Stephen Curry’s shot chart (r)evolution

We are proud to present this guest post from Shane Sanders, who holds a Ph.D. in economics and is currently an Associate Professor of Sport Analytics at Falk College, Syracuse University.

To begin a revolution, the “Splash Brothers” first had to revolt against themselves. Or, rather, against a low-yield element of their respective shooting games. In order to find a truly revolutionary number of three-point shot opportunities during the past two regular seasons (2014-15 and 2015-16), Stephen Curry and Klay Thompson have increasingly eschewed the long-range two-point shot.

Stephen Curry’s shot chart (r)evolution

In each of the last four regular seasons, Curry has reduced the proportion of his shots that are long two-pointers. The cumulative effect is dramatic. Curry has reduced his proportion of shots taken between 16 feet and the three-point line to about 30 percent of its 2011-12 high. In that season, Curry “settled” for a long two-point attempt on nearly one-third of all field goal attempts. In 2015-16, Curry’s “settle rate” had reduced to about 8.9 percent of all field goal attempts. From 2014-15 to 2015-16 alone, Curry nearly cut his settle rate in half (from 0.163 to 0.088) after already nearly cutting his settle rate in half from 2011-2012 to 2014-2015 (from 0.301 to 0.163). The table below provides a more complete characterization of Curry’s shot distributional shift.

Curry loved the long two in his first few NBA regular seasons. Subsequently, he has gradually purged the shot from his repertoire. This is a common progression among young jump shooters in the modern NBA, most of whom enter the League having developed “college-three” range (20.75 feet). From the perspective of Stephen Curry’s shooting statistics, it appears that the Warriors are yet to have found too much of a good thing in three-point territory. They have heard the critics and, nonetheless, continue to deviate further from basketball as defined by a conventional shot distribution chart.

In the generalized context of an NBA possession, to take the typical long two-point shot is to have settled. It is a relatively low-percentage, low-yield shot. This is certainly true in the case of Stephen Curry. During his career, Curry has averaged about 0.92 points per shot on long two-pointers, and 1.33 on three-pointers. That is, Curry needed 1.45 “average” long two-point attempts to match his output from one average three-point attempt. For a long-range shooter like Curry, the long two is a(n) (opportunity) costly proposition, it eats roughly the same number of possessions as a three point attempt while yielding far fewer points. League-wide in 2015-2016, the average yield per three-point attempt was 1.062 points, while the average yield per long two-point attempt was 0.796. That is, the typical three-point attempt had 1.33 times the yield rate of the typical long two-point attempt.

The first table demonstrates another interesting aspect of Curry’s shot chart evolution, one that has been noted by Benjamin Morris of FiveThirtyEight. As Curry has shifted further away from long twos (further toward threes), he has not become less efficient on three-pointers and his return, as compared to two-pointers, has remained high.

In just seven seasons, Curry has gone from shooting a roughly equal number of threes and long twos to shooting more than six times as many threes. Most of this transformation occurred in the 2015-2016 season alone, in which Curry drastically decreased his long two attempts, while increasing his three point attempts. If we examine the (small sample) correlation between Curry’s three point premium and his ratio of three point attempts to long two attempts from season to season, we find that it is actually moderately positive at 0.438! If a player simply redistributes his shots (without any underlying change in shooting skills), we would expect this correlation to be quite negative.

The reason for this is straightforward. Each year, we would expect such a player to eschew his lowest percentage types of long two attempts for additional (marginal) three point attempts that, while bearing a higher expected return than his displaced two point attempts, have a lower expected return than his previously-established set of three point attempts (If the new threes had a higher expected return than the old threes, the shooter would have been shooting them all along!).

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In a “clean” setting, we expect this process to continue until the three point premium diminishes to a value near zero. That is, we expect the premium to diminish toward zero as the ratio of three point attempts to two point attempts increases (i.e., negative correlation between the two variables). In economics, this process is known as equilibration. It appears, however, that before Curry ever approaches an equilibrium (or even a dis-premium), his three-point proficiency has improved drastically from season-to-season. His skill is accumulating at such a drastic rate that even a majority share of field goal attempts from beyond the arc has not decreased his three-point attempt premium. In 2015-2016, 55.4 percent of Curry’s field goal attempts were from beyond the arc. He made almost as many field goals from beyond the arc as from two-point territory (402 to 403). It follows that about 75 percent of his points from the field derived from three point attempts. And this extreme shift does not appear to have been enough given Curry’s growing proficiency in shooting a wide assortment of three point attempts!

As Morris notes, Curry has become much better at three point proficiency and volume at the same time! He has extended his range in an effective manner and has become more proficient in creating high-quality three point opportunities. At the same time, Curry has focused less and less upon setting up high-quality long two opportunities.

Klay Thompson shot chart (r)evolution

In a very similar manner as Stephen Curry, Klay Thompson has also gradually defriended the long two-point shot over the past five regular seasons. In each of his five NBA regular seasons, Thompson’s settle rate also declined. In his rookie season of 2011-12, this rate was 0.316 for Thompson. In 2015-16, it had fallen to 0.138 (i.e., to approximately 44 percent of its 2011 2012 high).

