For the past 50 years, NBA basketball players successfully shoot about 75% of free throws, so it's natural to think that is the natural limit. But that's before science got involved:
Sharon Begley of Reuters has the scientific secrets of nailing free throws: Link
Using a computer simulation of millions of trajectories based on shots by the best free-throw shooters, Silverberg and colleague Chau Tran determined how various factors affect the chance of success. The magic formula: a launch angle of 52 degrees, three revolutions per second of backspin, and aiming for a spot 7 centimeters (2.8 inches) back from the center of the basket, toward the back of the rim.
"With backspin, if the ball hits the rim or backboard, the contact deadens the ball," said Silverberg. "That means it comes off slower, stays closer to the basket and is more likely to fall in."