When watching a basketball game on the playground or on television, one cannot help but wonder why some shots go in the basket and others do not. Is shooting accuracy purely a function of player skill developed through countless hours of practice? Or is there another explanation for it? It turns out that physics provides at least part of the answer.

The flight of the ball as it moves from the player's hand until it arrives at the rim of the basket traces an arc. The arc is determined by the angle and speed at which the ball is shot. In the controlled environment of a gym, gravity is the only force affecting the ball as it flies through the air. In this scenario, the arc reflects both the ball's forward motion and its downward motion.

The arc of a shot is measured in terms of the angle that the ball enters the hoop. If it enters directly from above—as might occur with a powerful "dunk"—the ball's flight path would reveal a 90-degree arc. If the ball is shot from any distance away from the basket, the arc would be somewhere between 0 and 90 degrees. The explanation for whether a shot does or doesn't enter a basket is determined in part by this arc.

A regulation-size basketball is roughly 9.5 inches in diameter, while the hoop it travels through is 18 inches in diameter. This leaves a margin of 8.5 inches over which other errors, such as shooting with too much or too little force can be accommodated and the ball can enter the hoop without deflecting off the rim. Depending on the angle at which the ball approaches the rim, the margin will vary. The lower the arc's angle, the smaller the margin becomes. For example, while the margin for a ball shot with a 55-degree arc is 5.0 inches and one shot with a 45-degree arc is 3.0 inches, at 32 degrees, the margin is 0 inches, allowing no room for player error where distance control is concerned.

The degree of arc, then, can explain why shots are too short or long. It does not account for a player's aim, however. Aim determines whether or not a shot will be on course to begin with. But all other things being equal, players stand a better chance of making a shot by shooting with a higher arc. Those who are able to control the arc and repeatedly keep it within a narrow range enjoy greater success.

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