In Thompson’s case as well, to take the typical long two-point shot is to have settled. Moreover, Thompson preserved much of his three point attempt premium as he scaled his number of three point attempts and reduced his number of long two attempts. However, Thompson has been subject to a dis-premium effect across his small sample of NBA seasons. The correlation between his three point attempt premium and his ratio of three point attempts to long two point attempts is -0.400. While there is still plenty of space for Thompson to further scale his three point shooting, the relationship between his three point shooting scale and proficiency does not defy all logic as in the case of Curry. That is to say, though unusually skilled as a long-range shooter, Thompson appears subject to the normal logic of shot distribution, unlike Curry.

Why do the Splash Brothers still take long twos?

Despite heavily decreasing their emphasis on long twos, the Splash Brothers still take about one-tenth of all shots from that region. Why shouldn’t they reduce this proportion even further? After all, their original arbitrage opportunity—the opportunity to substitute low-yield long twos for relatively high-yield threes—still exists. Even in 2015-16, Curry averaged 1.36 points per three-point attempt and 0.89 points per long two-point attempt, while Thompson averaged 1.28 points per three-point attempt and 0.91 points per long two-point attempt.

There are several ways to approach this question. Firstly, shot chart transformations may be “sticky” (to use a macroeconomic term). That is, it may take time for shooters to learn to effectively create new three-point shot opportunities, and defenses certainly do not accommodate shot chart redistributions that are designed to create points per possessions. As Michael Lewis revealed in a 2009 New York Times article on the topic of Shane Battier’s defense, analytic-minded defenders work in a deliberate manner to coax shooters into low probability field goal attempts (prevent high probability field goal attempts). As such, a player may adjust his shot distribution only gradually to prevent his marginal efficiency from “falling off the table” (e.g., should he begin forcing additional three point attempts rather than learn effective new three point attempts to incorporate).

Certainly, such an explanation is consistent with the steady, five-year transformation we have observed in the shot distributions of Curry and Thompson. Another explanation may be that—given the pace of an NBA game—players do not have perfect information (e.g., of foot position) when taking a shot. An NBA game is certainly not like a game of horse. A shooter cannot always pick or even know his spots. In some cases, a shooter will step into a three point jump-shot and accidentally put his leading foot on the three-point line. In other cases, a player will find himself in long two territory with the shot clock or game clock winding down. In still other cases, a long two may be the best shot available on a given possession. While the Splash Brothers are likely to further reduce their respective settle rates, low yield shots will always be taken in the NBA.

Avoiding the long two: A Splash Brothers trend or a Warriors trend?

The Splash Brothers are not the only Warriors who have avoided the long two in recent years. In fact, Draymond Green has undergone an even more dramatic shot distributional transformation since joining the League in 2012-13. In that year, 24.1 percent of Green’s field goal attempts were long twos. He has reduced that proportion in each of his three subsequent regular seasons, suggesting that the evolution of the Splash Brothers’ shot chart is one part of an analytically-driven, team-wide movement. In 2015-16, just 2.9 percent of Green’s field goal attempts were long twos! That is, Green averaged roughly one long two attempt per 34 field goal attempts!

As a team, the Warriors have gone on an extreme long two diet over the course of the past five seasons. While they are still not the best in avoiding the long two, they have come a long way in this respect. This is especially true if one accounts for the overall number of outside shots the Warriors attempt. The table below shows that the Warriors have cut their settle rate by more than half since 2011-2012. In 2011-12, the Warriors were among the league’s worst teams in terms of settle rate. Something dramatic happened before the 2013-14 season, however, a season in which the team cut its settle rate by six percentage points. This progression continued steadily into the recent season.

In terms of swearing off the long two point attempt, the Warriors were not the first to that particular punch. It appears that the 2011-12 Denver Nuggets (under the guidance of analytics pioneer Dean Oliver) followed by the 2012-13 Houston Rockets (under the guidance of analytics pioneer Daryl Morey) were first and second to purge the long two. The Warriors have covered a great deal of ground in the past three seasons, however, rising from twenty-eighth to fourth in the NBA in terms of avoiding long two-point attempts.

What should we expect from the Warriors’ offense next season?

To a lesser extent than many of his new teammates, Kevin Durant has also gone on a long-two diet over the past several years. Since joining the NBA in 2007-08, Durant has cut his settle rate nearly in half (from 0.318 to 0.161), while greatly increasing his proportion of shots taken from three-point range (from 0.15 to 0.348). In this respect, Durant is likely to gel within the Warriors’ offensive system. Given the offensive weapons surrounding him, moreover, Durant is likely to further reduce his settle rate. With four solid offensive options, the Warriors as a whole will likely settle for even fewer long twos next season. That is to say, the Warriors will have even more firepower positioned beyond the three-point line during 2016-17 such that it will be even more difficult for opposing defenses to induce long twos.

Next: Hopefully possible 2016-17 win projections

Durant will also provide the Warriors’ offense with greater variety, as more than one-fifth of his field goal attempts are taken from within three feet of the basket. Durant converted these shots at the astronomical rate of 0.737. With both Durant and Curry penetrating the lane effectively next season, the Warriors will get additional high-yield shot opportunities in the paint, as well as additional uncontested three point attempts (from kick-outs). Thompson, an adept corner three point shooter who is assisted on more than 90 percent of his three point attempts, may become the chief beneficiary of these additional kick-outs. Given his adaptability, moreover, we may see a higher rate of corner three point attempts from Draymond Green in the coming season(s). Provided the ongoing evolutions of Curry, Thompson, and Green and the overwhelming depth of offensive options that the 2016-2017 Warriors will enjoy, it is likely that the Warriors will reduce their settle rate to single digits in the coming season.