# The 3-Point Percentage Inflection Point

Well, that’s embarrassing.

Modern NBA media and analytics put extreme emphasis on the 3-point shot and its efficiency over several 2-point shots. After all, 3 > 2 is indisputable. Out of all the metrics created, 3 point percentage is one of the remaining useful statistics from a traditional box score. But why is this? Why do media members harp on this statistic so much? Why are fans so quick to blame shooting?

It’d be easy to blame Steph Curry and the jump shot happy Warriors for afflicting this strategy upon the NBA. However, it started much earlier than that. Mike D’Antoni and the 7 seconds or less Nash led Phoenix Suns showed a revolutionary pace and space offense. The Spurs played them, beat them, and later appropriated their style with various adaptations. Then the Warriors put the strategy on overdrive with numerous off ball actions in addition to the best shooting, possibly ever. Now, you’ve got fans, analysts, and talking heads on sports shows saying the same things:

• Can he well enough to stay on the floor?
• Can he play against the Warriors? Or the Rockets?
• What’s his 3 point percentage?
• “WHY CAN’T [MY PLAYER] SHOOT? TRADE HIM IMMEDIATELY. SIGN SOMEONE IN HIS PLACE.”
• Why is that guy open?!

# Math Required:

To begin seeing the importance of the 3-point shot, we have to start with expected value. The formula is simple.

Probability of an event * Point value = Expected Value

It’s not whether you’d get 3 points or 2 points from a shot. It’s the value you expect to return per shot taken. The values will look pretty funny, but I promise it will make more sense at the end of this article. We don’t need to be afraid of decimals anymore.

During Steph Curry’s insane MVP season, he shot 45.4% on 3-pointers. That broadly translates to 1.362 points per shot. To contrast this with a mid-range heavy player, Kobe Bryant’s scored 35.4 points per game on 48.2% 2-point FG% during his phenomenal 2005-06 season. This equates to 0.964 points per 2-point shot attempt. That’s a whopping 41.2% more expectation per shot for Steph! Granted, no players can shoot like Steph Curry can. but this feat remains an impressive increase in EV.

To further illustrate the value of a 3 point shot, we have to look at another statistic, team offensive efficiency:

Offensive Efficiency Formula = 100 * (Points Scored)/(Possessions)

You can usually find offensive efficiency abbreviated as Ortg.

This equates to how how many points a team is expected to score over 100 possessions. To scale this to expected value, we can simply divide by 100. I’m going to use team offensive efficiency as the relative standard to illustrate why 3-point shots and thus, shooting ability is so valuable now.

In the last three seasons, the league average offensive ratings were 108.6, 108.8, and 106.4 from newest to oldest. This averages out to 107.9. So the average NBA possession came out to 1.079 points per possession. This alone already illustrates how terrifying a Steph Curry 3-point shot really is and was especially during his MVP season.

# The 3-Point Inflection Point

So how well do players need to shoot to remain a threat? We can solve this with some simple algebra.

1.079 PPP < 3P% * 3

This equates to about 36% to be equal to the average NBA possession. At first glance, that looks really, really high. I thought it’d end up being about 33% or a little bit less because all 2-point shots look pretty difficult on TV.

According to data from basketball-reference.com, there are 319 unique players of 713 total unique players who have a 3P% of 36% or higher in the past three seasons. Out of those 319 players, 110 players played at least 8 minutes per game and shot at least 1.5 3-point attempts per game.

Let me repeat. Only 110 out of 713 players in the past 3 seasons were significant players who shot better than 36% from 3. That includes some odd bench players. That includes the rotation players. It’s everyone in the past 3 seasons.

Just for fun, we can look at the last season too. The 2017-18 season had a total of 540 players. 113 had a 3P% better than 36%, played 8 minutes or more, and attempted 3 3-pointers per game.

To generate the same 1.079 PPP with a 2-point shot, the shot must at least have a 53.95% to go in. Generally, that means only paint shots are acceptable and why midrange shots are shunned so harshly. Well, unless you’re Steph Curry who shoots 60% in midrange shots. Then you can just shoot whatever you want. Because who cares? You’re Steph Curry. Everything coming out of your hands may as well be on fire. ?

# How Spacing is Created

36% is the magic number for whether or not you close out on a 3-point shooter. It means those are the players that defenders either must guard diligently or stay near enough to make a worthy close out effort. An extra step or two away matters in the NBA with players this big and fast. Extra spacing warps a defense further out of formation and makes the point of attack more dangerous. Without spacing, a team can send extra defenders to stifle pick and rolls, deter drivers, step into passing lanes, and pack the paint. This is the mechanic governing spacing on the basketball court. The extra space is created simply by a threat of making a 3-pointer.

The offensive players’ shooting abilities will also determine how a pick and roll is guarded. If the ball handler is a great shooter, it can make a mess of defenses as evidenced by Curry-Thompson pick and rolls. Switches are one method, but they’re prone to error. One miscommunication? Someone is suddenly wide open, and everyone on defense is looking around, pointing fingers, and asking “whose fault is this?” Fighting over good screens fatigues players mentally and physically throughout the game and season. Having the screen defender hedge out to give your primary defender time to recover can put your screen defender out of position. He needs to be fast enough to run back to a screener if he shoots well. If the ball handler can’t shoot well, the primary defender will always go under to recover for the drive. If the ball handler can’t shoot better than 36% from 3, you’d rather give it up than allow for other, more valuable plays.

Just let 6’8″, 220 lbs Jimmy Butler tell you how hard screens can be.

Shooting is hard. Shooting is a skill. JJ Redick’s podcast with Kyle Korver shares just how much preparation goes into the mechanic that is shooting a basketball from 23 feet away. It shows how much a few little injuries can affect and throw off the entire, polished mechanic. It is further evidenced by how the percentages can change depending on how wide open a player is.

# Caveats and Simplifications

1. One major caveat to my article is the 1.079 PPP value includes 3-pointers in it. In the last decade or so, teams have used the 3-point line more and more. If we isolated just 2-point field goals and recalculated the minimum 3P% needed, I suspect it would be lower by at least 5%. Unfortunately, I don’t have the dataset to do this yet.
2. 3-point percentage in this article is extremely simplified. It’s an all encompassing statistic that is accounting for every kind of shot. This includes catch and shoot or off the dribble. Off the dribble shots are known to be far more difficult given a defender is closer, and the mechanic seems more complicated than catching and shooting. The percentage is swayed by the difficulty of shots.
3. Last second heaves and super late in the shot clock shots should be tossed out to get a more accurate sense of what a player’s true 3-point percentage is. I think this point is a good point of discussion. Several teams run actions and still get a decent shot at the ends of the shot clock. However, we could still find a way to throw out end of quarter heaves even if they have little effect.

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#### About the Author: Benjamin Xiao

I am a data practitioner who loves making simple, powerful visualizations and working with machine learning algorithms to learn more about the world. Basketball is incredibly dynamic, and it only takes one player to change an entire game plan. Data has stories hidden within it, and I want to reveal why my favorite team is better than yours is. And why Ben Simmons is amazing.