Paris Olympics: How U.S. swimmers are using math to win gold in the pool

PARIS — Dr. Ken Ono shared his screen and, on a Zoom one week before the Olympics, began teaching me about Benford’s Law and plane partitions.

Ono, a 56-year-old mathematics professor at the University of Virginia, pulled up a recent paper, and explained how he and one of his students had proven a probabilistic theorem.

He walked me through formulas and long strings of characters that mean nothing to the average human. “This is hardcore math,” he said with an enthusiastic grin.

He also raved about the student, who was doing things “really well beyond what we expect for our master's students at UVA,” Ono said.

Her name was Kate Douglass. And two weeks later here in Paris, she swam to Olympic gold.

She had taken two classes with Ono while working toward a master’s degree in statistics. And this, their second published paper together, was the fruits of her spring-semester work. It caught the attention of one of the world’s leading number theorists. “This is a big deal,” Ono said.

Their first co-authored paper, though, was the reason I wanted to chat with Ono. It covered his secondary passion, his pioneering work with elite athletes and data analytics.

Together, he and Douglass, citing Newton's laws and personal experience, explained in The Mathematical Intelligencer how "the introduction of mathematics, physics, and technology has revolutionized swimming" — and, now, helped Team USA win Olympic medals.

A theoretical experiment

Ono's journey into this role of "secret weapon" — as Alex Walsh, a Virginia swimmer and Olympic silver medalist, called him — was a winding one full of happenstance.

The son of first-generation Japanese immigrants, Ono had long been captivated by Olympic sports, especially cycling. As a grad student at UCLA, he joined a community track club. Years later, while a professor at Emory University in Atlanta, he decided to try his luck as an amateur triathlete — which required learning how to swim.

He also accompanied a colleague to a math conference in Norway, and, “out of dumb luck, at a reception,” Ono recalled, “I bumped into a group of scientists who worked at the Norwegian college for sports science.”

They struck up a conversation. The Norwegians had been using devices called "accelerometers" — devices with sensors that can quantify movement — to analyze the technique and efficiency of cross-country skiers. Ono had a thought: Could we apply this to swimming?

Around that same time, he says, “a miracle happened.” In 2014, an aspiring walk-on swimmer, Andrew Wilson, enrolled in one of Ono’s classes at Emory.

They bought some accelerometers and dove into what Ono calls a “theoretical experiment” to collect data and figure out how to use it to improve performance.

Over the years that followed, their experiments frequently failed. They began with surgical gloves, Saran Wrap and tiny sensors designed for shark tracking. Ono's wife crafted no-frills belts, with a small pocket for the accelerometer, that swimmers could wear around their core. The tech was nascent; the project was amateur. The data, therefore, was often spotty. (The accelerometers often fell from the belts to the bottom of the pool.)

But throughout the 2010s, they refined the operation. Wilson, meanwhile, grew from Division III walk-on to NCAA champion to 2021 Olympian. And Ono’s work became a subject of fascination in swimming.

He moved to the University of Virginia in 2019. His “day job,” as he calls it, was still as a professor and advisor to the provost. In fact, he was so busy building a program in the UVA math department that “I thought I was done with [the swimming work],” he says.

But he eventually connected with Virginia coach Todd DeSorbo. They resumed the work, with Ono as an unofficial “consultant.” The women’s program — led by Douglass, Alex and Gretchen Walsh, and other Olympians — has won every available championship since.

They have not won exclusively or even primarily because of data analysis, of course. Ono, DeSorbo, Douglass and others repeatedly clarify that any associated gains are marginal ones. The swimmers are primarily responsible for their own success.

But they all believe the analytics have had an impact. Ono and his team work with the swimmers on deck once every few or several weeks. They outfit the swimmers with belts, deconstruct their strokes, and pair underwater video with the accelerometer data to scrutinize all the ways in which they are slowing themselves down or could be speeding up. “The effect from every rotation, splash, pull, and kick can be quantified in each direction and analyzed,” Ono, Douglass and their co-authors write in their paper. The sensors collect data 512 times per second.

They now place high-tech bands on a swimmer’s hands as well. Those yield “nuanced force field data.”

“What was previously evaluated purely by looking at the swimmer above the water can now be distilled into a sequence of vector fields that show the distribution of force in all three axial directions,” they write. “Force applied in any direction other than forward is not helping an athlete achieve their dream of Olympic gold.”

All of it allows the quants to create an athlete’s “digital twin.” The digital twins can be compared to an optimal prototype. “They allow us to make recommendations that immediately improve technique, offer suggestions for race strategy, and point to long-term aspirational goals,” the authors write — “all in pursuit of the optimal race.”

Shaving tenths = Olympic gold

Douglass had never heard about any of this when she enrolled at Virginia with a math-y brain and an interest in computer science. Then, separately, she migrated toward stats and data science in school, and got to know Ono via his work with the swim team.

After graduation, she stayed at Virginia as a master’s student, and has now taken two independent study courses with Ono. The first was on data analytics in swimming. The second was “completely unrelated,” she said — “he was teaching me a lot of arithmetic statistics,” real abstract stuff.

All the while, she was also training, often twice a day; and Ono was helping her tweak her angle off the wall or her head position. The accelerometer work, Douglass said this spring, has “definitely helped me figure out areas of my stroke where I can be more efficient.”

In their paper, they went into more detail — on how her imperfect head position was creating “extra turbulence and drag.” They estimated that, by correcting it, after 36 months of practice, she had shaved 0.11 seconds off each of four “streamlined glides” off the wall — or 0.44 seconds throughout a 200-meter breaststroke race.

Then, in their paper, they addressed the elephant in the room: “Is that savings significant?”

Laypeople would assume that it is not; that all of this painstaking work for a mere half-second of time is essentially worthless.

But on Thursday here at Paris La Défense Arena, Douglass glided through a pool with the refined technique. She followed an oft-rehearsed stroke count — 14 strokes over the first length of the pool, 16 on the second, 17 on the third, 19 on the fourth. She knew, or at least was confident, that if she swam her race, she could break an American record and win an Olympic gold.

And sure enough, in the 200-meter breaststroke final, she finished in 2:19.24 — 0.36 seconds ahead of South Africa’s Tatjana Smith.

She smiled, in apparent relief and satisfaction, as she celebrated her first Olympic title — and a race that had gone almost precisely to plan.

“It was just a long time coming,” Douglass said afterward. “This whole year, I've just been training and physically preparing for this exact race. And seeing it all come together, and sticking to my race plan, I just was so excited to see that I'd gotten first. … It's a surreal moment.”