Does the NBA Three-Point Premium Still Exist?
Econometrics II - Exercise 12
DJ Barry
Introduction
There is a reason NBA fans call the past 15 years or so The Steph Curry Era. Steph and others changed the game through shot selection, spacing, and the value teams placed on the three-point shot. That impact is not going away.
The question now is whether the advantage, or premium, of the three-point shot has finally crossed the Rubicon. Teams take more threes than ever, defenses have adapted, and the league may have reached the point of diminishing returns. When you look at the numbers, it seems like volume has started to catch up to the advantage.
The shot chart lecture is important here because it shows why shot value is not as simple as three is worth more than two. A normal shot chart can make the three-point shot look clearly superior because it focuses on field-goal location and field-goal points. The true shot chart idea complicates that by also thinking about free throws and the full value created by a shot location.
That does not mean the three-point premium is gone. It means the answer is more complicated than more threes equals better offense. This project uses cluster modeling to test that idea, starting with a simple model that groups teams by three-point attempt rate and true shooting percentage to see whether higher volume still connects to better scoring efficiency.
The second model adds free throw rate and offensive rating because offense is not only about where the shot comes from. Good threes create spacing, rim pressure creates fouls, and shot quality still matters. The goal is to see whether the three-point premium still shows up by itself, or whether it now depends more on the offense around it.
Why K-Means Clustering Fits This Question
K-means clustering is useful here because it lets the data sort teams by style instead of forcing an answer before the analysis starts. I am not trying to predict wins, crown the best offense, or say every good team has to play the same way. The goal is simpler than that: group teams that look similar offensively and then see what those groups tell us about the three-point premium.
That matters because the modern NBA is not just high-volume threes versus low-volume threes. Some teams take a ton of threes and score efficiently. Some take a ton and do not. Some teams create efficient offense through foul pressure, rim pressure, or balance instead of pure three-point volume.
2025-26 NBA Team Offensive Profile
| 2025-26 NBA Team Offensive Profile | |||||||||
| Sorted by offensive rating rank. | |||||||||
| ORtg Rk | Team |
Record
|
Team Strength
|
Shot Profile
|
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|---|---|---|---|---|---|---|---|---|---|
| W | L | Win% | ORtg | NRtg | 3PAr | TS% | FTr | ||
| 1 | DEN | 54 | 28 | 65.9% | 122.6 | 5.2 | 40.8% | 61.6% | 29.4% |
| 2 | BOS | 56 | 26 | 68.3% | 120.8 | 8.1 | 46.7% | 58.3% | 20.7% |
| 3 | NYK | 53 | 29 | 64.6% | 119.8 | 6.5 | 42.8% | 59.0% | 23.8% |
| 4 | SAS | 62 | 20 | 75.6% | 119.6 | 8.3 | 42.2% | 59.5% | 27.4% |
| 5 | CHO | 44 | 38 | 53.7% | 119.4 | 5.0 | 48.7% | 58.9% | 24.4% |
| 6 | CLE | 52 | 30 | 63.4% | 119.2 | 4.1 | 44.2% | 59.5% | 26.5% |
| 7 | OKC | 64 | 18 | 78.0% | 118.9 | 11.2 | 42.6% | 59.9% | 26.1% |
| 8 | HOU | 52 | 30 | 63.4% | 118.6 | 5.4 | 35.0% | 57.6% | 26.0% |
| 9 | LAL | 53 | 29 | 64.6% | 118.2 | 1.8 | 39.4% | 60.9% | 32.0% |
| 10 | DET | 60 | 22 | 73.2% | 117.9 | 8.2 | 34.5% | 58.3% | 29.2% |
| 11 | LAC | 42 | 40 | 51.2% | 117.3 | 1.2 | 40.4% | 60.2% | 29.5% |
| 12 | MIN | 49 | 33 | 59.8% | 116.8 | 3.3 | 42.0% | 59.2% | 28.5% |
| 13 | MIA | 43 | 39 | 52.4% | 116.7 | 2.2 | 40.6% | 58.0% | 26.8% |
| 14 | ATL | 46 | 36 | 56.1% | 116.1 | 2.4 | 42.9% | 58.4% | 23.4% |
| 15 | TOR | 46 | 36 | 56.1% | 115.9 | 2.9 | 36.3% | 58.1% | 26.5% |
| 16 | PHO | 45 | 37 | 54.9% | 115.4 | 1.5 | 45.3% | 56.8% | 22.5% |
| 16 | PHI | 45 | 37 | 54.9% | 115.4 | −0.1 | 39.1% | 57.2% | 27.5% |
