What are the mathematics behind dosage?

Dosages are a mathematical formula for showing the influence of certain great thoroughbreds within a pedigree. These influences are the breed-shaping stallions including Northern Dancer, Star Kingdom, etc, and are known as "chefs-de-race".

The five categories of influence

The influence of a stallion is divided into five categories that were first proposed by Franco Varola. They are:

Brilliant
Intermediate
Classic
Solid
Professional

They largely cover the range from speed to stamina. Stallions can contribute in more than one area such as Brilliant/Classic for example. The points that he contributes are split between the two categories. Classification of a stallion depends on those attributes that he contributes to his progeny on a consistent basis and does not relate to his own racing aptitude or performance.

What are points and how are they calculated?

A chef-de-race in the first generation contributes 16 points. In the 2nd generation, they contribute 8 points, then 4 in the 3rd and 2 in the 4th. This is simply an extension of Galton’s Law of genetics that says that an ancestor’s influence is reduced the further back in a pedigree it appears.

Center of Distribution

The Center of Distribution (CD) is the balancing point between speed and stamina in a pedigree. It can range from extreme speed at +2 to extreme stamina at -2. There are a lot of studies that show a distance aptitude of a horse that relates to this figure. These can vary from country to country as different conditions and marked differences in racing patterns can influence the performance of a horse.

The mathematical equation is

([(Brilliant x 2) + Intermediate] - [Solid + (Professional x 2)])/Total Points

Dosage Index

The Dosage Index was invented by Dr Steven Roman. It is the ratio between speed and stamina. Again, it can be used as a guide to distance aptitude and numerous studies have been conducted relating this figure to preferred distances.

The mathematical equation is

(Brilliant + Intermediate + ½ Classic)/(½ Classic + Solid + Professional)

Dosage Profile

The Dosage profile is an expression of the points of all the chefs in a horse’s pedigree. It is simply a list of 5 numbers that refers to the points a horse has in the 5 categories read from left to right as Brilliant-Intermediate-Classic-Solid-Professional.

Do the total number of points matter?

This is a subject open to some debate. Dr Roman suggests that most stakes winners have higher total points than non-stakes winners and he is no doubt correct. However, as much of the basis of classification of chefs-de-race is calculated on their stakes winning progeny, it becomes a little self fulfilling. The total number of points however allows us to be more confident in our assessment of a horse’s performance.

What is a trivial dosage profile?

A trivial dosage profile exists when no single column has a number higher than 10. While these profiles can still be accurate, the possibility is greater that a non-chef close up in a pedigree may have a much higher influence on aptitude than the dosage profile indicates. Dr Roman has created a list of non-chef-de-race stallions that can be included in the calculation in these instances.