Some coaches, in their efforts to help the men estimate the necessary height of the arch before the descent of the ball on its way to the backboard, fix an imaginary spot approximately twenty-five feet in the air and twenty feet out in front of the basket. The player, when shooting, can imagine a line described by the course of a ball from this spot in the air to the basket. The ball which describes this imaginary line deflects into the basket on a carom shot.
This line should be the locus of the highest points of all arches used for rebound shots from any ordinary scoring distance directly in front of the basket. The ball in its arch after it leaves the player's hands describes a curve similar to a parabola, the highest point of which intersects the imaginary locus. The distance of the shooter from the basket determines the point of intersection of the crest of the parabola with the line. The closer-in the shots are made, the farther down on the imaginary line will be the point of intersection.
It is good pedagogy to teach the men to shoot for a direct looping hit into the basket. And this scheme of describing the imaginary line from a spot in the air is a means of stressing upon the players' minds the importance of shooting high. Most players shoot too low and too short. Should they overshoot, by correctly arching the shots, they will always have an extra chance for a goal on the rebound.
_from Chapter III, Individual Offense, of the 1924 edition of My
Basket-ball Bible by Forrest C. Allen
[Before I knew about Phog Allen's book, I got in trouble with my high shool basketball coach by suggesting that aiming for the vertex of the parabola might be a good way to shoot. He thought I was being a wise guy, but he should have let me try it - it couldn't have hurt my shooting. LMH]