| 18 | GSW | 37 | 45 | 45.1% | 115.0 | −0.6 | 49.7% | 58.4% | 23.8% |
| 19 | ORL | 45 | 37 | 54.9% | 114.9 | 0.6 | 38.6% | 57.6% | 31.1% |
| 20 | POR | 42 | 40 | 51.2% | 114.4 | −0.3 | 46.9% | 57.0% | 28.0% |
| 20 | NOP | 26 | 56 | 31.7% | 114.4 | −4.5 | 35.5% | 56.8% | 28.4% |
| 22 | UTA | 22 | 60 | 26.8% | 114.1 | −8.2 | 40.2% | 57.5% | 27.7% |
| 23 | CHI | 31 | 51 | 37.8% | 113.0 | −5.1 | 44.3% | 58.0% | 24.6% |
| 24 | MEM | 25 | 57 | 30.5% | 112.9 | −5.9 | 43.6% | 57.0% | 25.1% |
| 24 | MIL | 32 | 50 | 39.0% | 112.9 | −6.4 | 45.7% | 58.9% | 22.3% |
| 26 | SAC | 22 | 60 | 26.8% | 111.4 | −10.1 | 33.9% | 56.0% | 25.6% |
| 27 | DAL | 26 | 56 | 31.7% | 111.2 | −5.3 | 35.5% | 56.4% | 28.7% |
| 28 | WAS | 17 | 65 | 20.7% | 111.0 | −11.7 | 40.3% | 56.6% | 23.5% |
| 29 | IND | 19 | 63 | 23.2% | 110.9 | −7.9 | 42.2% | 56.8% | 25.2% |
| 30 | BRK | 20 | 62 | 24.4% | 108.7 | −10.3 | 45.5% | 55.9% | 27.2% |
| Green indicates higher values within each colored column. Red indicates lower values. For 3PAr and FTr, color shows offensive profile, not automatic shot quality. | |||||||||
This table gives the baseline before the clustering starts. 3PAr shows how much each team leans into the three-point shot, while TS% shows whether that shot profile is turning into efficient scoring. If the three-point premium were automatic, the high-3PAr teams would also separate cleanly near the top in efficiency.
This is also where the shot chart lecture matters. A normal shot chart can make the three-point shot look cleaner because it focuses on field-goal attempts and field-goal points. True shot charts complicate that by accounting for more of the value connected to shot location, especially free throws. That is why FTr belongs in this project instead of only looking at three-point volume.
That is why the other variables matter. FTr captures foul pressure, ORtg captures total offensive production, and Win% adds basic team context. For the 2025-26 season, the league average 3PAr is 41.5%, the league average TS% is 58.1%, the league average FTr is 26.4%, and the league average ORtg is 115.8. Now the question becomes whether K-means sees the same patterns once the teams are grouped by style.
Correlation Check: Is Three-Point Volume Still the Edge?
Before clustering the teams, it helps to take a step backkask the simplest version of the question first: does more three-point volume actually connect to better offense?
This is where correlation comes into play. Clustering shows offensive styles, but correlation gives a cleaner first test of the premium. If the three-point premium were still automatic, 3PAr should have a strong positive relationship with TS% or ORtg. In other words, teams that take more threes should clearly be more efficient or score better overall.
If that relationship is weak, then the argument changes. It does not mean threes are bad. It means the easy edge from simply taking more threes is probably gone. The premium would still exist, but only when the threes are good shots, taken by the right players, inside an offense that also creates pressure in other ways.
| Correlation Check: Does More Three-Point Volume Still Mean Better Offense? | ||||
| Pearson correlations across teams in the offensive profile data. | ||||
| Relationship | Correlation | R² | P-Value | Strength |
|---|---|---|---|---|
| 3PAr vs TS% | 0.170 | 0.029 | 0.3690 | Very weak |
| 3PAr vs ORtg | 0.085 | 0.007 | 0.6569 | Very weak |
| FTr vs ORtg | 0.082 | 0.007 | 0.6672 | Very weak |
| TS% vs ORtg | 0.790 | 0.624 | 0.0000 | Strong |
| Correlation measures the direction and strength of a linear relationship. R² shows how much variation is explained in a simple one-variable relationship. | ||||
This is the cleanest evidence that the old version of the three-point premium is not really there anymore. If simply taking more threes still created a clear edge, 3PAr should have a strong positive relationship with either TS% or ORtg.
