This is beautiful
the simple solution wrote:
The league average field goal percentage is 46%, and the average 3-pt percentage is 36%, so the expected value of a 2-pt shot is .92 points while the expected value of a 3-pt shot is 1.08 points.
The league average free throw percentage is 77%, so when you shoot 2 free throws, the expected value of those shots is 1.54 points. In other words, the penalty carries a 67% benefit (you would have got .92 points if you'd been able to attempt the field goal, but being allowed to shoot free throws gives you .92*1.67 = 1.54 points).
So what they should do is adjust the point value of the foul shots that you take when fouled during a 3 point shot. Instead of being worth one point each, they should be worth .6 points each. Then shooting foul shots after a 3 point shot would give you an expected number of points equal to 167% of the expected value of a 3 point shot (3*.6 = 1.8 = 1.08*1.67), and the penalty would carry equivalent benefit to the shots taken after a foul inside the arc.
This seems like the simple solution to me.