Strong Start or Late Kick? The Math Behind Racing Strategy

Mathematicians at the School for Advanced Studies in the Social Sciences in Paris have analyzed racing strategy by looking at the data behind thoroughbred horse racing.

Quentin Mercier and Amandine Aftalion placed GPS tracking tools under the jockey’s saddles at the Chantilly racetrack to determine how best to regulate a horse’s speed to optimize performance over courses of 1,300, 1,900 and 2,100 metres.

“Because Thoroughbred horses are not capable of running the whole race at top speed, determining what pace to set and when to unleash the burst of speed is essential,” the pair reported in PLOS ONE, a peer-reviewed scientific journal published by the Public Library of Science.

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Considerations such as the aerobic (requiring oxygen) and anaerobic (not requiring oxygen but creating waste products that lead to fatigue) muscle exertion of the horses, motor control and the slope and bend of the track were taken into account. The mathematical model they produced was meant to be helpful to the industry, as Thoroughbreds’ racing careers are not typically long and every race is critical.

At 1,300 metres they noted a strong start with the maximal velocity being reached in 200 meters. Then the velocity decreases, particularly in the turn, between 300 and 600 meters from start in the case of the Chantilly track, which features both uphill and downhill sections and gentle turns. The last stretch is uphill and the velocity decreases even though the horse reaches the straight, something which takes place even on a flat track.

The 1,900 metre races saw a strong start with the maximal velocity being reached in 300 meters. Then the velocity decreased and between 900 and 1400m the effect of the bend came into play. The end of the race involved strong acceleration before the final slight slow down.

At 2,100 metres they observed a strong start with the maximal velocity being reached in 200 meters. Then the velocity decreased and reached a plateau, which has been analyzed in human races. The end of the race is similar to the 1300 meters, with a strong acceleration before the final slow down.

The research also provided a better understanding of the effects of turns which can have an effect on the entire race. “We see that horses have to start strongly and reach a maximal velocity. The velocity decreases in the bends; when going out of the bend, the horse can speed up again and our model can quantify exactly how and when.”

Velocity data for the 1900-meter race.

The conclusion? Mercier and Amandine Aftalion found that to win, horses have to start strongly and reach a maximal velocity which will decrease in the turns and increase coming out. “The horse that slows down the least at the end of the race is the one that wins the race,” the pair wrote. “We understand from the optimal control problem that this slow down is related to the anaerobic supply and the ability to maintain maximal force at the end of the race. Therefore, horses that have a tendency to slow down too much at the end of the race should put less force at the beginning and slow down slightly through the whole race in order to have the ability to maintain velocity at the end.”

In a nutshell: start strong and keep just enough in reserve to provide a final kick to the finish line.

Not surprisingly, they also concluded that “to maximize an individual horse’s potential for winning, it should be entered in races appropriate for its racing ability” ‒ something horsepeople have been doing since the dawn of racing anyway. The authors also noted that future studies take into account drafting (tracking behind another horse) to reduce wind resistance and horse psychology.

While the report is interesting in theory, racing insiders would argue that there are a myriad of situations that can occur any day in any race that will affect the outcome.