Basketball Physics: The Anatomy of the Free Throw

In theory, the free throw is a gift. The shooter shoots with no elbows thrown in his direction, no seven-foot-tall man trying to block the shot, and no screaming crowd (unless he plays for the visiting team). So what makes this solo shot so choke-worthy? In the spirit of March Madness, we break down the anatomy of this seemingly simple shot.

Body Mechanics

"The lift that you have as a free-throw shooter starts from the feet," says Bruce Kreutzer, a shooting specialist at the Mark Price Basketball Academy in Suwanee, Ga., who has been working with the NBA and amateur players for 25 years. "The majority of players today use their upper body first, which really throws off the rhythm."

When they step up to the line, players should align their body?toes, hips, and shoulders?directly with the basket, Kreutzer says. Seems easy enough, but things soon become complicated. The amount of bend in the knee needed to make a shot is directly proportional to a player's distance from the hoop, and players often struggle to find the amount of bend that correlates with the right amount of energy buildup. Too much energy and your shot is a brick off the backboard; not enough and it's an air ball.

As a player prepares to shoot, the ball should be resting on the finger pads (that first roll of knuckles just above your palms) and not the fingertips, Kreutzer says?"This way there's no snap, just a rhythmic flop." In the release, the shooting arm and support arm should extend toward the basket. The same goes for the rest of the body; the shooter's weight should be traveling forward in a controlled calf-raise motion.

Debunking the Swish

North Carolina State University mechanical engineering professor Larry Silverberg, an avid baller himself, set out to determine the physics behind the perfect free throw. With his colleague Chau Tran, he co-wrote a software program to analyze three-dimensional computer-simulated free-throw trajectories.

"If you take top athletes in any sport, most have a really hard time explaining what they're doing," Silverberg says. "By simulating millions of shots we could see patterns that tend to confirm best practices."

Their extensive research allowed them to establish a few guidelines for the foul line: aim toward the back of the rim with 3 Hz of backspin and at 52 degrees to the horizontal. Oh, and do all this at a perfectly smooth and consistent speed.

Let's take the first piece of advice: Aim for the back of the rim. Despite what most people may think, Silverberg found that aiming for the center of the basket actually decreases the likelihood of a successful shot by almost 3 percent. Silverberg and Tran found that the sweet spot is actually 2.82 inches past the center of the hoop. You might make less "nothing but net" shots this way, as the ball is more likely to hit the back of the rim and go in, but your overall shooting percentage will be greater.

Second piece of advice: the backspin. Three Hz of backspin translates to three complete revolutions of the ball before it reaches the hoop, and the reason you want this backspin is that it deadens the ball, should it hit the rim or backboard during flight. In their simulations, Silverberg and Tran found no additional advantage to more than three revolutions; plus, they found that players struggle to put more backspin than this anyway.

Finally, the angle: Without a protractor in your sneakers, it might be difficult for players to execute a launch angle of exactly 52 degrees. The shorthand version that Silverberg tells players, then, is to shoot the ball so that it's about 2 inches below the top of the backboard at its highest point.

"Imagine you drew a line from where the ball is released to the hoop?that's the angle from the horizontal," he says. "A good way to visualize this is aiming pretty close to the top of the backboard at the top of [the ball's] trajectory."

Of course, this is a loose rule, in part because basketball players vary wildly in height. Silverberg and Tran came up with the 52 degrees rule for a six-foot-six player, so the angle would be different for a seven-foot center, a six-foot-six point guard, or a five-foot-eight insurance salesman playing with buddies on the weekend.

But of all the parameters of the free throw, maintaining a constant speed is the most important but also the most difficult, Silverberg says. Unlike the geometric conditions, backspin and speed are variables that rely on the shooter's ability to maintain a consistent motion?arguably the most difficult aspect of any shot.

Noah's Arc

Football players watch endless game film; baseball players in a hitting slump head to the video room to see what's amiss with their swing. And basketball players can watch video of their free-throw attempts with a full statistical analysis of each shot.

John Carter, CEO of Noah Basketball, is one of the people bringing big data to basketball. He developed a little device called Noah that analyzes the arc of the ball once it leaves a player's hands, computing its angle of entry into the basket and spitting out this number in real time so that shooters can adjust their arc accordingly. For a free throw, entry-angle perfection is around 43 degrees. And, unlike the launch angle, which varies with player height, the entry angle is the same for all shooters.

"If a player shoots flat, the hole closes up," Carter says. "There's a sweet spot in the mid forties where you can have a little bit of variation in the arc, but the ball goes in at almost the same distance from back of rim every time."

Noah devices have compiled statistics for thousands of free-throw shots, confirming what Silverberg's simulations showed. Even though an entry angle of about 50 degrees corresponds to a perfect swish, the Noah data showed that players' overall shooting percentage started to decrease at above 45 degrees. So great shooters hit the back of the rim more often than they swish.

Source: http://www.popularmechanics.com/outdoors/sports/physics/basketball-physics-the-anatomy-of-the-free-throw-7556633?src=rss

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