Q: How much arch should you put on a shot?
A: You should release the ball at a 52 degree angle.
Q: How much backspin should you put on a shot?
A: The ball should spin at 3 Hz, or 3 spins per second.
Wait, what? How on earth could we know such things?
Well, it turns out that statistical studies and computer simulations have been done to determine the most optimal shot. In fact, this has been known since the 1980′s when a physics professor, Peter Brancazio at Brooklyn College, did the studies. Back then, he determined that a shot by an average sized player (roughly 6 feet) on a free throw (which gets the shoot off at roughly 7 feet high) should release the ball at a 51 degree angle.
“Brancazio explains that you need 45 degrees plus half the angle formed by a straight line between the position of the ball at launch and the basket. Depending on your height and where you are on the court, that typically ranges from 7 to 14 degrees. Thus, for a shot leaving your hands at eight feet above the floor from 18 feet out, you’ll want to launch the ball at a bit more than 48 degrees. For most players at a distance of 10 to 25 feet, the least-effort angle ranges between 47 and 52 degrees.”
Over twenty years later, in 2008, engineers from North Carolina State did a similar study. Only this time they had the invention of computers on their side. Interestingly, they came up with almost the exact same angle. The concluded the shot should leave an average shooters hands at a 52 degree angle and also that the optimal backspin is roughly three rotations per second (3 Hertz).
Engineers at North Carolina State University published an analysis of hundreds of thousands of 3-D computer simulations of free throws. Their optimal angle: 52 degrees. (Seen from the side, a 52-degree free-throw parabola has its highest point just about even with the top of the backboard.)
The exact angle of course depends on your height, whether it is a set shot or jump shot (affecting the height of ball release) and your distance from the hoop. These optimal projections are also determined by shooting the ball with the least effort as well, in order to produce a shot that gets off quickly and easily.
So, while both studies have produced an optimal angle for free throw based on ideal angle entering the hoop and ease of shot, I am still not sure that adding more arch is not such a bad thing. If you have the strength to get those shots off consistently and quickly, from my understanding of shot trajectory and ball-hoop entry, I think extra arch cannot hurt. Plus, as a player gets tired, the arch surely decreases on the shot. Practicing a loftier shot will keep the arch higher when the shots can really count toward the end of the game.
Lastly, it is almost impossible to know the exact angle you are shooting at during your shots. However, you can tell afterward if you videotape your shot from the side. Put the video onto your computer and pull out a compass to measure the angle of release. If you’re only getting your shot off at a 40 degree angle, you may want to aim a bit higher during your next shooting session.