That is not what the data shows. The correlation between 3PAr and TS% is 0.17, while the correlation between 3PAr and ORtg is 0.085. Those numbers do not prove that threes have lost value. They show something more specific: three-point volume by itself is not enough to explain offensive efficiency.
A good three is still valuable. A clean catch-and-shoot three from a Steph Curry is still one of the best shots in basketball. What the correlation check shows is that the league has already adjusted to the basic math. The easy advantage from simply taking more threes has been squeezed out.
The comparison with the other relationships helps explain why. The correlation between FTr and ORtg is 0.082, while the correlation between TS% and ORtg is 0.79. That matters because offense is not only about where the shot comes from. It is about whether the offense creates efficient shots, foul pressure, spacing, and enough stress on the defense.
That is why the premium is better understood as conditional now. More threes are not automatically better threes. The premium still exists, but it belongs to teams that create the right threes inside a complete offense.
Determining the Cluster Groupings
Before grouping teams, we needed to decide how many clusters made sense. That is what this chart is doing. It is not testing whether the three-point premium exists. The correlation section does that more directly. This chart is about model setup: how many offensive style groups should the K-means model use?
The chart uses the elbow method, which runs K-means over and over with different numbers of clusters. I tested cluster counts from 1 through 10. For each number of clusters, I calculated the within-cluster sum of squares, or WCSS.
WCSS measures how spread out the teams are inside their assigned clusters. A lower WCSS means the teams inside each group are more similar to each other. That sounds good, but there is a catch. WCSS will almost always go down when you add more clusters because the model has more groups to work with. If every team had its own cluster, the fit would be perfect, but the model would be useless.
This shows the impportance of the elbor, we are looking for the point where adding more clusters still improves the fit, but the improvement starts getting smaller. That point gives a reasonable balance between accuracy and readability.
The first line is the simple model using only 3PAr and TS%. The second line is the expanded model using 3PAr, TS%, FTr, and ORtg. Both versions help answer the same question: how many groups are enough to describe different offensive styles without turning every small difference into its own category?
I ended up going with four clusters because it gives the model enough room to separate different offensive styles without making the results too noisy. The chart shows that the biggest gains come early. After that, each additional cluster still lowers WCSS, but the improvement is less meaningful.
The trade-off withh K clusterins means more clusters will always make the math look better, but they do not always make the basketball explanation better. Four clusters gives a cleaner structure: high-volume and efficient teams, high-volume but less efficient teams, lower-volume but efficient teams, and lower-volume teams that do not separate as much offensively.
Bringing it back to the three-point premium question, we use this because we aren’t just trying to sort teams by who shoots the most threes. We are trying to see whether three-point volume still lines up with better offense, or whether the value of the three now depends on efficiency, foul pressure, and overall offensive balance.
Model 1: Does More Three-Point Volume Mean Better Efficiency?
This first model keeps the question as clean as possible. It only uses 3PAr and TS%, so it is testing the basic version of the three-point premium. If taking more threes still creates a clear advantage by itself, the higher-volume teams should separate as the more efficient teams.
This is also the closest part of the project to the basic shot chart idea from the lecture. It looks at where the offense is leaning and whether that shot profile turns into efficiency. The limitation is that this view does not fully capture the free throw value that true shot charts are trying to include.
| Simple Cluster Summary | ||||||
| Four offensive profiles based only on three-point volume and true shooting. | ||||||
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Cluster Group
|
Shot Profile
|
Context
|
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|---|---|---|---|---|---|---|
| Cluster | N | Teams | 3PAr | TS% | ORtg | FTr |
| ● High 3PA / High Efficiency | 8 | ATL · BOS · CHI · CHO · CLE · GSW · MIL · NYK |
45.6% | 58.7% | 117.0 | 23.7% |
| ● High 3PA / Lower Efficiency | 5 | BRK · IND · MEM · PHO · POR | 44.7% | 56.7% | 112.5 | 25.6% |
| ● Lower 3PA / High Efficiency | 6 | DEN · LAC · LAL · MIN · OKC · SAS | 41.2% | 60.2% | 118.9 | 28.8% |
| ● Lower 3PA / Lower Efficiency | 11 | DAL · DET · HOU · MIA · NOP · ORL · PHI · SAC · TOR · UTA · WAS |
37.2% | 57.3% | 114.7 | 27.4% |
| Cluster colors match the plot. This simple model only uses 3PAr and TS%; ORtg and FTr are shown as context. | ||||||
The results show why the three-point premium is not automatic anymore. The correlation between three-point attempt rate and true shooting percentage is only 0.17, so higher volume does not clearly equal better efficiency.
