Overhand or underhand? Fast or slow? Study explores optimal throwing strategies

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Whether you’re pitching in a major league baseball game or tossing crumpled paper into the trash, the act of throwing is incredibly complex and usually subject to a trade-off between speed and accuracy. A Yale researcher’s new study looks at why this is.

Throwing fast and accurately is a uniquely human ability (monkeys also throw things, but they’re really bad at it, say scientists). The study, published April 26 in Royal Society Open Science, focuses on the origins of the speed vs. accuracy trade-off with a series of calculations that look strictly at the physics of throwing. The researchers also explain why certain throwing strategies work best with certain tasks.

One common theory is that the faster one throws a ball, the more difficult it is to release it at exactly the right time. But lead author Madhusudhan Venkadesan, assistant professor of mechanical engineering & materials science, said the new study actually found that even if a person is equally good at controlling the release at all speeds, faster throws will still be less accurate. The differences in accuracy between a fast throw and a slow one all happen after the ball is released.

“Once you launch the ball, there’s nothing you can do,” said Venkadesan, who worked on the study with L. Mahadevan at Harvard University. “The ball’s just going to carry out the consequences of what you did.”

The ball travels in a nearly straight line in fast throws, so errors in the angle at which the ball is released are amplified; small errors in controlling speed have no effect. The opposite is true for slow and curved flight paths, with small errors in the angle of release having little effect. It’s a trade-off that favors slower throws, said Venkadesan.

“What we find is that almost the slowest arc is often the most accurate,” he said. “We’ve compared these calculations to published data of people throwing into wastebaskets; we’ve compared it to a study on dart throwing.”

Of course, throwing at near-minimal speed wouldn’t work for most baseball pitchers, let alone our rock- and spear-throwing ancestors, whose hunting abilities were crucial to our evolutionary development, he noted.

“You don’t just want to be fast or just accurate, you want to be fast and accurate, and this work tells us that this is particularly challenging. The faster you are, the less accurate you are, so how can we be both? That’s a question we’re pursuing.”

Cricket fielding is one of the exceptions to the slow-is-more-accurate rule, the study showed. To strike the nearby vertical wickets, players fare better with a fast underhand toss.

As for the question of whether to throw overarm or underhand, that depends on such factors as the target’s shape, height and distance, said the researchers. Experienced dart players, for instance, throw overhand (optimally releasing the dart 17 to 37 degrees before the arm becomes vertical, and at about 5.5 meters per second). On the other hand, if your wastebasket is fewer than three arm lengths away and below shoulder height, a gentle overhand toss is your best strategy.

Even without working out such calculations, most people throw in ways close to the mathematically optimal methods, Venkadesan said, noting this is likely a result of learning through trial and error over our lifetimes.

One exception is the underhand free throw in basketball, he said. The now-retired Rick Barry set NBA records with his underhand technique, and the researchers’ calculations find that it has a marginal advantage over the overhand throw. Yet it has all but disappeared from professional basketball. Venkadesan blames this on its nickname, “the granny throw.”

“One suspects there are social and cultural reasons you don’t see that practiced too often,” he said.

Science & Technology

Media Contact

William Weir: william.weir@yale.edu, 203-432-0105