Olympics 2024: Swimmers are turning to math for a moment’s edge at Paris Games

Kate Douglass, a statistics graduate student and the second-fastest swimmer in the world this year in two Olympic swimming events, has always been good with numbers. But before she enrolled at the University of Virginia, she never considered that swimming itself was a math problem that she could try to solve.

That changed when she realized the concepts she was studying in the classroom could be used in her sport. These days, Douglass often gets into the pool while wearing a belt that holds an accelerometer, the same device found in smartphones and fitness watches. As she swims, the sensor measures her movement in three spatial directions 512 times per second.

“That’s helped me to figure out areas of my stroke where I can be more efficient,” said Douglass, 22. So far, so good: On Saturday, she began a busy Olympics schedule by winning a silver medal in the 4x100 freestyle relay.

The swimmers at the Paris Olympics all have the same challenge: to swim as fast as they can by moving through the water in a way that maximizes the force propelling them toward the finish line, while minimizing the force that slows them down. Elite swimmers use familiar tricks to reduce the resistance known as drag, like shaving before big meets and wearing swimsuits made from the same material as Formula One racing cars.

Though the sport has long relied on a swimmer’s feel in the water or a coach’s eye from the pool deck, Douglass and several of her U.S. Olympic teammates are exploring a new competitive frontier. Under the direction of a Virginia mathematics professor, Dr. Ken Ono, they are measuring and analyzing the forces they create as they swim, to optimize the way they move through the water. Details as seemingly small as Douglass’ head position in her underwater breaststroke pullout, or how her left hand enters the water on her backstroke, have been focal points as she has worked to trim the hundredths of a second that make the difference between medals in the sport.

While Douglass is almost certainly the only swimmer in Paris who has co-written a peer-reviewed research paper about this work, similar ideas are catching on elsewhere. As part of a government-funded research program in France aimed at giving the country an edge in its home Olympics, Léon Marchand was tested last summer to learn his “hydrodynamic profile.” And Kyle Chalmers, the Australian sprinter who is a three-time Olympian, has partnered with a Sydney-based sports technology lab that created a device to measure the force generated by a swimmer’s hands as they stroke through the water.

“It gives us a mental edge knowing that we have access to this information that you can’t see with the naked eye,” said two-time Olympian Paige Madden, who recalls researchers using plastic wrap to affix a sensor to her back when she was an undergraduate at Virginia.

Ono’s methods have advanced over time. At a conference in Norway about a decade ago, he met a group of mathematicians from the Norwegian School of Sport Sciences who worked with Olympic cross-country skiers, using accelerometers to analyze their movement patterns. A light bulb turned on for Ono, a number theory specialist who is also a triathlete and swim dad.

Ono, then at Emory University in Atlanta, had a willing test subject in Andrew Wilson, a math student who had walked on to the swim team. They started with accelerometers that were designed to track sharks and learned as they went, developing a protocol to home in on the weaknesses in Wilson’s breaststroke. As Wilson shot up in the sport, becoming a Division III national champion and later winning a medley relay gold at the Tokyo Olympics, other members of the U.S. national team began to learn about his and Ono’s project.

Ono has since tested about 100 top American swimmers, but he works most closely with the group at Virginia, where he is a regular presence on the pool deck. He also offers an independent study class for STEM students, who learn to analyze the data collected from swimmers like Douglass and Gretchen Walsh, the world-record holder in the 100 butterfly. Thomas Heilman, who, at 17, is the youngest American male swimmer to qualify for the Olympics since Michael Phelps, said one of the reasons he committed to swim at Virginia was to take part in this work regularly.

The 512 snapshots of data captured per second help researchers to create a digital twin for each swimmer, a numerical representation of how the athlete moves through the water. That data pointed to Douglass’ breaststroke pullout as an area where she was losing time. She looked at video to compare her form with that of Lilly King, a breaststroke specialist, and saw that the forward bend of her head was likely creating extra drag that was slowing her down. Mathematical modeling predicted that with a form adjustment, Douglass, who is now the American-record holder in the 200 breaststroke, could save as much as 0.15 seconds per pullout.

“Swimming is the perfect application of mathematics and physics,” Ono said. “We were never designed to swim in water. So to swim quickly in water is a really unique and complicated combination of athletic prowess and attention to detail in terms of physics and mechanics. That’s why I like it.”

The hydrodynamic profiling of the French national team is based on similar principles. Dr. Ricardo Peterson Silveira, a scientist from Brazil, came to a university in Rennes, France, three years ago to participate in France’s sports science project. He set up a demonstration in the warm-up pool at last year’s French championships that caught the eye of Bob Bowman, Marchand’s coach, who asked if his swimmer could be tested.

On the final day of the meet, Silveira tethered Marchand to a motorized device attached to the wall. The first test measured his drag while being pulled through the water in a streamlined position. Marchand registered the lowest value for this attribute, which they call passive drag, of any swimmer Silveira and the French researchers had tested, an indication that his body was built like a torpedo ready to shoot through the water.

A second test measured his speed while swimming against different resistance levels. Silveira then calculated how much power Marchand generated while swimming freestyle — the stroke he targeted for improvement in the Olympics — and the percentage that was used to propel him forward. Aquatic creatures like fish are very efficient at swimming, but even the best human swimmers are able to apply only about 60% of their effort in the direction of their swim. Based on Marchand’s results, Bowman said they incorporated short bursts of race-speed freestyle against heavy resistance into his training, aiming to boost both his power and his propelling efficiency.

To Bowman and Todd DeSorbo, the coach for Virginia and for the U.S. women for the Paris Games, more information allows them to better help their athletes, though the sport’s embrace of data has happened haltingly. Russell Mark, the former high-performance manager for USA Swimming, who introduced Ono to DeSorbo, recalled receiving mixed reactions from coaches 20 years ago when handing out paper printouts with race analytics.

“We are just at the cusp of this data revolution in swimming, and the athletes are hungry for it, the coaches are hungry for it, the sport is hungry for it,” Mark said. “You see it with the excitement over what Ken and Todd are doing and the success that they’re having on a program-wide scale. That’s the dream, and that’s the potential.”

The U.S. swimming team in Paris includes six athletes with ties to the University of Virginia. Madden no longer trains at Virginia, but this spring Ono and one of his interns visited her in Arizona, where they tried out the force paddles that Australian sprinter Chalmers has used. The data they captured during their testing showed that Madden’s efficiency plunged when she reacted to a swimmer racing in the lane next to her. She felt as if she were going faster, but she was actually out of sync, like a car whose timing belt is off.

Her takeaway for the Olympic trials: Swim her own race. In the final of the 800 freestyle, the second individual event Madden qualified in, she sensed that Jillian Cox, who ended up finishing third, was creeping up on her. But she reminded herself to stay focused on her stroke form. “I was actually thinking about Dr. Ono during my race,” Madden said.

Given her understanding of statistics, Douglass is careful not to say that any one variable has been the reason for her rise in her sport. Later this week, she will compete in the 200 breaststroke and 200 individual medley. Her preparation for Paris has required rigorous attention to detail in her pool and dry land training, sleep, nutrition, race strategy and more. Using math to become a more efficient swimmer has enhanced that work.

As Douglass wrote in the research paper: “Force applied in any direction other than forward is not helping an athlete achieve their dream of Olympic gold.”