How has the NBA changed?
İlhan Güner and Amrit Amirapu
We’ve all seen it. Damian Lillard brings the ball up court, takes one dribble over the half-court line and - standing on the logo, just seconds into the shot clock - takes and drills a three from 30+ feet away. What seems like sheer insanity, what should get him benched instantaneously, appears to be the new normal. Because it’s not just Damian or Steph Curry - the greatest shooter the game has ever seen and the first one to make us rethink what we thought was physically possible about the range, accuracy and volume of long distance shots. Players the league over (Trae Young, Luka Doncic, James Harden, Kevin Durant - even Lebron James, who used to be left open behind the three point line) seem to be getting more accurate from further away with each passing season.
Prompted by these developments - and by the presentation of data such as this revealing graph from Kirk Goldsberry - we decided to take a closer look at the evolution of field-goal usage and efficiency from 2-point and 3-point range over time.
As Kirk Goldsberry’s graph above makes clear, the game has changed over the last 20 years. The analytic revolution has made the mid-range shot a thing of the past - like the Caspian Tiger or moderate republicans. Even though the 3-point line had already been around for more than two decades by 2001, team strategy and player skill had not yet fully taken account of the line’s potential.
The following graph shows how players’ effectiveness from 2-point and 3-point range have changed over time, starting from 1950 for twos and 1979 for threes. The two series represent the expected points scored per shot-attempt from 2-point range (dashed line) and 3-point range (solid line), each averaged over all shots taken from that range in an NBA season. So, for example, the solid line gives the average 3-point field goal (FG) percentage in a season multiplied by 3. Points scored on free throws resulting from fouls are not included, which we imagine makes 2 point shots more effective in practice than shown here.
Expected points over time, weighted average
From the graph we see that shooting effectiveness from 2-point range increased dramatically from 1950 to about 1980, when expected points from 2-point range starts to level off - though you can see a dip in the mid-90s (possibly a reflection of the hard-nosed defense emblematic of the period), a recovery in 2004 when hand-checking is eliminated and a sharp increase over the last 5 years. When the three-point line was introduced in 1979, the three point shot was a highly inefficient tactic on average, earning about 20% less in expected points per attempt compared to two-pointers. But after a few years of experience, expected points from 3-point range started to increase dramatically - surpassing expected points from 2-point range around 1990 and leveling out after the mid-90s - where it continues to reward players with more expected points per attempt - on average.
The next graph displays the number of field goals attempted - per minute played - from 2-point and 3-point range over time. The most striking pattern is - unsurprisingly - a secular increase in the number of threes attempted per season (and a corresponding decrease in the number of 2s). Linearly increasing until 2012 or so, the number of attempted threes seems to have started growing exponentially over the last few years. In other words, the three point shot has been getting more popular every year since it was introduced - but the nature and speed of growth has exploded over the last 7 or 8 years. Let’s call that the Steph Curry effect.
Field goal attempts
Note that the sharp increase in the number and effectiveness of 3-point FGs between 1994/5 and 1997/8 correspond to the seasons for which the three-point line was shortened to a uniform 22 feet. Some commentators have suggested that this temporary reduction in 3-point distance is what nudged players and teams into learning to love the three. The data don’t support that hypothesis: 3-point usage was already on an increasing trend, and the shorter 3-point line only led to a temporary blip, after which 3-point usage resumed it’s earlier trend.
The graph above depicting 3-point and 2-point effectiveness represented all-NBA averages, where efficiency in scoring was implicitly weighted by the number of attempts taken by different players. But of course, shot attempts are not distributed randomly - the best 3 point shooters take more threes (usually!). So it is interesting to look at unweighted figures. What we do next is to calculate expected points scored from 2s and 3s for each player in the NBA, and then take an unweighted average over all players. The resulting figures - shown in the graph below - tell us that average effectiveness across players in shooting the three point shot has been increasing constantly. In other words, it is not just that better shooters have been shooting more - the average player in the NBA is a much better three point shooter than ever. There has been no leveling off at any time in this regard.
Moreover, in contrast to the graph showing weighted averages, the unweighted figures show that expected points from 3 point range are not now and have never been as high as expected points from 2 point range. In other words, the average NBA player is more effective when shooting from 2. It’s only certain players that particularly excel at the three point shot. But those players are tasked with shooting far more often, which is why - when you weight effectiveness by the number of shots taken - the three point shot looks to be more effective on average than the 2-point shot.
Expected points over time, unweighted average
So who are these players that shoot the three so well? They’re mostly who you think they are! In the two interactive graphs below, we show expected points from 3-point range and 2-point range by season for a collection of the most iconic shooters and scorers over the last three decades (from the list of players chosen, you can probably detect a generational bias - from which you can back out our ages. But if there is someone you feel is missing from the list, please: write their name down on a postcard and send it to Car Talk Plaza.). The size of each bubble represents the number of shots attempted.
Expected points from 3-point range
Expected points from 2-point range
There are some interesting differences between the two graphs. A careful observer will notice that efficiency from 2-point range shows a persistent inverted U-shaped pattern over the course of an individual’s career. Great players tend to become increasingly efficient after they first enter the league, before reaching a peak level of efficiency and then starting to decline. There are differences across players in how this trend plays out (e.g. Lebron James entered the league with relatively low efficiency but improved dramatically over the next 10 years - an astonishingly long period of sustained improvement) but the general inverted U-shape is a reliable pattern. In contrast, efficiency from 3-point range shows no such career trajectories. Great 3-point shooters enter the league shooting well and maintain their effectiveness throughout their careers - often with remarkable year-to-year consistency. Moreover, it seems that the best shooters over the last three decades have consistently earned about 1.2 expected points (or slightly better) per 3-point attempt, and this benchmark seems to have held largely fixed since the 90s. If there are stand-outs, they must be Steph Curry (for the volume as well as the efficiency of 3-point FGs), Kyle Korver, Steve Nash and Steve Kerr (though we imagine MJ deserves some of the credit for Kerr’s remarkable efficiency…).
So what is our main takeaway from this… let’s call it ‘analysis’ for lack of a better word? What strikes us most is that three-point efficiency has not changed much since the mid-90s - either for the league average or for the top shooters. This might seem surprising, given how different the NBA looks and feels when you turn on the TV - assuming you don’t do that during a global pandemic when there is no basketball :( . But it doesn’t mean that player skill has plateaued. On the contrary: the NBA has changed because the best three-point shooters are taking more shots and shooting from further away than they ever have before, and it is a testament to their increasing skill that this hasn’t translated into a reduction in 3-point efficiency.
There is one more takeaway from this analysis. If you’re going to have a child and you want her to shoot the three well, name her Steve.