My co-authors (Allan Maymin and Eugene Shen) and I have written a paper analyzing free throws based on the optical data of STATS LLC. It is forthcoming in JQAS.
The PDF of the final preprint is available on SSRN.
Here's the abstract:
We use three-dimensional optical tracking data on the 25-frames-per-second positional data of 2,400 free throw shots by the twenty players with at least twelve tracked makes and twelve tracked misses over the course of the 2010-2011 NBA season, fit each trajectory to a comprehensive physics model to find the implied backspin, initial launch height, velocity, angle, and left-right deviation, and examine the differences of those five factors between makes and misses for each player with sufficient attempts in our sample. We find that usually one or two factors are most responsible for a given player's misses, but the particular factors at fault differ across players. Thus, the causes of successes and failures in free throw shooting are idiosyncratic. This framework may also be useful in analyzing jump shots taken during the game.