3-point shot evolution – Vol. 2

Welcome back to Hack a Stat! One of my very first articles on statistics was this one, about the evolution of the 3-point shot in Italy. With this new article, I want to re-propose an analysis of the evolution of the 3-point shot, exploiting however new and more in-depth data, observing the differences between catch and shoot and pull-up threes. Here we go!


The idea of analyzing the 3-point shot again comes from a concept mentioned by Hugo Sconochini during the commentary; Hugo stated that: “If the defender is away from the shooter, it would be better not to try to contest the opponent’s 3-point shot, as he could commit a foul that leads to 3 free throws or, worse, a 4-point play”.

So I wondered if what Hugo was saying was true. In other words, is it better to risk committing a foul on a 3-point shot or to let the shooter shoot unguarded? In this analysis, I will not only answer this question, but I will also cover several other aspects related to the 3-point shot.

3-point shooting fouls evolution

Let’s start by saying that one thing of what Sconochini said is certainly true: the fouls on 3-point shots have increased. Thanks to the NBA data, we can observe the trend of this specific foul from the 2000-01 season to the current one.

3-point shooting fouls

As you can easily see, the general trend of fouls committed on 3-point shots (blue line) shows an increase. Today about two shots out of one hundred are interrupted by a foul. This chart considerably reduces the current perception of fouls committed on this type of shot. The trend is similar also for the Euroleague: this season the ratio is equal to 1%.

Returning to the graph, the same can be said for three-and-ones, which have increased over the seasons (purple line; the number of 4-point play is compared to the number of fouls). The reasons for these two trends are obvious: today 3-point shots are used more. Consequently, the drawn fouls also increase. However, numerically speaking, it remains a quite rare event.

Breaking down three-point shots

Conscious that only one shot out of one hundred leads to free throws, let’s go into more detail, analyzing how the 3-point shots are taken. At the beginning of the season, I had made an article about the importance of shooting from beyond the arc highlighting that it is reductive to mention only the global percentage. The heavy conclusions can in fact be divided by:

  1. Shooting dynamic:
    • Pull-up;
    • Catch and shoot;
  2. Defender’s distance:
    1. Unguarded or uncontested;
    2. Guarded or contested;

The two types can obviously be crossed: we can have unguarded and guarded pull-up threes, for example. By splitting the 3-point shot in this way, we get a much clearer and more correct view of three-point shots.

Shooting dynamic

Now, I would like to observe the trend of the 4 categories mentioned above. Let’s start with the shooting dynamics, using the tracking available on the NBA website.

3-point shot dynamics

Data is available from season 13-14. In the chart above you can see the trend of the frequency (left graph) and the quality (right graph) of catch and shoot and pull-up over the last few seasons. Starting from the frequency, if we compare the number of shots taken in those ways with the total number of field goals (dotted lines), the trends are obviously increasing. In modern basketball, teams shoot more from 3-point range than in the past and both shooting dynamics have seen an increase in their volume.

If, on the other hand, we compare the number of pull-ups and catch and shoots over the total 3-pointer attempted, the situation changes: the initial distribution of about 80-20 in favor of the CAS has varied over time towards a 70-30. Therefore, most of the shots from beyond the arc are still carried out not by dribbling, but in recent seasons the pull-up shots have seen a marked increase. Just think of players like Harden, Lillard, Doncic: thanks to their skills in creating separation with the defender, they manage to take a shot from beyond the arc while dribbling. The pull-up shot is assuming greater importance in the economy of the game.

If instead, we look at the PPS trend, we can see how the shots in catch and shoot have maintained an almost similar value over the last few seasons; pull-ups, on the other hand, increased their PPS value, even if slightly. However, considering that in recent seasons the number of conclusions has increased, that small increase in PPS must not go unnoticed.

Defender’s distance

3-point shot defender's distance

Now I propose the same chart format again, but for contested and uncontested shots. A clarification before analyzing it: NBA website divides the shots according to the defender’s distance. Depending on the distance, the shooter can attempt a “very tight”, “tight”, “open”, or “wide open” shot. For simplicity, I added the very tight and tight together assuming them as contested, while the open and wide open together make up the uncontested.

Regarding the frequency, it is interesting to note how the distribution of uncontested and contested has remained almost unchanged over the seasons; however, if these two types are compared with the total shots, it can be seen that only the uncontested have had a significant increase. In other words, NBA teams have developed plays to create as many open shots as possible, increasing the amount from season to season.
About PPS, on the other hand, we can see a constant trend of the values. However, these PPS have remained unchanged while the volume of shots taken has increased.

