What If Basketball Had a 4-Point Line? A Mathematical Take

Imagine basketball with an extra twist: a 4-point line. This line would be further out than the current 3-point line, rewarding players who can make shots from really far away. Let’s dive into how this could change the game, using some simple math and recent shooting data.

Current Long-Range Shooting Stats

First, let's look at some players who are already shooting from way beyond the traditional 3-point line. Here's how they did last season from 30+ feet:

• Damian Lillard: Made 32.5% of 117 attempts

• Trae Young: Made 31.3% of 83 attempts

• Jordan Poole: Made 33.3% of 66 attempts

• Stephen Curry: Made 22.6% of 62 attempts

• LaMelo Ball: Made 38.9% of 54 attempts

The Math Behind a 4-Point Line

Let's dive deeper into the numbers to understand the potential impact of a 4-point line. To do this, we can calculate the expected points per shot (EPPS) from beyond this new line. This calculation helps us see just how valuable these long shots could be compared to current 3-pointers.

Calculating Expected Points per Shot

The EPPS is calculated by multiplying the probability of making the shot (the shooting percentage) by the number of points that shot is worth. Here’s how you would calculate it for both 3-point and hypothetical 4-point shots using LaMelo Ball’s stats as an example:

• 3-Point Shot EPPS: EPPS3pt=38.9%×3=1.167 points per shot

• 4-Point Shot EPPS: EPPS4pt=38.9%×4=1.556 points per shot

From these calculations, we see that if LaMelo Ball’s long-distance shots were worth 4 points instead of 3, his expected points per shot increases, making those shots significantly more valuable.

Comparing to League Average

Now, let’s compare these figures to the league average for regular 3-point shots:

• League Average 3-Point Shot: Suppose the average 3-point shooting percentage in the NBA is about 36%. Then the expected points per shot would be: EPPSLeague Average=36%×3=1.08 points per shot
  

This comparison shows that a proficient long-range shooter could contribute more to the team's scoring with a 4-point line, surpassing even the league average for 3-point shots in terms of efficiency.

Implications for Team Strategy

With these numbers in hand, teams would need to strategize not only around who can make these shots but also when and how often to attempt them. This could lead to a new era of statistical and strategic planning in basketball, emphasizing a balance between risk and reward on the court.

This simple mathematical analysis illustrates just one of the many ways that introducing a 4-point line could fundamentally change basketball, making it an exciting prospect for the future of the sport.

Potential Game Changes

1. More Space on the Court: Players would spread out more to guard against 4-point shots, which could open up more room for driving to the basket.

2. New Player Skills: Players who can shoot from really far away would become super important. Teams might even start training players differently, focusing on really long shots.

3. Different Defenses: Defenses would have to change. They might have to guard players closer, even when they are far from the basket, which could make it easier for other players to score from closer in.

Visualizing the Impact

To visualize this, imagine a basketball court where players are not just guarding around the 3-point line but are also way out near a new 4-point line. This would stretch the defense and create new opportunities for offense.

Conclusion

Adding a 4-point line could make basketball even more exciting. It would reward players who can make tough shots and change how teams play defense. Whether this change would be good for the game is up for debate, but it's fun to think about how it would shake things up!