About 24 feet from the hoop, the upward trajectory of the orange sphere germinates with a simple flick of the wrist, during which it rotates laces over laces until reaching its zenith and falling gracefully toward the intended target. Mere seconds later, it produces that satisfying swishing sound as the ball rips through the nylon and adds three points to the scoreboard.

The three-pointer has come to define the modern NBA. Led by sharpshooters such as Ray Allen, Stephen Curry, Klay Thompson and Kyle Korver, professional basketball has shifted from the inside-out mentality that defined the physical 1980s and ’90s to today’s pace-and-space era. Once a gimmick that existed only for crowd-pleasing purposes in the ABA, triples are the lifeblood of present-day offenses, even accounting for 31.6 percent of all field-goal attempts in 2016-17.

That’s a drastic uptick from what we’ve seen in the past, and that trend might not end for quite some time:

Heading into 2017-18, the league-wide three-point attempt rate has now trended upward for eight consecutive campaigns, nearly doubling the mark at which it sat as the world fretted about Y2K. And why should that stop anytime soon? More teams are willing to copy the Golden State Warriors/Houston Rockets model by eschewing mid-range jumpers for looks at the hoop and from beyond the arc. They’re simply more efficient than post-up tries and attempts from the elbows.

San Antonio Spurs head coach Gregg Popovich helped jumpstart the trend by seeking out shots from the corners, but now everyone is helping progress closer and closer to the logical conclusion. And yet, the basketball-watching world still doesn’t do a perfect job pinpointing the best snipers. It relies on volume and efficiency to find the premier producers from downtown, but it largely fails—at least from an objective standpoint—to account for one important factor.

In the future, we’d like to bring in even more variables (proximity of the closest defender, time remaining on the shot clock, game situation, etc.). But for now, we’re focusing on the three main components that determine true three-point proficiency.

Volume obviously matters, because maintaining positive numbers becomes more difficult as players take more attempts. Efficiency falls into the same “duh” category, as throwing up boatloads of attempts is detrimental when a player isn’t connecting at a strong rate. And shot creation is our third variable, since breaking down a defender off the bounce before rising and firing typically requires more skill than serving as a spot-up sniper.

That’s not to discredit off-ball work. Navigating screens and finding even the tiniest modicum of space is a skill that requires plenty of practice, and it’s inherently important to the gravitational pull produced by any offense. But if we’re measuring pure shooting ability, catch-and-shoot work is objectively easier than pulling up. In 2016-17, the NBA as a whole shot 37.2 percent on catch-and-shoot treys. On pull-up threes, that percentage dropped to 32.2. This isn’t an aberration.

Ideally, a shooter is capable of creating his own shots off the dribble, frequently takes deep looks and connects at an impressive percentage. Few are actually able to fill all three criteria successfully, with—spoiler alert that really doesn’t spoil anything—Curry serving as the notable exception.

But who joins the Dubs’ leading shooter in that elite class?

To figure that out, I turned to a cluster analysis in Tableau with the three overarching skills—volume, efficiency and shot-creation—serving as the variables.

Picking the value for k (the number of clusters) is an inherently subjective process, and setting it at six made the most sense. Up it to seven, and the reason for delineation between the league’s worst qualified shooters (at least one three-point attempt per game, 10 minutes per game and 40 appearances) was unclear. Drop k to five, and the range in attempts per contest grows unwieldy within a single cluster.

Again, this isn’t perfect. Context must still be applied, even if you’re simply identifying the players subjected to tighter defensive pressure because their teammates couldn’t properly space the floor around them.

But as you can see in the graphic below, six shooters emerged as superior to all the rest for their work in 2016-17:

Low-Volume/Poor-Percentage Spot-Up Threats

No cluster contains a wider range of players than the one represented by the gray dots. But without fail, these are the shooters who almost entirely operated as spot-up threats and rarely found much success doing so.