Conclusion on the 3-point shot evolution

Thanks to these two infographics, we understand how 3-point shots have developed over the last few seasons in the NBA:

  • Pull-ups are more used than in the past;
  • Pull-ups’ efficiency has increased;
  • Catch and shoot threes are also more common;
  • Catch and shoot 3-point shots have the highest PPS value;
  • Teams try to create more uncontested 3-point shots as possible;

I am sure that the analysis carried out so far is also valid for the Euroleague. From the European league, I only have the data for this season (you can see the comparison in the table below): by comparing the values of the two seasons in progress, the data coincide. I, therefore, believe that even in the Euroleague the evolution of the 3-point shots took place with a very similar path to what has been shown so far for the NBA.

3-point shots breakdown
CAS: catch and shoot; PU: pull-up; CON: contested; UN: uncontested;

Commit fouls or not?

Until now, I have used the powerful tools of the NBA website to show the evolution of the 3-point shot over the last few seasons. But now let’s jump to Europe: thanks to the Instat data I was able to carry out a more in-depth analysis on heavy shooting.

Three quick tips before starting: Instat divides the shots into uncontested and contested. Comparing the Euroleague values with the NBA ones, I noticed that the contested-uncontested distribution only matches if the very tight, the tight, and the open shots are summed together. I deduced that Instat considers only wide-open shots as unguarded. Furthermore, Instat’s tools do not allow you to select only catch and shoot or pull-up shoots. I then tried to filter them based on play-types. For the catch and shoot I have selected:

  • Catch and shoot (stationary shot);
  • Screen-off;
  • Pick and pop;

For pull-ups:

  • Pick and roll handler;
  • Hand-off;
  • Iso;
  • Catch and drive;

By splitting the shots in this way, I got a distribution very similar to the NBA one: in the USA, as seen in the table above, the distribution of CAS and PU is 72-28, while in Europe it is 74-26.
Lastly, due to the distances from the defender chosen by InStat, it is very rare (if not impossible) to create an unguarded shot at the rim. This for a mere geometric fact: the conclusions in the area, being in the center of the offensive playing area, will always have an opposing player close enough to make that shot appear as contested. Therefore, in the graphs relating to uncontested shots, there will be no rim shots.

PPS euroleague

This is the shooting map where you can see frequency and PPS for each zone. As known, the most efficient shots are at the rim and from beyond the arc. In Europe, unlike the NBA, corners are less used, as the space available is not as comfortable. If instead we filter only for contested and uncontested shots the map are the following:

PPS euroleague
PPS euroleague

I think it’s clear why teams try to create open threes. An uncontested mid-range or long-2 shot has PPS around 1; the unguarded 3-point shots reach, instead, a very valuable PPS. On the other hand, you can understand why coaches and players want to contest any shot: the decrease in the PPS value is obvious. And here we can finally answer the first question of the analysis: taking the risk of committing a foul on a shot, in general, is a good choice.

By committing a foul on a 3-point shot, the defender grants 3 free throws with a PPS of 2,4 (3 times 0,8, which is the Euroleague average free throw percentage this season). With a 4-point play, the PPS value is 3,8 points. But these two cases occur altogether at most 2% of the time. In the remaining 98% of cases, the PPS value granted is equal to 1,03. If we calculate an average of the PPSs weighted on the probabilities of committing a foul or not, we obtain that adjusted contested shots have a PPS value equal to 1,06.

OK, there are cases in which it is necessary not to commit a foul in any way, but, that said, it is wrong to say that a defender should leave the shooter shooting unguarded if far away from him. The difference in PPS is too obvious.

Creating shot chances

The charts shown in the previous paragraph helped us to understand what difference there is in contesting or not 3-point shots. But as already mentioned, thanks to Instat we can also take into account the shots from beyond the arc by filtering both the shooting dynamics and the defender’s distance. By doing this, we can really understand what the attack is looking for and why.

PPS 3-point shot euroleague

In the graph above you can see the shooting frequency and the PPS of the catch and shoot and pull-up 3-pointer attempted uncontested and contested. Also, I have counted the transition threes separately. The frequency, in this case, is related to the defender’s distance: for example, 31% of all contested shots are pull-up ones. Additionally, I created a similar graph where, however, the frequency is relative to the total number of threes:

PPS 3-point shot euroleague

In this case, therefore, 20% of the total 3-point shots are contested pull-ups. So, teams’ priority is to find unguarded catch and shoot threes: this type of shot reaches a PPS value of 1,3. In fact, it is also the second most used shooting case: 30% of the total 3-pointer are attempted in this way. The first one is instead contested catch and shoot. It is interesting to note that they still reach a PPS value of 1,05. This is almost equal to the rim shots and greater than the uncontested mid-range and long-2 shots.

On the other hand, observing the difference in PPS of the contested shots in the two different dynamics, we note that it is very low (1,05 against 0,99). In other words, contested pull-up and catch and shoot conclusions are shots with very similar efficiency. This is not to be taken for granted, because a pull-up shot is on average more difficult than a catch and shoot one. This kind of conclusion remains suitable only for specific players (James, Larkin), but it is spreading more and more, both because it has good efficiency, and because more players are able to make this type of shot.

