Making shots at different angles

Q: What is the best angle for the ball to approach the basket?

A: I've heard that 60° above horizontal is the most optimum angle, other studies say 50°. Which is more optimal is not relevant. Just get it up higher and you'll see the ball comes in more softly and the landing area is larger.

Five or six years ago I tried to do a calculation of how big the landing areas are for different angles coming in. I just sort of estimated where on the rim shots could hit and still go in for angles of 30, 45 and 60°. I drew ovals of the rim and then drew ovals over that of where the balls could land, and then I tried to calculate the area of the ovals. Not very mathematically provable, but I came up with these estimates:

A ball coming in at 30° has a certain sized landing area. (X)
A ball coming in at 45° has a landing area 60% bigger than 30°. (1.6X)
A ball coming in at 60° has a landing area 120% bigger than 30°. (2.2X)

These are just my crazy estimates.

If these statistics are true or even close, a ball coming in at a very high angle (~60° above horizontal) has a landing area over twice as big as for a flat shot of only 30°. (Note you also get a softer landing because gravity has had a chance to slow the movement of the ball upward.)

Bigger target, softer landing, who wouldn't want to shoot this way if she or he knew?