Pau Gasol might stand out as an exception after shooting 53.8 percent from downtown while taking 1.6 attempts per game, but literally every single one of his 56 makes came after a teammate’s feed. If you’re surprised, you might want to start watching the Spurs’ ball-sharing stratagems a bit more closely.

On the other end of the spectrum sits Marcus Smart, who inexplicably took 4.2 attempts per game while shooting just 28.3 percent. Quite a few players produced a lower percentage, but only Jeff Green, Dragan Bender and Andre Roberson did so while taking even half as many attempts.

Poor shooting or extremely low volume, though, aren’t the sole defining characteristics of this group. If they were, Luke Babbitt (41.4 percent on 3.1 attempts per game) and Garrett Temple (37.3 and 3.4), among others, might show up in a different color—yellow, most likely. Every single player in the cluster relied on assists for at least 80.6 percent of their makes, with Trey Burke setting the bar over which everyone else jumped.

Shot-Creators but Middling Shooters

On the flip side, everyone in this cluster attempted to create far more looks off the dribble, ranging from Terry Rozier (80.7 percent assisted) to Tyler Ulis (47.6). Whereas the first cluster’s average member relied on assists for 94.7 percent of their makes, this one saw the number drop to 69.3.

Based on the prototypical numbers within this segment (69.3 percent assisted, 2.8 attempts per game and a 33.6 percent clip), Randy Foye and Dwyane Wade stand out as the best examples. Despite the flame-throwing habits the latter showcased at the beginning of his Chicago Bulls tenure, neither is known as a legitimate marksman. They’ll occasionally take shots and make them, and they often operate with the ball in their hands.

As for the best shooters in the group? Darren Collison (41.7 percent, 2.6 attempts per game, 75.3 percent assisted), Manu Ginobili (39.2, 3.3 and 78.7), Jameer Nelson (38.8, 3.6, 72.6) and Austin Rivers (37.1, 4.0 and 70.3).

High-Volume Shot Creators

Ordering this group and the next is tough, because this cluster contains a wide variation in the two typical metrics used to evaluate three-point shooting.

Brandon Knight, who recently tore his ACL and will likely miss all of 2017-18, shot only 32.4 percent from beyond the arc while taking 2.6 attempts per game. He’s in the same group as Mike Conley, who knocked down his 6.1 attempts per contest at a 40.8 percent clip. Ditto for Brandon Jennings (31.3 and 3.1) and Kyrie Irving (40.1 and 6.1).

What gives? How is the player who had the confidence and ability to drain the above look in the same group as a brick-layer like Jennings?

Well, every player in this cluster creates his own looks with aplomb. They’re all skilled ball-handlers who can throw a defender off balance and quickly rise for a shot; whether it falls is an entirely different story. This time, the average percent assisted in the cluster stood at a meager 54.7, ranging from Chris Paul (39.5) to George Hill (67).

Additionally, this group was almost entirely limited to point guards. LeBron James and Tyreke Evans, both of whom often operate as primary facilitators in the half-court set, served as the lone exceptions.

Traditional Off-Ball Spacers

The average player in this group used a set-up pass for 89.9 percent of their makes. Four players—Frank Kaminsky, Channing Frye, Dirk Nowitzki and Anthony Tolliver—needed an assist on every one of their successful treys, while no one did more shot-creation than C.J. McCollum (74.1), Seth Curry (74.5) and Gordon Hayward (74.5). Without fail, these men filled the exact role you’d expect: They set up off the ball, provided spacing for their teammates and, for the most part, knocked down their attempts more frequently than the average NBA shooter.

Dario Saric was the biggest exception on the accuracy front (31.1 percent), but the rest of his profile keeps with the description of this cluster. Ditto for Darrell Arthur, whose reliance on feeds and remarkable accuracy made up for his meager 2.9 attempts per outing.

But we have to talk about the positive outliers.

Plenty of phenomenal shooters populate this group—Otto Porter Jr., C.J. Miles, J.J. Redick, Kyle Korver, Ryan Anderson, Bradley Beal and Klay Thompson chief among them. And it’s those last two names that are questionable, since their 2016-17 seasons almost unquestionably left them among the true elites. Why then, aren’t they displayed in orange?

