.75-0.15+0.60 Al Horford+2.23+2.45+0.22 You can download a complete set of DRAYMOND data dating back to 2013-14 at this link.But does DRAYMOND measure something that’s actually meaningful? To test this — and I have to apologize because there are a lot of similarly named statistics here with confusing acronyms — we regressed DRAYMOND and defensive BPM5Specifically, the raw version of BPM, without the adjustment for team performance. against five-year defensive Regularized Adjusted Plus-Minus (RAPM). What the hell does that mean? BPM is based on conventional box score statistics — most importantly rebounds, blocks and steals for the purposes of measuring defense. DRAYMOND is based on opponents’ shooting. RAPM, meanwhile, measures how much better or worse a team plays when a player is on or off the floor. In the long run, RAPM is basically6I have a couple of technical objections to RAPM, based on the question of whether a player should essentially be punished for his teammates performing well while he’s off the floor, but I’ll spare you those for now. the “right” way to measure player value, since it can account for all the direct and indirect contributions a player makes that may or may not have a corresponding statistic attached to them. In the short run and even the medium run, however (remember all that misleading data people cited about how the Warriors were so good without Kevin Durant?), RAPM can be extremely noisy. So RAPM is great if you’re looking back over a five-year sample, as we’re doing here, but on-court/off-court statistics need to be treated with extreme caution over small samples.In any event, what we found is that BPM and DRAYMOND basically do equally well in predicting long-term RAPM. What that means is that the opponents’ shooting data is basically as powerful as all box score defensive statistics combined in predicting how much value a player’s defense truly has over the long run.We also found, however, that BPM and DRAYMOND are largely not redundant with one another. Blocks, steals and rebounds, which BPM captures, are certainly valuable things, and DRAYMOND does not purport to measure those. But they are also not especially good proxies for shooting defense. There are some players such as Green and Gobert who are even better defenders than you’d gather from their box score stats, even though those stats are pretty good. But there are others like Trevor Ariza, who gets lots of steals but has been rated poorly by DRAYMOND in recent seasons. That doesn’t mean that Ariza is a poor defender, just that you need to take the good (steals) with the bad (allows opponents to convert field goals at a high rate) when evaluating him.Let’s conclude with a list of players who are most affected, positively or negatively, by the incorporation of DRAYMOND. The table below compares our old CARMELO defensive ratings, which were based on a mix of two-thirds RPM and one-third BPM, to our new version, which still uses these statistics but also uses DRAYMOND.7As a technical aside, RPM is essentially a combination of BPM and one-year RAPM. That is, it leans fairly heavily on box score statistics because RAPM is quite noisy over the short run. Therefore, DRAYMOND is picking up information that isn’t well-measured by either RPM or BPM. Here are the old and new defensive ratings for everyone with at least 10,000 