ESPN has produced a brief "Sport Science" segment analyzing the physics of how close Butler University's potential game-winning shot (released 46 feet from the basket) came to going in, at the end of the Bulldogs' NCAA men's basketball championship battle vs. Duke. A video of the segment is available here. The video identifies three parameters of a shot's trajectory: "launch angle, release velocity, and aim."
The 54-degree launch angle would be considered "good," according to the video. The release velocity, which was 28 miles per hour, was considered close to ideal; had the shooter, Gordon Hayward, heaved the ball with a velocity 0.5 mph less, the shot "has a chance."
With the two aforementioned variables optimized, according to the video, if aim were such that the ball "hits just 3 inches to the left on the backboard [compared to where it actually hit], Butler wins."
There actually has been considerable physics research on the trajectory of the basketball shot. A book came out a few years ago entitled The Physics of Basketball, which I reviewed here.