Study: The best free-throw shooters share these biomechanical traits


There’s rarely time to write about every cool science-y story that comes our way. So this year, we’re once again running a special Twelve Days of Christmas series of posts, highlighting one science story that fell through the cracks in 2020, each day from December 25 through January 5. Today: Using markerless motion capture technology to determine what makes the best free throw shooters in basketball.

Markerless motion-capture technology shows the biomechanics of free-throw shooters. Credit: Jayhawk Athletic Peformance Laboratory.

Basketball season is in full swing, and in a close game, the team that makes the highest percentage of free throws can often eke out the win. A better understanding of the precise biomechanics of the best free-throw shooters could translate into critical player-performance improvement. Researchers at the University of Kansas in Lawrence used markerless motion-capture technology to do just that, reporting their findings in an August paper published in the journal Frontiers in Sports and Active Living.

“We’re very interested in analyzing basketball shooting mechanics and what performance parameters differentiate proficient from nonproficient shooters,” said co-author Dimitrije Cabarkapa, director of the Jayhawk Athletic Performance Laboratory at the University of Kansas. “High-speed video analysis is one way that we can do that, but innovative technological tools such as markerless motion capture systems can allow us to dig even deeper into that. In my opinion, the future of sports science is founded on using noninvasive and time-efficient testing methodologies.”

Scientists are sports fans like everyone else, so it’s not surprising that a fair amount of prior research has gone into various aspects of basketball. For instance, there has been considerable debate on whether the “hot hand” phenomenon in basketball is a fallacy or not—that is, when players make more shots in a row than statistics suggest they should. A 1985 study proclaimed it a fallacy, but more recent mathematical analysis (including a 2015 study examining the finer points of the law of small numbers) from other researchers has provided some vindication that such streaks might indeed be a real thing, although it might only apply to certain players.

Some 20 years ago, Larry Silverberg and Chia Tran of North Carolina State University developed a method to computationally simulate the trajectories of millions of basketballs on the computer and used it to examine the mathematics of the free throw. Per their work, in a perfect free throw, the basketball has a 3 hertz backspin as it leaves the player’s fingertips, the launch is about 52 degrees, and the launch speed is fairly slow, ensuring the greatest probability of making the basket. Of those variables, launch speed is the most difficult for players to control. The aim point also matters: Players should aim at the back of the rim, which is more forgiving than the front.

A 2021 study by Malaysian scientists also analyzed the optimal angle of a basketball free throw based on data gleaned from 30 NBA players. They concluded that a player’s height is inversely proportional to the initial velocity and optimal throwing angle and that the latter is directly proportional to the time taken for a ball to reach its maximum height.

Graphic showing the contrast in release angles between proficient and nonproficient shooters.
Enlarge / Graphic showing the contrast in release angles between proficient and nonproficient shooters.

Jayhawk Athletic Performance Laboratory.

Cabarkapa’s lab has been studying basketball players’ performance for several years now, including how eating breakfast (or not) impacts shooting performance, and what happens to muscles when players overtrain. They published a series of studies in 2022 assessing the effectiveness of the most common coaching cues, like “bend your knees,” “tuck your elbow in,” or “release the ball as high as possible.” For one study, Cabarkapa et al. analyzed high-definition videos of free-throw shooters for kinematic differences between players who excel at free throws and those who don’t. The results indicated greater flexion in hip, knee, and ankle joints resulting in lower elbow placement when shooting.

Yet they found no kinematic differences in shots that proficient players made and those they missed, so the team conducted a follow-up study employing a 3D motion-capture system. This confirmed that greater knee and elbow flexion and lower elbow placement were critical factors. There was only one significant difference between made and missed free-throw shots: positioning the forearm almost parallel with an imaginary lateral axis.


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