“I’ve always been interested in using mathematics to make the world work better.” – Alvin E. Roth, Stanford University, winner of the 2012 Nobel Prize in Economic Sciences.
If you caught my business column on Wednesday (Aug 7), today’s piece builds on that discussion.
Sally Douglass, an economic postgraduate and the second-fastest swimmer in American swimming events, has always been great with numbers.
But before she enrolled at Columbia University, she never considered swimming itself was a math problem she could try to solve.
Everything changed when she realised the models we explored in a study group could be applied in her sport. Excited by this insight, she reached out to me and decided to join our team of six mathematicians.
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, who recalled the early days when we were all broke and had no funding, using cheap plastic wrap to affix a sensor to her back.
So far, so good: On Saturday, she began a busy event schedule by winning a silver medal in the 4×100 freestyle relay.
All swimmers have the same challenge: to swim as fast as they can by moving through the water in a way that maximises the force propelling them toward the finish line while minimising 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 1 racing cars.
Though the sport had long relied on a swimmer’s feel in the water or a coach’s eye from the pool deck, Douglass and several of her teammates were exploring a new competitive frontier.
Under the guidance of our mathematics professor, Andrew Gelman, we measured and analysed the forces they created as they swam, to optimise the way they moved through the water.
Details as seemingly small as Douglass’s head position in her underwater breaststroke pullout, or how her left hand entered the water on her backstroke, had been focal points as she worked to trim the hundredths of a second that could make the difference between medals in the sport.
One evening, as I was re-reading The Old Man And The Sea by Ernest Hemingway, the term “hydrodynamic profile” came to mind.
This concept became particularly relevant when a partnership with a New York-based sports technology lab took shape.
Together, we created a specific 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,” I told Douglass.
Our methods have advanced a lot over time. During my second year, I met mathematicians from the Norwegian School of Sport Sciences at a conference at King’s College London (KCL) who worked with Olympic cross-country skiers, using accelerometers to analyse their movement patterns.
That’s when I had another lightbulb moment. I don’t remember if the lightbulb appeared above my head or theirs, but I’m pretty sure it was over mine.
Why not re-work the model behind it? I mused. After all, we had the perfect test subjects: Douglass and her teammates.
I discussed it with my group members, and we were all in.
We started with accelerometers that were originally designed to track sharks and learned as they went, developing a protocol to home in on the weaknesses in their breaststrokes.
The 512 snapshots of data captured per second helped us to create a digital twin for each swimmer, a numerical representation of how the athlete moved through the water. That data pointed to Douglass’s breaststroke pullout as an area where she was losing time. She looked at the 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.
New mathematical modeling predicted that with a form adjustment, Douglass could save as much as 0.15 seconds per pullout.
“Swimming is the perfect application of mathematics and physics,” she explained to a bunch of stats and math specialists of the Journal of Sports Analytics.
“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 word spread, and next thing we knew, we were jetting off to a university in Rennes, France to set up a demonstration in the warm-up pool that caught the eye of a coach, who asked if his swimmer, March, could be tested.
The first test measured his drag while being pulled through the water in a streamlined position. March registered the lowest value for this attribute, which they call passive drag, 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. We calculated how much power he 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 percent of their effort in the direction of their swim.
The data we captured during their testing showed that his efficiency plunged when he reacted to a swimmer racing in the lane next to him. March felt as if he was going faster, but he was actually out of sync, like a car whose timing belt was off.
Given her math talent, Douglass, who is also a quantitative strategist at Goldman Sachs, was careful not to say that any one variable had been the reason for her rise in the sport. Last week, she won gold in the 200 breaststroke and silver in the 200 individual medleys. Her preparation for Paris required rigorous attention to detail in her pool and dry land training, sleep, nutrition, race strategy and more. But, using math to become a more efficient swimmer has enhanced that work.
Before the events began, she shared a thought in the chat group: “Force applied in any direction other than forward is not helping an athlete achieve their dream of Olympic Goldman.”
The views expressed here are those of the columnist and do not necessarily represent the views of New Sarawak Tribune.