possessions played since 2013-14. Wayne Ellington2,965+0.02 Kenneth Faried-0.30-0.82-0.52 PlayerOld (based on RPM and BPM)New (incorporating DRAYMOND)Net Change Marc Gasol+2.49+2.36-0.14 LaMarcus Aldridge+1.19+1.62+0.43 Gerald Green-1.82-1.44+0.38 Wesley Matthews30,095+0.06 Harrison Barnes33,280-0.28 Andre Iguodala+1.89+1.27-0.61 Jose Calderon16,539-1.54 Eric Bledsoe5,900+1.23 Jae Crowder+0.38+0.39+0.01 Thon Maker2,220+1.11 Jamal Crawford-3.25-3.54-0.29 * Defensive Rating Accounting for Yielding Minimal Openness by Nearest Defender Jared Dudley2,749+1.40 Draymond Green38,282+3.16 Quincy Acy10,497+0.61 Malik Beasley4,532-1.88 Anthony Davis4,014+1.15 Rajon Rondo22,941-1.55 Andre Roberson+2.47+3.07+0.60 Wayne Ellington17,863-0.68 Dwight Howard24,588+0.20 Klay Thompson-0.91-0.34+0.57 Dante Cunningham19,597-1.17 Nicolas Batum+0.15-0.22-0.37 Wendell Carter Jr.2,311+0.65 Tyreke Evans-0.64-0.74-0.10 Gerald Henderson16,500+0.31 Mirza Teletovic-1.67-1.20+0.47 Rodney Stuckey-1.33-1.47-0.15 Jimmy Butler+1.32+1.28-0.04 Giannis Antetokounmpo33,511+1.23 Joe Harris13,015-0.19 D.J. Augustin-2.33-2.45-0.12 Jonathon Simmons2,408-0.79 Kyle Lowry6,510+0.57 Rudy Gobert+4.66+5.09+0.43 Trey Burke-2.72-2.36+0.36 Kevin Love28,026-0.24 * Defensive Rating Accounting for Yielding Minimal Openness by Nearest Defender Thaddeus Young5,391-0.08 Langston Galloway-0.81-0.30+0.51 Larry Nance Jr.3,684+0.23 Elfrid Payton-0.35-0.65-0.30 Bismack Biyombo17,520+0.78 Spencer Hawes+0.77+1.12+0.36 Alec Burks2,874-1.06 Evan Fournier-1.48-1.45+0.02 Luol Deng+0.57+0.56-0.01 Hassan Whiteside+2.74+3.08+0.34 Alex Len+1.05+1.38+0.33 Josh Richardson+0.43+0.75+0.32 Jamal Crawford2,647-2.40 Will Barton20,048-0.54 Marcus Morris-0.48-0.42+0.06 Hollis Thompson-2.08-1.77+0.31 Victor Oladipo2,362-1.84 Pat Connaughton3,493+1.90 Deandre Ayton4,645+0.62 Doug McDermott14,334-0.74 Patrick Patterson21,197+0.47 Rodney Hood19,067-0.62 Greg Monroe21,907-0.56 Rodney McGruder3,272+0.03 Julius Randle18,720-0.72 CJ McCollum28,793+0.38 Dewayne Dedmon13,581+1.25 Eric Gordon-1.76-1.41+0.35 PlayerOld (based on RPM and BPM)New (incorporating DRAYMOND)Net Change Aaron Gordon+0.27+0.52+0.25 Tristan Thompson27,936+0.36 Darius Miller3,861+0.70 Nikola Vucevic26,406+0.16 Quincy Acy-0.21+0.19+0.39 Devin Harris-0.80-0.67+0.13 Jonathon Simmons-0.92-1.47-0.55 Zach Randolph21,896-0.84 Mason Plumlee22,777+0.21 Jabari Parker3,713-0.40 Trevor Ariza37,477-1.25 Langston Galloway15,734+0.62 Joakim Noah+3.28+2.97-0.30 Austin Rivers-1.70-1.49+0.21 Kristaps Porzingis+1.50+2.65+1.15 Justise Winslow4,093-0.41 JaVale McGee3,690+2.17 David West+2.61+2.53-0.08 Bojan Bogdanovic24,638-0.74 Chris Paul4,743-0.89 Damian Lillard-1.27-1.08+0.18 J.J. Barea-2.39-2.41-0.01 Kyle Anderson+2.91+2.14-0.77 Richard Jefferson14,457-0.35 Joel Embiid+3.16+4.17+1.01 Deron Williams-0.92-0.74+0.17 Dennis Schroder23,921-0.33 John Collins4,039+0.88 Julius Randle-0.62-0.94-0.33 Nerlens Noel14,418+0.51 Tony Parker22,184-0.55 Andrew Wiggins-2.06-1.82+0.24 Doug McDermott-2.42-2.53-0.11 Patrick Patterson+0.14+0.31+0.18 Jason Smith-0.44-0.30+0.15 Willie Cauley-Stein4,851-0.37 Andre Drummond+1.84+1.40-0.44 Bogdan Bogdanovic4,205-0.48 Terry Rozier13,805+0.03 Rudy Gay4,216+0.69 Gordon Hayward4,582+0.74 Mike Conley23,955+0.23 Brandon Jennings-2.44-2.53-0.09 Nicolas Batum31,707-0.13 D’Angelo Russell16,686-0.90 John Henson15,221+1.14 DeMar