Forget the 4-point line. Where should the 7-point line be?

ESPN managed to gin up a little 4-point line talk recently with rumors that the league had talked about adding such a line. The reports turned out to be way overblown but it got me thinking about the issue. What this issue calls for, clearly, is a completely absurd approach via analytics!

I set out to completely redraw the NBA court with only one rule: PPS (points per shot) should be the same from anywhere on the court up to say, 30 feet away from the hoop. I used all shots taken in the current season to determine what NBA average FG% is 1 foot away from the hoop, 2 feet away from the hoop, 3 feet away and so on. Then, I picked point values for these distances such that PPS was equalized at all distances. It’s no good to start with 1 or 2 point shots, because doubling the point value of a shot means you need a huge decrease in FG% for PPS to stay the same.

After fiddling with the number for a bit, I decided that the lowest point value shot would have to be 3 points. Which means that on the high end we’re going to need, well, a 7-point line. Here’s the court:

New NBA court

What surprised me the most in looking at how FG% degrades as you move away from the basket was that once you’re 3 feet away, FG% doesn’t change for another 22-ish feet. Another 3 feet after that it takes another hit, although this is probably because shots taken from 27 feet out are almost always rushed or pressured. If there was a reason to take shots that far out, players would shoot a better % from there, and we would have to move my 7-point line out. Anyways, expected PPS from every part of this court is about 2!