Four- vs. Five-Generation Dosage

Contemporary Dosage studies involve the analysis of four-generation pedigrees that are readily available from a variety of sources.  Some critics suggest that a five-generation analysis will improve the accuracy of the method by implicating additional, more remote chefs-de-race which may modify the pedigree interpretation.  To test that hypothesis we have briefly examined how a four-generation versus a five-generation analysis affects the Dosage figures of older Breeders' Cup winners on dirt between 1984-2003 and of Kentucky Derby winners between 1940-2003.

Chart 1 is a graphical display of the best straight lines generated by linear regression for a plot of the average race distance versus the average Dosage Index (DI) of winners of the Breeders' Cup Classic, Distaff and Sprint, and includes both four-generation and a five-generation Dosage data.

Chart 1.

We observe that the red line (the four-generation trend line) is displaced toward higher DI numbers and is both steeper and has a much higher R² value than the green line (the five-generation trend line).  The lower averages for the five-generation analysis are consistent with the greater number of stamina influences found in more remote generations.  The steeper slope of the four-generation analysis indicates greater separation of the figures by distance and confirms a "leveling effect" on the analysis as we incorporate more remote generations.  In other words, the more generations we involve in the analysis, the less differentiation we observe in aptitudinal type.  The higher R² value for the four-generation analysis means that the classic Dosage model, i.e., the correlation between Dosage numbers and distance, is better than for the five-generation analysis.

It may be argued that the data are skewed by the very high DI figure for 1990 Breeders' Cup Sprint winner Safely Kept (DI 31.00).  We can address this concern by using the composite DI rather than average DI figures.  The composite DI is calculated from the average Dosage Profile (DP) rather than by averaging the individual DI numbers.  In this way, we eliminate the variation created by outliers among the data points.  Chart 2 shows the results when using composite DIs instead of average DIs.

Chart 2.

Although the lines are now closer together, the relationships remain the same, with the four-generation analysis displaying higher DI numbers, a steeper slope and a higher R² value.

Chart 3 displays the four- and five-generation DIs by year for Kentucky Derby winners since 1940 along with the respective linear trend lines.  Once again we observe higher numbers for the four-generation analysis as well as a steeper slope.

Chart 3.

Perhaps the most significant outcome of this brief study is the realization that, if one believes an aptitudinal analysis is improved by doing a five-generation Dosage calculation (which, by the way, requires twice the effort of a four-generation calculation), the resulting numbers can not be directly compared to the population standards derived from the four-generation model.  We know that the five-generation numbers are lower.  Therefore, if we use the five-generation model to assess classic potential, for example, the resulting number can not be compared fairly to the traditional four-generation DI 4.00 classic guideline.  A new standard would have to be used based exclusively on the five-generation Dosage model.  As it turns out, using the five-generation model, no Derby winner had a DI greater than 3.34 until 1995.  Since then, three Derby winners (Thunder Gulch, Real Quiet and Charismatic) have exceeded that figure.  For reference, using the four-generation model, the first Derby winner to exceed the previous high figure of DI 4.00 was Strike the Gold in 1991 followed by Real Quiet in 1998 and Charismatic in 1999.  Both models, therefore, generate three exceptions since 1940 (all since 1990), with the four-generation model using a classic guideline figure of DI 4.00 and the five-generation model using a classic guideline figure of DI 3.34.

The same relationships almost certainly apply to every performance category.  Therefore, a five-generation model requires new population standards for sprints, routes, dirt races, turf races, races by age, etc.  Interpreting a five-generation Dosage number in the context of a four-generation population standard is an improper use of the methodology.