Detroit Bad Boys

Shaquille O’Neal’s 1-9 performance at the free throw line last night prompted Henry Abbott from True Hoop to dig up an old article from 2000 about Rick Barry’s underhanded “granny” shot. Anyone who’s ever watched a Pistons game knows this could be useful reading material for a Mr. Ben Wallace. From Discover:

As a boy in Elizabeth, New Jersey, in the 1950s, basketball legend Rick Barry got some painful coaching lessons from his father, a semipro. While the youngster’s friends liked to shoot their foul shots, or “free throws,” in the respectable overhand style, the old man wanted Barry to toss them just as he did— underhand. “That’s the way little kids shoot, and it didn’t help that everybody calls it the ‘granny shot,’” Barry says. “I didn’t want any part of it, but my father drove me nuts until I tried it. And amazingly, it worked.” Barry’s average from the free-throw line bounced from 70 to 80 percent and kept on climbing when he became a pro. “Nobody ever teased me, but then it’s hard to tease somebody when the ball keeps going in.”

Can anyone really argue with Barry when it comes to free throw shooting? He shot .900 for his career, and once went an entire season missing only nine shots in 169 attempts. And believe it or not, Barry also has science on his side. Peter Brancazio, a physics professor emeritus from Brooklyn College and author of SportsScience went so far as to calculate the optimal angle of the arc from the free throw line, determining that an underhanded attempt offered the best margin for error.

The key to a successful foul shot lies in the arc of the ball— in general, the higher the better. While an official-sized basket is 18 inches in diameter, the basketball itself is only about 9.5 inches, which gives a margin of 8.5 inches. But when the ball is thrown nearly straight at the basket— in the style of Shaquille O’Neal— the margin disappears because the rim of the basket, from the perspective of the ball, resembles a tight ellipse. “That’s why these guys miss so much,” says Brancazio. “Because of the sharp angle of the typical overhand throw, there ends up being a much smaller window for the ball to go in.” If the ball comes down at the basket from a steeper angle— the way it does if tossed up in the high arc characteristic of an underhand throw— the margin reappears. “That means there’s a far greater chance of making the basket,” he says.

Using lots of trigonometry, Brancazio calculated the optimal angle of the arc from the free-throw line. If tossed at 32 degrees or less, the ball will likely hit the back of the rim. “That doesn’t mean it won’t go in, but it will certainly bounce off the metal and reduce the chance of success,” he says. At angles greater than that, the ball has a chance of making a nice swish. The optimum angle, he calculated, is 45 degrees— plus half the angle from the top of the player’s hand to the rim.

If trigonometry makes your head hurt as much as it does mine, there’s also some simple common sense being applied, as well:

Another factor of the granny shot also helps a free throw win cheers rather than jeers: a backward spin added to the ball. If a ball with backspin happens to hit the metal rim of the basket, the friction of contact suddenly reduces its forward velocity. “It’s like a drop shot in tennis— the ball bounces, but it doesn’t have a forward motion on it,” says Brancazio. This effect tends to freeze the ball at the rim and greatly increases the chance that it will tip into the basket rather than ricochet off.

From an outsider’s view, Ben Wallace’s struggles at the free throw line seem to stem from his form. His shots go all over the place, in part because he’s not able to replicate a consistent release — whether that’s due to his wrist injury, lack of muscle memory or just a mental block is irrelevant. But the granny shot could help him with that, too:

The underhand throw can also minimize the drift of the ball. “A little sideward movement at the start of the throw will translate into a big movement toward the end,” says Tom Steiger, an assistant professor at the University of Washington in Seattle who teaches basketball physics in a sports science class. … The underhand throw provides better stability than the overhand “because you’re holding the ball with both hands,” Steiger says. This helps players balance the subtle motor muscles in the hands, and keeps them more relaxed. The movement of the underhand throw is a simple, easy-to-control upward pendulum motion. By contrast, the more conventional overhand free-throw shot involves separate movements of the wrist, elbow, and shoulder that can add errors. “If the ball ends up rolling off one side of your hand even a little bit, you’ll miss,” he says.

This isn’t the first time I’ve heard someone suggest players like Wallace and O’Neal adapt the granny shot, but it’s certainly the first time I’ve seen someone provide so much evidence in support of it. The Pistons are about to offer Wallace at least $10-12 million a year for the next 4-5 seasons; is it so much to ask that he at least spend a summer giving this a shot? I know NBA players are proud men, but it all comes down to winning games, and if Wallace could improve to even 60% at the line, there’s not a person in the world that would make fun of him.

The Physics of. . . Foul Shots [Discover, via True Hoop]
Rick Barry Statistics [Basketball-Reference.com]