So Why is the 3 Pointer Better Anyway?

These days, it seems like 85% of the conversation in the NBA is about the 3-pointer and how much better it is. Broadcasters, coaches, and players all stan for the shot, citing its remarkable “efficiency”. But how can some shots be better than others? That is what we will discuss here.

The technical definition of efficiency is “a measure of the extent to which input is well used for an intended task or function”. Efficiency is almost always represented as an output in terms of input. For example, fuel efficiency is noted as “miles per gallon” where miles are the output and gallons (of fuel) is the input. The same applies for basketball where the efficiency of a shot is measured by points per shot.

This “points per shot” expression is also known as the expected value of a shot which is calculated by multiplying the probability of a shot going in and the maximum points return (For example, the maximum points return of a 3-pointer is 3 points).

Here are some examples of expected values of 3-pointers by various players:

1. 1.032 points per shot
2. 0.981 points per shot
3. 1.2 points per shot

(Career 3 point% used)

Can you guess which players these are?

In descending order from number 1, they are LeBron James, Michael Jordan, and Ray Allen.

From the numbers, it is very clear who the most efficient 3-point shooter is: Ray Allen, who expected 1.2 points for every 3 pointe he took in his career. This aligns with our intuition that out of any of these 3 players, we would want Ray Allen to take an important 3-pointer (unless you are a Spurs fan).

Let’s look at the same 3 players but this time using their percentages from a long-midrange 2 pointer (16ft~3 pointer):

1. 0.4 points per shot
2. 0.61 points per shot
3. 0.346 points per shot

(Career 2 point% from 16–3 point line used)

Again, this lines up with our intuition, Michael Jordan is by far the most efficient mid-range shooter out of the 3. Lebron James misses out on more than 2 times the points he expects to score from a 3-pointer and Ray Allen loses out on nearly 3-times the number of points per shot.

From the data, it is a no-brainer that all 3 of these players would benefit from shooting the 3 more often than the midrange and this is not an isolated case from 3 of the best shooters/offensive weapons in the history of the sport.

From the 2019–2020 season, the average NBA players efficiency per shot was:

1. 0.7383 points per midrange
2. 1.0361 points per 3-pointer

From these figures, it’s pretty self-explanatory why the 3-pointer is so popular, it maximizes the gain from each and every shot and in a game like basketball where each point matters so much, it doesn’t take a genius coach to figure out that teams should be shooting more threes.

Data from: Basketball-Reference

Thumbnail: Bleacher Report