HOUSTON, TX - APRIL 28: James Harden #13 of the Houston Rockets looks to pass the basketball in front of Al-Farouq Aminu #7 of the Dallas Mavericks during Game Five in the Western Conference Quarterfinals of the 2015 NBA Playoffs on April 28, 2015 at the Toyota Center in Houston, Texas. NOTE TO USER: User expressly acknowledges and agrees that, by downloading and/or using this photograph, user is consenting to the terms and conditions of the Getty Images License Agreement. (Photo by Scott Halleran/Getty Images)

Modern basketball offenses are devoted to the pursuit of efficiency; but, frustratingly, it’s not entirely straightforward to identify who are the NBA’s most-efficient scorers. The league’s antiquated measure of scoring efficiency — field goal percentage — has been replaced by its more-sophisticated cousin, true shooting percentage; but the business of efficiency ranking is still a bit murky. Consider this year’s true-shooting top-10 — which includes superstars (No. 3 Kevin Durant and No. 10 Stephen Curry), supporting role players (No. 6 Kyle Korver and No. 7 Otto Porter), and dunk-only big men (No. 1 Rudy Gobert and No. 2 DeAndre Jordan).

Of course, the trouble is that a player’s efficiency is closely tied to the difficulty of the shots he takes. Players who are asked to take more-difficult shots for their teams can be forgiven for shooting lower percentages. In contrast, players who feast on wide open or very short shots may convert a higher percentage, but they’re not necessarily great scorers. So, to rank the best scorers in the league, it’s necessary to first consider the roles they play within their offenses.

Below, I group players by their offensive roles and then rank the scorers within each group.

Defining offensive roles

I characterized offensive roles using the NBA’s individual play-type data provided by Synergy. These stats show the number of possessions during which a player attempted to score as the pick-and-roll ball-handler, in isolation, with a spot-up shot, working around an off-ball screen, in transition, from a handoff, as the pick-and-roll roll man, off a cut, on a putback, or on a post-up (there is also a “miscellaneous” category, which I have ignored, here). From there, I calculated the percent of each player’s individual scoring attempts attributed to each type of play.

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I used hierarchical clustering (hclust in R) to form groups of players by offensive role as defined by their use of the ten types of scoring. That is, I grouped players based on the ways they TRIED to score — not whether or not they actually COULD score. Using NBA.com jargon, I grouped individuals by play-type frequencies and ignored points-per-possession (PPP, and the corresponding percentile ranks). I included players who used a minimum of 250 possessions during the 2016-17 regular season and play-type data were available only for a player’s most recent team, so some players who changed teams midseason (Korver and Brandon Jennings), who didn’t play much (Paul Pierce and JaVale McGee), or who didn’t shoot much when they did play (Pascal Siakam and Lucas Nogueira) were excluded. In the end, I was left with 296 qualified players to group and rank.

Reassuringly, the three biggest branches of the clustering tree are recognizable as the three major player types on offense: ball-handlers (21 percent of all players), wings (58 percent), and bigs (21 percent). A majority (54 percent) of the scoring opportunities for ball-handlers were generated by pick-and-roll or isolation. The wings got most (60 percent) of their shots by spotting up, working around off-ball screens and handoffs, or in transition. The bigs were usually (75 percent) set up to score as the roll man in pick-and-roll or off of cuts, on putbacks of offensive rebounds, or with a post-up.

As the clustering tree continues to branch into twigs, we’re forced to abandon the old-school roles of PG, SG, SF, PF, and C. Instead, we find six groups: the ball-handler group remains intact; the wings are split into attackers, shooters, and bullies; and the bigs are divided into guys with skill and their more-limited counterparts. In the second graph, the color scheme continues from the first, but now each of the ten play types are shown.

The attack wings are characterized by a big chunk of pick-and-roll ball handling duties (20 percent) — about half as much as the players in the pure ball-handler group (43 percent) — to go along with their spot-up shooting (26 percent). In contrast, the shooting wings were more dependent on their spot-up chances (41 percent), whereas the bully wings got some of their looks via the interior play types (in orange), including post-ups (8 percent). The skilled bigs had post-up games too (27 percent), but the limited bigs relied more on their teammates to set up their rolling (25 percent) and cutting (27 percent).

The clustering continued to expand from the three branches, to the six twigs, and finally into 18 leaves — representing a hierarchy of 18 different offensive roles.