Thompson, who took 8.3 attempts per game for Golden State and connected at a 41.4 percent clip, looks like the biggest outlier. But he created only 4.5 percent of his own looks, and no one in the six-member group of true elites checked in below 15.9 percent. As we’ve been hammering home, shot-creation should matter.

For that very reason, Beal was likely the closest to changing colors. During his breakout season for the Washington Wizards, the 2-guard hit 40.4 percent of his deep attempts and took 7.2 attempts during his average appearance—both numbers inferior to Thompson’s. However, he needed assists only 80.7 percent of the time, which gives him the off-the-dribble ability his Warriors counterpart didn’t quite possess.

It just still wasn’t enough, leaving him feeling as left out as these next two players.

Sky-High-Volume, Inefficient Creators

James Harden and Russell Westbrook, 2016-17’s two leading MVP finishers, basically functioned as their own offenses. Each generated a tremendous number of assists for their teammates and shouldered ridiculous scoring responsibilities, which were completed almost entirely in solo fashion. They had the ball in their hands so frequently that relying on external assists was almost impossible.

Unsurprisingly, they had the NBA’s lowest percent assisted on their three-point makes. Westbrook sat at 35 percent, while Harden checked in at 31.7 percent. That’s not all they had in common, however. Both jacked up shots as frequently as almost any player, and they each finished below the league average in three-point percentage.

Had that final point changed by even a small margin, they might have overcome their relative levels of inefficiency and joined the final sextet.

Elite Marksmen

Technically, these players aren’t ranked. But just as we subjectively called Beal the player closest to joining this final category, we’ll attempt to put them in order from least to most impressive. And to be clear, all of them are quite impressive.

Eric Gordon is the shooter in greatest danger of turning another color, if only because of his role for the Houston Rockets. He functioned as a tremendous sharpshooter off the bench, connecting on 37.2 percent of his treys while taking a whopping 8.8 per game—more than anyone not named Harden or Curry. But he also needed assists on 84.1 percent of his makes, which feels more like it belongs in the Thompson/Beal range than alongside these other five.

Next up is Isaiah Thomas, who almost generated 40 percent of his treys off the bounce. Another player who was asked to create a jaw-dropping amount of offense for his troops, he doesn’t quite have the efficiency levels you’d expect from someone who had the luxury of more spot-up opportunities than the next man in the countdown. And that would be Damian Lillard, who created nearly 11 percent more of his own triples and had a comparable three-point percentage—37.0 percent, which falls just behind Thomas’ 37.9 percent. He may as well be on the same level, but we’ll allow the change in role to ever so slightly trump Thomas’ additional 0.8 attempts per game.

Kemba Walker and Kyle Lowry are one rung higher on the three-point ladder, with the Toronto Raptors floor general narrowly edging out his Charlotte Hornets rival. Though Lowry required assists on marginally more makes (1.5 percent more), he took slightly more shots per game (0.2 more) and recorded a slightly higher three-point percentage (1.3 percent higher).

That leaves Curry, who’s unsurprisingly in a class of his own.

Throughout this article, we’ve tacitly hinted at a natural tradeoff that occurs for every player in the NBA. Those who create more of their own looks are typically a bit more inefficient. Those who shoot more frequently have a tougher time maintaining lofty percentages. Excelling in all three areas is an almost impossible task. But Curry, who’s on track to shatter every three-point record into smithereens, is the exception who proves the rule. In 2016-17, he needed assists only 64.2 percent of the time, shot 10 times per contest (0.7 higher than anyone else) and found twine on 41.1 percent of his looks.

For at least one more year, everyone is staring up at him, hoping against hope they can emulate at least some of his skill. He’s essentially the perfect long-distance shooter.

Adam Fromal is the founder and Editor in Chief of NBA Math. Follow him on Twitter @fromal09. 

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Unless otherwise indicated, all stats are from NBA Math or NBA.com.