DeRozan36,103-0.85 Nikola Mirotic3,444+0.39 Wesley Matthews-0.46-0.35+0.11 Serge Ibaka5,258+2.63 Kevin Knox4,596-1.42 Doug McDermott2,906-0.45 Justin Holiday-0.09+0.09+0.18 Bojan Bogdanovic-2.29-2.20+0.09 Aaron Brooks-2.47-2.38+0.09 Markieff Morris+0.76+0.85+0.09 Jordan Clarkson4,606-0.40 Bobby Portis-1.45-1.37+0.08 Donovan Mitchell+0.26+0.34+0.08 Jodie Meeks-1.90-1.75+0.15 Zaza Pachulia+2.47+1.74-0.72 Karl-Anthony Towns+0.31+0.38+0.07 Russell Westbrook35,302-1.04 Robin Lopez25,657+1.43 DeMarre Carroll26,019+0.29 Marcus Morris5,009-0.33 Brook Lopez25,200+1.60 Pau Gasol+2.16+2.21+0.05 PlayerPossessions playedDRAYMOND RATING Eric Gordon28,024-0.26 Kemba Walker-0.80-0.10+0.70 D.J. Augustin4,990-1.77 Jared Dudley+0.88+1.07+0.19 Ramon Sessions-1.74-1.70+0.03 Tony Allen+2.82+2.86+0.03 Brook Lopez6,040+2.53 Tyson Chandler+2.47+2.23-0.24 Shaun Livingston21,495+0.79 Joel Embiid5,419+2.40 Jonas Jerebko15,123+0.14 Wayne Selden3,048-1.49 Gary Harris4,427+1.42 Jarrett Allen4,774+0.87 D’Angelo Russell5,600+0.33 Montrezl Harrell11,001+1.44 Darren Collison4,693-1.44 Klay Thompson7,394+0.80 Cory Joseph-0.15+0.06+0.21 Wesley Johnson19,012-0.22 Robin Lopez3,387+2.35 Malcolm Brogdon-0.63-0.62+0.00 Dario Saric-0.80-0.79+0.00 Pascal Siakam12,798+0.88 Trey Lyles2,390+0.64 The best defender according to DRAYMOND is DraymondNBA players by DRAYMOND* defensive ratings, based on opponents’ shooting data in the regular season and playoffs, with a minimum of 10,000 possessions played since 2013-14 Rondae Hollis-Jefferson+1.15+0.80-0.35 Bruce Brown3,135+2.21 Alfonzo McKinnie2,709-0.22 Dirk Nowitzki+0.06+0.05+0.00 Taurean Prince11,091-0.62 Rudy Gobert5,786+2.82 CARMELO DEFENSIVE RATING Maurice Harkless20,198+0.77 Kentavious Caldwell-Pope4,447-2.49 LeBron James4,228+0.40 Taj Gibson26,231+0.96 Ben Simmons+1.70+1.49-0.21 Dewayne Dedmon3,516+0.76 Andrew Wiggins29,659-0.60 Robert Covington2,548+0.69 Arron Afflalo19,467-0.71 Otto Porter Jr.+0.78+0.15-0.63 Anthony Morrow-1.67-1.86-0.19 Jonas Valanciunas2,345+2.25 CJ Miles-0.86-0.63+0.23 Justin Holiday5,432+0.31 Bam Adebayo4,006+0.73 Evan Fournier25,823-0.85 Justise Winslow+1.41+1.34-0.07 Bobby Portis2,773-1.50 Joe Ingles+0.83+0.48-0.35 James Johnson2,419+2.19 Khris Middleton-0.17-0.11+0.06 Jonathon Simmons11,869-1.05 Andre Drummond5,709+1.01 Alec Burks14,268-1.49 Delon Wright3,611+0.43 Austin Rivers23,087+0.07 Giannis Antetokounmpo+1.80+1.94+0.14 Fred VanVleet4,882+0.08 John Henson+1.31+1.42+0.12 Stephen Curry+0.33+0.39+0.06 D.J. Augustin22,122-1.22 Joe Harris5,271+0.02 Kosta Koufos15,534+1.11 Kent Bazemore+0.31+0.21-0.11 Trevor Booker16,039+0.72 Blake Griffin5,538-0.61 Thabo Sefolosha16,186+0.95 Jason Smith11,230+0.05 Gerald Henderson-0.76-0.60+0.15 Maurice Harkless+0.41+0.42+0.02 Wilson Chandler2,670-0.33 Arron Afflalo-2.24-2.36-0.12 Malcolm Brogdon12,073-0.06 Zach LaVine-2.74-2.76-0.02 Kemba Walker33,021+0.81 CARMELO DEFENSIVE RATING Karl-Anthony Towns23,043+0.07 Kelly Olynyk+0.90+0.71-0.18 Spencer Dinwiddie4,395+0.77 Aron Baynes2,033+2.17 LeBron James+1.74+1.58-0.15 Marvin Williams4,467-1.22 Timofey Mozgov+1.38+2.11+0.72 Kristaps Porzingis11,714+2.57 Andrew Bogut13,887+2.01 Rodney Hood-1.25-1.34-0.09 Willie Cauley-Stein14,903-0.17 George Hill3,632+0.69 Trey Lyles10,302+0.34 Shaun Livingston+0.18+0.21+0.03 Hassan Whiteside18,508+1.87 Monta Ellis-0.39-0.58-0.19 D.J. Wilson2,055+0.96 Marco