The ball-handlers can be divided into individuals playing three different roles: rock pounders who ran non-stop pick-and-roll (58 percent), creators who scored in the pick-and-roll (39 percent) and isolation (20 percent), and distributors who scored in the pick-and-roll (42 percent) and when spotting up (18 percent).

Likewise, the attack wings fall into three roles: secondary creators who had more than a quarter of their scoring opportunities as a ball-handler in the pick-n-roll (26 percent), off-ball workers who ran around screens (29 percent) and used handoffs (11 percent) to get shots up, and glue guys who did a little bit of everything.

The shooting wings make up three more roles: spot-up wings who still had a little bit of bounce (8 percent PnR ball handler), stretch bigs who took more than half (52 percent) of their shots after spotting up, and pick-and-pop bigs who did a little rolling (19 percent) and a little spotting up (36 percent). It’s a bit surprising that two of these three groups of shooting “wings” were actually comprised of taller players. In the modern NBA, though, there are plenty of these shooting bigs who are essentially wings on offense and bigs on defense.

On the other hand, the bully wings comprise the smallest group and it’s shrinking fast. There were four roles: ball-stoppers who took a plurality of their shots in isolation (25 percent), point forwards who were equally comfortable scoring off an iso (15 percent) as in the post (13 percent), reluctant shooters who scored more than any other group in transition (22 percent), and bigs-with-touch who stepped out and spotted up (20 percent), but also rolled (20 percent).

The versatile bigs also spotted up (18 percent) and rolled (20 percent), but they could post-up, too (24 percent). Of course, nobody posted up as frequently as the post-up bigs (33 percent).

Finally, the limited bigs encompassed three more roles: roll-and-cut bigs rolled (23 percent) and cut (27 percent), parasitic bigs rolled (36 percent) and cut (23 percent) even more, and unskilled bigs pretty much just stuck the ball back in the hoop on put-backs (29 percent).

Ranking scorers by offensive role

Now that we’ve defined the full variety of offensive roles filled by NBA players, we can start talking about which players are in which groups and get to ranking.

In the table below, I list a fun fact that gives some additional context about the players in each group as well as the average efficiency (points per possession) of each group. I also rank the best and worst scorers by role. The “go-to” play types were any for which the group average frequency exceeded the overall league average by at least 50 percent.

The rock pounders are a small group of point guards — including Kemba Walker, Jrue Holiday, and Reggie Jackson — who specialized in running the pick-and-roll. While on the court, these guys used more of their offense’s time of possession than the players from any other group — a whopping 42 percent on average. Walker was the best in that role by a healthy margin, scoring 1.05 points per possession. On the other end of the spectrum, rookie Tyler Ulis was the least efficient rock pounder, converting just 0.84 PPP.

The creators are a star-studded bunch: including two MVP candidates (Russell Westbrook, James Harden), three more All-NBA selections (DeMar DeRozan, John Wall, Jimmy Butler), and three other star-level primary ball handlers (Damian Lillard, Kyrie Irving, Chris Paul). The players in this role had a higher usage rate (29 percent on average) than any other group, acting as creative forces at the center of their team offenses. Irving (1.06 PPP), Butler (1.06 PPP), and Lillard (1.05 PPP) were the most efficient of the group. Dion Waiters has all the confidence that he belongs alongside his more-decorated group members, but he was the least efficient of the bunch (0.90 PPP).

The distributors are a wide-ranging group comprising another 44 primary ball handlers (the biggest of the 18 groups). It’s hard to lump them all together under one umbrella, but a lot of the distributors were “table-setting” point guards like Ricky Rubio, T.J. McConnell, and Rajon Rondo — guys who held on to the ball a lot, without shooting it much. They averaged just 2.6 field goal attempts per minute of individual ball possession. Of the 20 players with the lowest rates of field goal attempts per time of possession, 19 of them were from the distributor group. Isaiah Thomas (1.11 PPP) was the best scorer of the distributors and Kris Dunn (0.73 PPP) was the worst.

The secondary creators are another big, diverse group characterized broadly as wings who can score off the bounce with big-name guys like Kawhi Leonard, Paul George, Gordon Hayward, Bradley Beal, and — the best scorer in this role — Kevin Durant (1.19 PPP). If you sort the players from each team by individual time of possession per game, the secondary scorers were generally the second, third, or fourth-ranked ball handler among their teammates. One notable exception was the second-best scorer of the group, Steph Curry (1.11 PPP), who was the lone primary ball handler clustered into this group. Curry’s play-type stats were a bit deceiving, because he was frequently forced to give up the ball in pick-and-roll situations and, as a result, he recorded fewer pick-and-roll possessions (29 percent) than most of his ball handling peers. Justise Winslow was the worst scorer in the role of secondary creator (0.72 PPP).