The highest-volume cluster is Cluster 1: High 3PA / High Efficiency, with an average 3PAr of 45.6% and an average TS% of 58.7%. The most efficient cluster is Cluster 3: Lower 3PA / High Efficiency, with an average TS% of 60.2%.
According to this, shooting more threes can still be part of a great offense, but it does not guarantee one. Volume has to come with shot quality, spacing, personnel, and enough pressure elsewhere on the floor to keep defenses honest.
This also connects back to the shot chart lecture. A basic shot-profile view can show where value seems to come from, but it does not fully answer whether the offense is creating the best total scoring chances. That is why the next model adds foul pressure and total offensive rating.
Model 2: Adding Context to the Three-Point Premium
The simple model says three-point volume is not enough by itself. This expanded model tries to explain why. It still includes 3PAr and TS%, but it also adds FTr and ORtg so the model can account for foul pressure and overall offensive strength.
This connects directly to the shot chart lecture. A basic shot chart can make the three-point shot look like the obvious answer because it focuses on field-goal points from different locations. The true shot chart idea pushes that further by asking whether the shot location creates other value too, especially free throws. That is why FTr matters here.
Efficient offense is not created by shot location alone. A team can take a lot of threes and still struggle if those shots are rushed, contested, or disconnected from the rest of the offense. The better question is whether the three-point shot is part of a complete offensive profile.
| Expanded Cluster Summary | ||||||
| Four offensive profiles based on volume, efficiency, foul pressure, and offensive rating. | ||||||
|
Cluster Group
|
Shot Profile
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Pressure / Results
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|---|---|---|---|---|---|---|
| Cluster | N | Teams | 3PAr | TS% | FTr | ORtg |
| ● Rim and Free Throw Pressure | 7 | CLE · DEN · LAC · LAL · MIN · OKC · SAS | 41.7% | 60.1% | 28.5% | 118.9 |
| ● Efficient Perimeter Offense | 7 | ATL · BOS · CHO · GSW · MIL · NYK · PHO | 46.0% | 58.4% | 23.0% | 117.1 |
| ● Rim and Free Throw Pressure | 10 | DAL · DET · HOU · MIA · NOP · ORL · PHI · SAC · TOR · UTA |
36.9% | 57.4% | 27.8% | 115.0 |
| ● Three-Heavy Without Premium | 6 | BRK · CHI · IND · MEM · POR · WAS | 43.8% | 56.9% | 25.6% | 111.8 |
| Cluster colors match the plot. The expanded model uses 3PAr, TS%, FTr, and ORtg. | ||||||
The expanded model gives the simple model a better explanation. The chart still shows 3PAr and TS%, but the clusters are now built with FTr and ORtg included. That means teams can move into different offensive groups even if they look similar on the basic shot-profile chart.
The best offensive-rating cluster is Cluster 2: Rim and Free Throw Pressure, with an average ORtg of 118.9, an average TS% of 60.1%, and an average 3PAr of 41.7%. The highest three-point-volume cluster is Cluster 4: Efficient Perimeter Offense, with an average 3PAr of 46.0% and an average ORtg of 117.1.
The foul-pressure piece matters too. The strongest FTr cluster is Cluster 2: Rim and Free Throw Pressure, with an average FTr of 28.5%. That helps explain why the three-point premium cannot be judged by volume alone. A team can create value by spacing the floor, but it can also create value by pressuring the rim, getting to the line, and forcing defenses to guard more than one thing.
Shot location matters, but total value matters more. A three-heavy offense only captures the premium if those threes are good shots and if the rest of the offense still creates pressure.
The simple model says volume is not enough. The expanded model shows why. The three still matters, but it works best when it is part of a fuller offensive profile.
The Numbers Behind the Pattern
The clusters show the pattern. This table puts numbers on it.
