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# The best way to win a horse race? Mathematicians may have the answer

Attention racehorse jockeys: Start fast, but save enough energy for a final kick. That’s the ideal strategy to win short-distance horse races, according to the first mathematical model to calculate how horses use up energy in races. The researchers say the approach could be used to identify customized pacing plans that, in theory, would optimize individual horses’ chances of winning.

Every racehorse has different capabilities. Like humans, some excel at sprinting, whereas others are marathoners. Figuring out which is which, and how to pace them, can be the difference between faltering in the final furlough and taking home the Kentucky Derby’s \$1.3 million winner’s payout. Jockeys and trainers have traditionally relied on centuries of experience, data from previous races, and intuition to plan their races.

Amandine Aftalion, a mathematician at the School for Advanced Studies in the Social Sciences (EHESS) in Paris, thought she could add to that. Since 2013, she has been analyzing the performances of world champion runners like sprinter Usain Bolt. She’s found that short-distance runners tend to win when they start strong and gradually slow down toward the finish line. But in medium-distance races, such as the 1600-meter, runners perform better when they start strong, settle down, and finish with a burst of speed.

Her model shows how those winning strategies maximize the energy output of muscles reliant on two different pathways: powerful aerobic ones that require oxygen, which can be in limited supply during a race, and anaerobic ones, which don’t need oxygen but build up waste products that lead to fatigue.

Aftalion wondered which strategy would be best for horses. So she and Quentin Mercier, another EHESS mathematician, took advantage of a new GPS tracking tool embedded in French racing saddles. The trackers let fans watch digital images of the horses move across a screen, and they gave Aftalion and Mercier real-time speed and position data.

The duo studied patterns in dozens of races at the Chantilly racetracks north of Paris and developed a model that accounted for winning strategies for three different races: a short one (1300 meters), a medium one (1900 meters), and a slightly longer one (2100 meters), all with different starting points on the same curved track. The model takes into account not just different race distances, but also the size and bend of track curves, and any slopes or friction from the track surface.

The results, published today in PLOS ONE, might surprise jockeys who hold horses back early for bursts of energy in the last furlough. Instead, a strong start leads to a better finish, the team found. That doesn’t mean those jockeys are wrong, though. Too strong of a start can be devastating as well, leaving the horse “exhausted by the end,” Aftalion says.

In theory, the model could allow trainers to plug in parameters for individual horses—like their unique aerobic capacities—to get custom racing strategies, from pacing recommendations to ideal racing distances. And if there’s a market for it, developers might even create an app, Aftalion says.

That’s a nice thought, but it’s not likely to win over horse trainers and jockeys, says Peter Knight, a veterinarian at the University of Sydney with more than 30 years of experience working on horse racetracks. Various other scientific attempts to explain performance over the past 4 decades “haven’t been particularly successful,” he says—and not just because horses vary so much in body size and aerobic capacity: The models cannot account for the horse’s own behaviors.

For example, a horse might give up when another horse passes it, because it doesn’t understand that it’s supposed to win. Until researchers can get inside the horse’s head and account for psychological variables, Knight says, “we can’t truly model performance.”

“But perhaps the fundamental question is: Do we really want to?” he adds. “For people who love horse racing, the uncertainty provides the excitement, and the actual running of the horses provides the spectacle and the beauty.”

Posted in:

doi:10.1126/science.abf9799

### Christa Lesté-Lasserre

Christa Lesté-Lasserre is a journalist in Paris.

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