The glue guys are identifiable primarily for their lack of any true identity. If you calculate the average breakdown of play types for the whole pool of players- – all 296 of them — and compare it to the average breakdown within each role, the glue guys were the most unremarkable, the ones most similar to the overall average. They had no real “go-to” scoring play, aside from using handoffs more than most other players (8 percent). These guys were the “jack of all trade, master of none”, do-it-all perimeter players of the NBA last season: wings like Joe Ingles, Gerald Henderson, and Kent Bazemore. None of the glue guys were All-Stars this year, only four of the 41 ever have been in their careers (Vince Carter, Joe Johnson, Manu Ginobili, Devin Harris). Nick Young (1.14 PPP) was the best-scoring glue guy and Stanley Johnson (0.75 PPP) was the worst.

The off-ball workers are a unique group of sharpshooters like Klay Thompson and J.J. Redick that relished running their defenders around screens and handoffs in search of open 3-point looks. These deadeye shooters averaged more points per possession than any other group of perimeter players, with C,J, Miles (1.13 PPP) leading the way and Bojan Bogdanovic (0.98 PPP) bringing up the rear. The off-ball workers had the highest 3-point attempt rate of the 18 roles, as they shot 57 percent of their field goal attempts from deep.

Some of the league’s more-stationary 3-point shooters populated the spot-up wing role. These are the guys I might have labeled 3-and-D wings if I wasn’t ignoring defense here — players like Robert Covington, Trevor Ariza, and DeMarre Carroll. On average, more than half (51 percent) of the field goal attempts by spot-up wings came in the form of a 3-pointer following 0 or 1 dribbles. Otto Porter Jr. (1.23 PPP) was the best scorer of these spot-up specialist and Denzel Valentine was the worst (0.83 PPP).

The stretch bigs are the taller counterparts to the spot-up wings — distinguished by their relative lack of mobility (no use for off-ball screens or handoffs) and a tiny hint of roll-man capability which the true wings did not possess. Stretch bigs like Anthony Tolliver, Dante Cunningham, and Al-Farouq Aminu found a lot of space on the perimeter, taking an average of 50 percent of their field goal attempts in the form of open or wide-open 3-pointers, more than any other group. Davis Bertans (1.15 PPP) was the best at cashing in and Dorian Finney-Smith (0.88 PPP) was the worst.

The pick-and-pop bigs also specialized in spotting up from the perimeter, but players like Serge Ibaka, Marreese Speights, and Kelly Olynyk were frequently used as roll-men, too. Despite the fact that these guys were shaped like power forwards and centers, jump shots accounted for 70 percent of their field goal attempts. Channing Frye was the most effective pick-n-popper (1.17 PPP) and Boris Diaw was the least effective (0.82 PPP).

If I asked you to predict who would be the league’s next Carmelo Anthony, the name “Harrison Barnes” might not be on the tip of your tongue; but, they were actually a good match based on the 2016-17 play-type data. This pair of ball stoppers used isolation and post-ups more than any other group and shot the ball on nearly a third of their touches (31 percent). Barnes was slightly more efficient last year (1.01 PPP), but it was pretty close (0.97 PPP for Melo).

Likewise, if I were a psychologist giving you a word-association test and I prompted you with: “LeBron James and Giannis Antetokounmpo” you’d be hard-pressed to pull “Shaun Livingston” as the correct response; but, these point forwards did share some common strategies for attacking the basket. Out of the 296 qualified players, there were 73 players who — while they were on the court — possessed the ball for at least 20 percent of their team’s time on offense (a conservative indicator for primary ball handling duties). Each standing at least 6-foot-7 in height, these three point forwards were the tallest of those 73 (I had to go to NBA Draft “shoes-off” combine data to nudge Livingston ahead of DeMar DeRozan and Jimmy Butler). Of the three, James was the best scorer (1.08 PPP), but they were pretty tightly bunched (1.02 PPP for Livingston).

The reluctant shooters group features bricky wings like Tony Allen, Andre Roberson, and Michael Kidd-Gilchrist. These players leaned heavily on using cuts to score and shot fewer jump shots per game (5.9) than any other perimeter group. Andre Iguodala had the easiest time finding a way to score (1.15 PPP) and Tony Allen struggled the most (0.88 PPP).