Oftentimes the three-point premium is still talked about like it is automatic, when in reality, as we can see, it is not that anymore. If simply taking more threes still created a clear edge, 3PAr would have a stronger relationship with TS% and ORtg.
| The Numbers Behind the Pattern | |||||
| A tighter read on what the simple and expanded models are really showing. | |||||
| Model | Check | r | R² | Strength | Basketball Read |
|---|---|---|---|---|---|
| Simple | 3PAr vs TS% | 0.170 | 0.029 | Very weak | Volume alone does not explain efficiency. |
| Expanded | 3PAr vs ORtg | 0.085 | 0.007 | Very weak | More threes do not automatically lift offense. |
| Expanded | FTr vs ORtg | 0.082 | 0.007 | Very weak | Foul pressure still matters. |
| Expanded | TS% vs ORtg | 0.790 | 0.624 | Strong | Efficiency matters more than selection alone. |
| P-values are left out on purpose. With 30 teams, the better question is relationship strength, not whether one small sample clears a significance cutoff. | |||||
The first two rows are the heart of the argument. In the simple model, 3PAr has a very weak relationship with TS%, with a correlation of 0.17. In the expanded model, 3PAr has a very weak relationship with ORtg, with a correlation of 0.085.
That is the key point. Three-point volume is not strongly carrying efficiency or total offense by itself. The premium is still real, but it is not automatic.
The other rows explain why. FTr keeps foul pressure in the conversation, and TS% reminds us that shot selection only matters if it turns into efficient scoring. A team can take the mathematically correct shot and still waste the possession if the shot is rushed, contested, or taken by the wrong player.
In reality the better takeaway is not that teams should stop shooting threes. That would be ridiculous. The takeaway is that the modern three-point edge is earned. It comes from the right threes, taken by the right players, in an offense that still stresses the defense somewhere else.
When Volume Becomes Value
The table below is the cleanest way to answer the section title. Three-point volume becomes value when it shows up somewhere else: better efficiency, better offensive rating, or enough foul pressure to keep the defense from only guarding the arc.
In other words, it’s the difference between taking threes and actually capturing the premium.
| Volume-to-Value Check | |||||||
| The three-point premium shows up when volume turns into efficiency, pressure, and total offense. | |||||||
| Signal | Check |
Cluster Profile
|
Basketball Read | ||||
|---|---|---|---|---|---|---|---|
| Cluster | 3PAr | TS% | FTr | ORtg | |||
| Volume | Highest 3PAr | High 3PA / High Efficiency | 45.6% | 58.7% | 23.7% | 117.0 | This is the starting point, not the payoff. |
| Efficiency | Best TS% | Lower 3PA / High Efficiency | 41.2% | 60.2% | 28.8% | 118.9 | Volume starts to matter when it becomes efficient. |
| Value | Best ORtg | Rim and Free Throw Pressure | 41.7% | 60.1% | 28.5% | 118.9 | This is where the offense actually cashes in. |
| Pressure | Best FTr | Rim and Free Throw Pressure | 41.7% | 60.1% | 28.5% | 118.9 | Foul pressure keeps the three from becoming one-dimensional. |
| Volume becomes value when three-point rate is paired with efficiency, offensive rating, and pressure elsewhere on the floor. | |||||||
The first row is only volume. The highest-volume three-point cluster was Cluster 1: High 3PA / High Efficiency, with an average 3PAr of 45.6% and an average TS% of 58.7%. That tells us who leans into the three. It does not automatically tell us who gets the most value from it.
The second row is where the question starts to change. The most efficient cluster was Cluster 3: Lower 3PA / High Efficiency, with an average TS% of 60.2%. If this is not the same group as the highest-volume cluster, that is the warning sign. Taking more threes is not the same thing as creating better shots.
The expanded model makes the point more complete. The best offensive-rating cluster was Cluster 2: Rim and Free Throw Pressure, with an average ORtg of 118.9, an average TS% of 60.1%, and an average FTr of 28.5%. That is closer to value because ORtg captures the whole offense, not just shot selection.
It also shows why the foul-pressure row matters. The strongest FTr cluster was Cluster 2: Rim and Free Throw Pressure, with an average FTr of 28.5%. Free throws are not a side note. They are part of why a shot chart cannot just be about where the field-goal attempt came from.
Volume becomes value when the threes are connected to the rest of the offense. The right threes create spacing. Spacing creates lanes. Lanes create fouls, rotations, and cleaner shots. That is very different from just launching more threes and hoping the math handles the rest.
The edge of the three-point shot is not volume by itself anymore. The edge is volume that turns into efficiency, foul pressure, and a better offense.