Belinelli23,994-1.19 D’Angelo Russell-1.66-1.86-0.20 Gerald Green3,324-1.43 Raymond Felton-0.74-0.13+0.61 Harrison Barnes-0.33-0.54-0.21 Lou Williams26,587-0.81 JR Smith-0.99-1.21-0.22 Jeremy Lin3,270-1.96 Kemba Walker5,962+0.62 Jonas Jerebko2,863-0.56 Kyle Anderson2,606+1.50 Jared Sullinger+1.24+1.29+0.05 Derrick Williams-2.07-2.32-0.25 Anthony Tolliver2,328-0.40 Tony Snell2,947+0.11 Kelly Oubre Jr.4,215-0.56 Cody Zeller+2.11+2.05-0.06 DeAndre Jordan4,300+0.83 Cody Zeller2,639+1.64 Stephen Curry39,307+0.27 Mike Dunleavy+0.89+1.17+0.29 Trey Burke2,387+0.57 Terrence Ross-1.48-1.27+0.20 Chandler Parsons-0.00-0.30-0.30 Kevin Huerter4,544-2.46 Marco Belinelli4,179-0.55 Marco Belinelli-2.47-2.78-0.31 Marcus Smart+1.11+0.76-0.35 Corey Brewer-0.16-0.46-0.31 Julius Randle4,889-0.41 Gary Harris-0.94-1.04-0.09 Cheick Diallo2,016-0.02 Paul Millsap4,866+0.59 JJ Redick6,068-0.44 Dwight Howard+2.46+2.12-0.34 Marvin Williams25,849+0.06 Terrence Ross23,139-0.03 T.J. Warren-1.66-1.67-0.01 Mario Chalmers+0.25+0.53+0.28 Reggie Jackson25,636-0.67 Luis Scola11,128-0.26 Domantas Sabonis+0.93+1.03+0.09 Tim Hardaway Jr.22,178-0.52 Hassan Whiteside3,490+2.89 Kelly Oubre Jr.-0.95-1.30-0.35 Norman Powell-0.51-0.92-0.41 Al Jefferson14,574-0.15 Damyean Dotson4,241-1.36 Danny Green+2.20+2.32+0.12 Rodney Stuckey11,918-0.63 Anthony Davis30,484+2.05 Klay Thompson41,713+1.05 Victor Oladipo28,135-0.29 E’Twaun Moore-1.25-1.53-0.28 Kevon Looney4,145+2.72 Bradley Beal-0.95-0.64+0.30 The best DRAYMOND defenders of 2018-19NBA players by DRAYMOND* defensive ratings, based on opponents’ shooting data in the regular season and playoffs, with a minimum of 2,000 possessions played in 2018-19 Isaiah Canaan10,149-0.40 Miles Plumlee+0.85+1.15+0.30 Emmanuel Mudiay13,309-0.90 Torrey Craig3,798+2.33 Andre Iguodala4,742+0.52 Devin Harris2,267-0.85 Rondae Hollis-Jefferson12,081+0.21 Jeremy Lin-0.41+0.04+0.45 Marvin Bagley III3,418-0.30 Kyle Korver28,624-0.28 Markieff Morris26,032+0.12 Frank Jackson2,628-2.10 Kyrie Irving-1.42-1.79-0.37 Nikola Jokic19,092-0.29 Ish Smith19,446+0.07 Jusuf Nurkic4,212+3.03 Rajon Rondo-0.21-1.17-0.95 Omer Asik10,195+0.11 Dario Saric14,499+0.00 These are some pretty interesting lists. Porzingis, Embiid, Klay Thompson and Kevin Durant are among the players whose defense had been most underrated by BPM and RPM. There’s also new Boston Celtics point guard Kemba Walker and, in something of a surprise, former Celtics point guard Isaiah Thomas, who still rates as a pretty terrible defender, just not quite as terrible as before when you incorporate his DRAYMOND data. The most overrated defenders include players such as Westbrook, Rondo, Ariza, Otto Porter Jr. and Nikola Jokic.Cases such as Thompson and Westbrook are interesting because the conventional wisdom has been way off from where the advanced metrics have them. RPM and BPM say that Westbrook is the much better defensive player, when a lot of NBA general managers might prefer Thompson or at least would regard it as close. But Thompson is a good defender according to DRAYMOND, whereas Westbrook is a wretched one, which closes at least some of the gap. Undoubtedly, there are even better ways to use opponents’ shooting data than what we’ve established with DRAYMOND, but the data ought to be a central part of the conversation about player defense going forward. Check out our NBA player ratings.