The bigs-with-touch group is at the center of the spectrum between the stretch bigs and roll-and-cut bigs — its players possessing too much interior presence to fit in with the former group and too much mobility on the perimeter to join the latter. The group includes players like Julius Randle, Larry Nance, and Gorgui Dieng who can shoot a little bit, but don’t really stretch it to the 3-point line. These guys get a steady diet of open and wide-open 2-pointers — 31 percent of their field goal attempts, on average. Richaun Holmes (1.16 PPP) was the best scorer in the group and Noah Vonleh (0.90 PPP) was the worst.

The skilled bigs used a wide variety of plays to try to score — posting up inside, spotting up outside, and even isolating one-on-one. Skilled bigs are some of the most prized players in the NBA because of this versatility. Of the 19 skilled bigs, 12 have been All Stars — Anthony Davis, DeMarcus Cousins, Al Horford, Kevin Love, Paul Millsap, Blake Griffin, Marc Gasol, LaMarcus Aldridge, Dirk Nowitzki, Pau Gasol, Brook Lopez, and David West. Another four were recent All-Rookie selections and some of the best young big men in the league — Karl-Anthony Towns, Nikola Jokic, Joel Embiid, and Kristaps Porzingis. Two Nikolas bookended the group for scoring rates — Jokic on the top (1.15 PPP) and Vucevic (0.92 PPP) on the bottom.

The post-up bigs are a small group of old-school pivot men with the footwork to score on the box including Jahil Okafor, Al Jefferson, and Jusuf Nurkic. This group relied more on hook shots than players in any other role — hoisting 17 percent of their field goal attempts with the hook. Jonas Valanciunas (1.11 PPP) was the best post-up specialist and Zach Randolph (0.90 PPP) was the worst.

Parasitic bigs Nene Hilario, Cody Zeller, Myles Turner, and Dwight Powell got a vast majority (71 percent) of their scoring opportunities on teammate-dependent plays — by rolling, cutting, or spotting up. As a result, these four players required fewer dribbles to set up their shots than players in any other role — just 1.7 dribbles per field goal attempt. The parasitic bigs were also assisted on a overwhelming fraction of their shots — 83 percent on average. With all that help, it was easy for the parasitic bigs to score at the most-efficient rate of any role (1.13 PPP). The quartet spanned a very narrow range of effectiveness from Nene (1.14 PPP) to Turner (1.11 PPP).

The unskilled bigs consist of players like Dewayne Dedmon, Joakim Noah, and Gobert who live at the rim, finding 76 percent of their opportunities by way of layups and dunks. Each of the eight unskilled bigs were among the top-20 players for “shots-at-the-rim” rate. The unskilled bigs also got a bigger fraction of their scoring chances on offensive rebounds than players from any other role. With all these short shots, Tyson Chandler (1.30 PPP) and Gobert (1.24 PPP) had two of the most-efficient scoring rates in the league. On the other hand, Noah managed to botch a bunch of his bunnies (0.87 PPP).

The prototypical roll-and-cut big is DeAndre Jordan — he and his fellow group members like Steven Adams, Clint Capela, and Mason Plumlee are also largely one dimensional scorers. They spend all their time diving towards the rim — getting 59 percent of their touches in the “post”, “paint”, or “elbow”. Montrezl Harrell (1.28 PPP) was the best scorer of the roll-and-cut bigs and Derrick Favors (0.94 PPP) was the worst.

So there you go, the best and worst scorers for each of 18 different NBA roles. You can see from the six graphic examples just how much a player’s role dictates his ability to score efficiently.

The six individuals shown in the graphs above — James Harden, Troy Daniels, Jonas Jerebko, Harrison Barnes, Marc Gasol, and Tarik Black — all scored roughly one point per possession. Or, to put it graphically, each player had blocks of different sizes and shape, but if you found the area of each individual block and summed up all the block areas for each player, you’d find that the total size of the ten blocks was the same for each of the six players. Obviously, those players span a huge range of offensive capabilities — with stars like Harden and Gasol being able to create offense for themselves and role players like Black and Jerebko being more dependent on their teammates to facilitate their scoring chances.

So, as the cult of efficiency continues to spread throughout the NBA, keep in mind that a player’s efficiency is inextricable from his role in his team’s offense and that, to truly judge a player’s effectiveness on offense, both pieces of information must be considered together.