How much does weight really matter?

Today spawned some very interesting comments on both social media and HRN blogs with regards to the amount of weight carried by a horse in a race. The first group of comments was from a facebook post by Brian Zipse about Bob Baffert’s pending decision to race Game on Dude in the Santa Anita Handicap. The second set of comments was in result to a blog written by Laura Pugh about Violence and Orb’s finish in the Fountain of Youth.

The commonality between both of the resulting discussions can be made around the relevance and impact of the assigned weight a horse must carry during a race. The most frequent discussion point can be paraphrased as, “a horse weights 1100 pounds, and I refuse to believe the difference of a few pounds of assigned weight will make the difference in the outcome of a race.”

Why do organizers control the weight carried by a horse during a race? It could be because they think it will give an advantage to one horse over another, or because they want to feel like they have some level of control on the outcome. I have read that for every extra pound a horse carries it will run a mile race 1 length slower. I have no idea who came up with that, but I guess its just one of those things that has been assumed from decades of handicapping horse races.

Unfortunately, I don’t buy it that easily, so I wanted to find out for myself. How much of an impact of the weight carried by a horse during a race impact the outcome? As it turns out this is not so easy to answer. However, it can be simplified to try and make an estimate.

After lots of thought of how to take the complex motion of equine gait and convert it to something that can be used to model energy consumption, I decided to make some engineering assumptions. The first of which is that equine locomotion can be simplified into an inverted pendulum. It is a mass that is rotating about a fixed point at approximately a consistent distance from said point. I have attached a picture to help describe my key assumption.

Translated out of engineering language, this means that a running horse is just a weight on the end of a stick that is being repeatedly rotated about a point on the ground.

My second assumption is that all horses are the same size and weight (without rider and ballast) and have identical stride lengths. We know this is actually not true, but for the interest of comparing the impact of assigned weight on the race, this vastly simplifies the arithmetic involved. This means that all horses are required to overcome identical aerodynamic forces (more info on that here), ground friction, and body functions (breathing, sweating, anything else the body uses energy for).

Now, back to the physics. I will use the Fountain of Youth with both Orb and Violence as an example. We know the distance traveled (length of the race), the time it took to do so, and the weights assigned to each horse. But as it turns out, the only things that matter here are the distance travelled and the weight assigned. Looking strictly at equations of motion, the speed of the horse is not directly effected by the weight carried.

The problem can be expressed as the number of times the pendulum is rotated during a race (ie. the number of strides the horse takes during the race). The weight comes into play when we consider the force (technically the torque) it takes each time the pendulum is rotated. In terms of horse locomotion, the force I am referencing is the amount required to pull its heavy body over the point of contact on the ground and propel itself to the next point.

So when we know how much force it takes for each stride, and the number of strides taken in the race, we can calculate the amount of energy it took to move the horse a given distance. Based on all the assumptions and complex dynamics analysis above, Violence would have burned approximately 0.5% more calories than Orb during the race due to the added 6 pounds.

Does the weight carried impact the outcome of a horse race? Yes and No. Yes because a horse carrying more weight will have to work harder compared to a horse with lower weight. No because there are so many things that happen from when the gates open to the first horse crosses the wire.

Do I believe Violence would have won the Fountain of Youth over Orb under equal weights? Reality tells me there is no way to ever know. But I am of the opinion that 0.5% difference in energy expenditure is insignificant to the other events that occur during a race. Now if my assumptions above were in fact true, and all other factors of the race are equal, then under equal weights, yes I believe Violence wins. But guess what… no matter how much we try to control the outcome, or think we can control it [by adding weight], we are powerless. In the end, we are all just spectators. Handicap, weight-for-age, or equal weight, the horse that crosses the wire first can simply be called the best horse on that given day.