Few sports prompt fans to open their wallets quite like horse racing. Whether it's the biggest race of the year or the weekend race at the local track, fans come in droves to watch horses speed around tracks and bet on their favorites to win.
But every track rat knows that when all the bets are in and the race starts, favored winners may take the lead only to stumble at a bend, allowing underdogs to storm to the finish. Nothing is certain, and it's these sorts of rapid shifts that make horse races so unpredictable — and so thrilling.
But if you could pinpoint roughly when and where a horse slows down and speeds up on a race track, that knowledge could change everything, allowing you to predict how well a horse can perform on the track.
A new study on thoroughbred horses claims to have done just that.
Off to the Races — The study, published Wednesday in PLOS ONE, uses math to predict how well a horse may possibly perform on any given track. To do this, the researchers used videos of three different horse races on a track in Chantilly, France — a shorter 1300-meter race, a mid-range 1900-meter race, and a longer 2100-meter race. Each race follows a different trajectory, with a combination of straights and curves.
For each track-length, the researchers used a combination of data to predict when a horse needs to release maximum energy to meet its full potential in a race.
They built a mathematical model to assess each horse's energy output, mean oxygen intake, forward momentum, and motor control. From these factors, researchers can determine the horse's speed at different points in the race, and where potential hurdles might trip them up.
The model reveals horses often start strong at the start of a race and decrease their speed as they come into the bends in the track, reaching peak speed around 200-300 meters into the race. As it leaves the bend, the horse typically increases its speed. The model reveals how much each horse will pump the accelerator and how well it keeps speed up in the race.
The model "explains how and why the horse slows down in the bend," allowing scientists to predict how and when horses reach optimal speed during a race, Amandine Aftalion, a co-author on the study and an applied mathematician at École des Hautes Études en Sciences Sociales, tells Inverse.
But, in the final stretch of the race, the individual horse's stamina ultimately determines the outcome.
"Going up on the finish line makes the difference between horses — only the strongest can manage it," Aftalion says.
Horsepower — The model is adapted from one used to analyze human races at similar distances.
"We didn't 'compare' [to humans]. We, rather, adapted our biomechanical and energetical model for performance to horses," Aftalion says.
The researchers distinguished between aerobic and anaerobic exercise, which both deal with how much oxygen — and thus, energy — the body has to use to perform certain tasks.
"The anaerobic energy allows you to have a fast start, but if you deplete it too much at the beginning, then you will not be able to finish the race without slowing down," Aftalion says.
As a result, a horse with "lower anaerobic energy" will lose speed at the end of a race, Aftalion says.
The mathematical model uses the intersection between these different factors to predict the outcome of a race.
"For each value of these parameters, we can analyze how they influence the race. For instance, the VO2 [mean oxygen intake] — if a horse has a higher VO2, he will be able to run the race at a higher mean value, but he will reach this value in a larger time," Aftalion says.
Likewise, a horse's propulsive force matters at the beginning and end of the race, according to the model. But it matters the most when the horse navigates the bends in a track.
"The [horse] with bigger propulsive force or lower running economy is less affected by the bends," Aftalion says.
An ideal race — It is important to note that the model captures an ideal race — the race a horse could run. It does not predict how a horse will run the race, however.
"If, for instance, the jockey has stopped him at some point, or changed a lot the strategy from the optimal one, then we can do nothing," Aftalion says. Similarly, if the horse goes wildly off track, then the model can't account for that uncertainty.
But the model can enable trainers and industry experts to better understand how their horses perform in races.
"This study gives information on VO2 [and] how it evolves in a race that a lot of people didn't know about," Aftalion says.
It could also prevent trainers and jockeys from pushing their horses too far in the hopes of improving their performance.
"This study shows where it is worth pushing and that pushing [horses] too hard is not good," Aftalion says.
The findings could also enable racing insiders to design tracks made for optimal horse performance. For example, "strong bends are not good for performance" so "[track] radii smaller than 100 meters should definitely be avoided" according to Aftalion.
Likewise, minimizing slopes would enable horses to reach their potential more easily, but if there is a slope then placing it in the middle of a race track will have the best results. A slope at the beginning of a race is incredibly taxing on a horse and should be avoided at all costs.
"It depends on what your purpose is [for] the show — a tough track [or] an easy track," Aftalion says.
Finally, we can also use this model to select the right horse for each race track, depending on whether you're doing a short sprint or a long jaunt.
"In the future, I would hope it helps to select horses according to the distance of the race," Aftalion says.
Abstract: The objective of this work is to provide a mathematical analysis on how a Thoroughbred horse should regulate its speed over the course of a race to optimize performance. 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. Our model relies on mechanics, energetics (both aerobic and anaerobic) and motor control. It is a system of coupled ordinary differential equations on the velocity, the propulsive force and the anaerobic energy, that leads to an optimal control problem that we solve. In order to identify the parameters meaningful for Thoroughbred horses, we use velocity data on races in Chantilly (France) provided by France Galop, the French governing body of flat horse racing in France. Our numerical simulations of performance optimization then provide the optimal speed along the race, the oxygen uptake evolution in a race, as well as the energy or the propulsive force. It also predicts how the horse has to change its effort and velocity according to the topography (altitude and bending) of the track.