Teams’ values

Now it’s time to observe the values of the individual teams: I crossed the PPS of the two most common shots (unguarded and guarded catch and shoot) in the following chart.

3-point shot euroleague

The graph in this case is not meant to show any trend, but only to display the data for each team. We immediately notice that the teams in the first eight spots in the standings are almost all above average for contested catch and shoot. Real, Efes, and Bayern are the three “excluded”: the Spanish team has struggled to build clean shots since Campazzo has moved away and this has certainly affected these percentages. Similar speech for the Efes which has started to score once Larkin got into condition. Lastly, Bayern is among the worst teams for Offensive Rating. The graph also explains that, although unguarded threes in catch and shoot are the most valuable, they are not enough to win games. Khimki’s, Red Star’s, and Olympiacos’ positions seem to explain that.

That’s because 3-point shots are used also to spread the floor and create space to attack the rim. If a team is good at scoring unguarded catch and shoot threes but does not use them to create also rim shots, the opponent’s defense will eventually win the games.

In any case, in the following graph, we can finally see that, as expected, taking and scoring uncontested catch and shoot 3-point shots is the best solution to increase the overall 3-point shot percentage.

3-point shot euroleague

The disposition of the teams in the chart shows a fairly clear trend. Some teams deviate from the ideal trend line due to the percentages in other shooting types. But it is still evident that the uncontested catch and shoot threes are crucial for having good overall percentages. Thanks to the help of my mate Nick, I have been able to create this type of chart also for the NBA:

Clippers and Bucks “break” the scaling of the chart, but the global trend described before is confirmed.

Video analysis

We have therefore reached the last part of this analysis. Thanks to the Instat tools, we can in fact observe how catch and shoot 3-point shots are created. I selected three teams: Milano, Barcelona, and Bayern.

The first video, however, not only shows how to create an uncontested 3-pointer but is also a small appreciation video for Kyle Hines. The center is one of the reasons why Olimpia is in that position in the previous chart (the other is to have excellent shooters, which is trivial to say but still).

Olimpia’s offensive sets are based a lot on the IQ of people like Hines, Rodriguez, or Datome. Hines, for example, is a master of passing the ball after the short roll. His body control and excellent court vision allow him to know the right moment to pass the ball to the free shooter. In the video below you can see how Kyle waits for the defense’s reaction on his cuts before passing the ball; or also how the center knows where the unguarded teammate is, even if the shooter isn’t in his field of view.

In the video, it is also evident that to create uncontested shots, moving quickly the ball to the weak side is a good solution. Now, it is becoming increasingly common to pass the ball from side to side, skipping a pass and thus reducing the time available for the defense to come back on the unguarded player. This pass is not easy and can sometimes turn into an opponent’s fastbreak.

In the video above you can see some examples. Rodriguez and Higgins, two great artists of this pass, know how to properly calibrate the timing and the speed. It is a particular pass because it crosses a large part of the field and so it is difficult and dangerous, but at the same time very profitable.

One way to help the shooter reaming unguarded is to set a blind screen.

This type of screen has become famous thanks to the Spurs’ Hammer, a play designed to free the shooter in the corner. Although in the video there are not the exact reproductions of the Hammer set but only the final part (the part with the blind screen), the usefulness of that screen remains the same. Sometimes it is just the player’s ability to set this screen (Brooks is very good at this), understanding the situation, and start positioning himself to set the screen correctly.

Another play always present in the modern playbooks is the Spain Pick and Roll. The shooter sets a blind screen to the defender of the pick and roll screener and then moves behind the arc.

The video contains two mistakes by Delaney. In the first clip, he sets the screen on Hines, while in the third he does not move after the screen. Nevertheless, it is interesting to observe them because Milano still manages to build an excellent open shot. In fact, in the first clip, it is possible to understand how this collaboration creates a complex situation for the defense: even with an error of the attack, the defense has not been able to manage the rotations, leaving Delaney free.
In the third, Mickey lost Tarczewski, and Kaleb’s cut-assist generates enough space for Shields to have an open shot. The cut of the center (lost by Mickey because of Delaney’s screen) has lured Sharapov to the basket, leaving the Danish wing free.

In the videos, I have tried to show how most of the time the uncontested 3-point shots in catch and shoot are not the final goal of the attack: in fact, without considering the set used for creating a 3-point shot (such as a stagger set, a hammer set, or a Spain PNR), the unguarded threes are generated mainly through the ball movement and the defense’s rotations. This does not mean, however, that they are created randomly.

I hope this deep analysis has clarified how and why teams take certain types of shots. The 3-point shots are a crucial part of today’s basketball and they are not only fundamental for their efficiency, but also for the spaces they can generate.

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