Advanced Dosage Theory
Our approach, which first appeared publicly as a series of articles in Leon Rasmussen's Bloodlines column in Daily Racing Form just prior to the 1981 Kentucky Derby, has been to fuse the basic ideas of Vuillier and Varola, incorporating both quantitative and qualitative components in the hope of providing additional insights. In order to establish greater utility, we chose to use more accessible four-generation pedigrees instead of the extended pedigrees used previously. We also re-introduced Vuillier's approximation of orse being analyzed. The most significant point made by Varola was that the characteristics transmitted by his chefs were not necessarily those they possessed as runners. The focus, instead, was entirely on the qualities passed on as breeding animals. Thus, in contrast to conventional pedigree analysis based on an historical perspective of ancestral performance, Dosage relies on the dynamics of inheritance. As an alternative and complementary method of pedigree interpretation, it may help avoid potential problems associated with the traditional concept of "breeding the best to the best".
Our approach, which first appeared publicly as a series of articles in Leon Rasmussen's Bloodlines column in Daily Racing Form just prior to the 1981 Kentucky Derby, has been to fuse the basic ideas of Vuillier and Varola, incorporating both quantitative and qualitative components in the hope of providing additional insights. In order to establish greater utility, we chose to use more accessible four-generation pedigrees instead of the extended pedigrees used previously. We also re-introduced Vuillier's approximation of a genetic effect by halving the influence of any chef in each successive earlier generation. Finally, we established a statistical method for evaluating the results of our analysis. In this framework, Dosage in its latest configuration was developed.
Each chef is assigned to one or two of five aptitudinal groups (Brilliant, Intermediate, Classic, Solid, and Professional) covering the spectrum (from left to right) of speed to endurance. The assignments are made to best reflect the traits that these stallions predictably and consistently transmit to their offspring. For bookkeeping purposes we assign a total potential value of 16 points to each generation. Since there are, progressively, one, two, four, and eight sires in the first four generations, chefs that appear among these sires will contribute 16, 8, 4, and 2 points each as we work back. The points for all chefs present are then tallied in the appropriate aptitude columns. Chefs that confer two aptitudinal characteristics have their points split between the two aptitudes. In the end, the total points in each column produce the Dosage Profile, a series of five numbers that reflect the relative proportions of each of the five aptitudes and is expressed in the order:
For example, the DP of the leading classic sire Halo, dk.b. or br. c., 1969 (Hail to Reason-Cosmah, by Cosmic Bomb), himself a chef-de-race, is calculated as follows:
Generation (Pts) Sires B I C S P 1st Generation (16): Hail to Reason (Classic) 16 2nd Generation (8): Turn-to (Brilliant/Intermediate) 4 4 Cosmic Bomb (N/A) 3rd Generation (4): Royal Charger (Brilliant) 4 Blue Swords (N/A) Pharamond II (N/A) Mahmoud (Intermediate/Classic) 2 2 4th Generation (2): Nearco (Brilliant/Classic) 1 1 Admiral Drake (Professional) 2 Blue Larkspur (Classic) 2 Sir Gallahad III (Classic) 2 Phalaris (Brilliant) 2 Blue Larkspur (Classic) 2 Blenheim II (Classic /Solid) 1 1 Peace Chance (N/A) DP: 11 -6 -26 -1 -2
The ratio of points in the speed wing (Brilliant points + Intermediate points + one-half the Classic points) to points in the stamina wing (one-half the Classic points + Solid points + Professional points) is the Dosage Index. This number is directly proportional to the inherited prepotent speed in a pedigree and inversely proportional to the stamina. A DI of 1.00 indicates a balance of the two. The DI of Halo is 1.88 ((11 + 6 + 13) divided by (13 + 1 + 2)).
If we consider the five aptitude groups as points spaced equally along a linear scale where Brilliant is assigned a value of +2.00, Intermediate is +1.00, Classic is 0.00, Solid is -1.00, and Professional is -2.00, the DP allows for the calculation of the Center of Distribution, that point along the scale corresponding to the total combined influences of all chefs in the pedigree. In that sense, it is a balance point (analogous to a center of gravity) of all weighted aptitudes supplied by chefs in the four generations. Calculation of the CD is done by taking the sum of twice the Brilliant points plus Intermediate points minus Solid points minus twice the Professional points and dividing that number by the total points in the DP. An exact balance of speed and stamina yields a CD of 0.00. The CD for Halo is 0.50 (((2 x 11) + 6 - 1 - (2 x 2)) divided by (11 + 6 + 26 + 1 + 2)), which places the combined effect of all chefs in his four generation pedigree equidistant between the Classic and Intermediate aptitudes.
For reference, a current list of chefs-de-race is located at this site. The chefs are shown in alphabetical order along with their aptitudinal assignments where B=Brilliant, I=Intermediate, C=Classic, S=Solid, and P=Professional.
Research using the described methodology as a tool for pedigree classification has resulted in many revealing observations including the following:
1. There is a direct correlation between the DI or CD and performance at varying distances as determined from separate populations of stakes winning sprinters, middle distance runners, and routers. As expected, the sprinters have the highest values (reflecting the importance of speed in short races), the routers have the lowest (confirming the need for endurance in long races), and the middle distance runners fall in between. In general, the Dosage figures correlate with the average distance of the races in each category. The precision of the technique is highlighted in the table below where average Dosage figures are displayed for specific distances between 5.5 and 12 furlongs for open stakes between 1983 and 1999. The correlation is virtually linear, confirming the direct relationship between distance and the speed/stamina characteristics of pedigrees as expressed by Dosage figures.
Distance Average DI Average CD 5 1/2 f 4.75 0.86 6 f 4.80 0.90 6 1/2f 4.09 0.84 7 f 4.06 0.83 8 f 3.30 0.70 8f & 70 yds 3.39 0.73 8 1/2 f 3.24 0.70 9 f 3.03 0.65 9 1/2 f 2.65 0.58 10 f 2.65 0.58 11 f 2.10 0.45 12 f 2.09 0.42
2. Elite Thoroughbreds as a group (e.g., champions, classic winners, leading sires) have significantly lower DI's and CD's than the general population of stakes winners, suggesting that outstanding performance on the track or at stud benefits from a large component of inherited stamina. There is no evidence, however, of an inherent superiority associated with lower Dosage figures. In other words, a lower DI is not better than a higher DI. Rather, the lower Dosage figures merely reflect the fact that our most prestigious races are run at longer distances and that successful competitors are aptitudinally suited to those races. Elite Thoroughbreds also have a higher point total in their DP than do typical stakes winners, acknowledging the fact that they tend to be somewhat better bred, at least to the extent that more chefs in a pedigree correlate with superior breeding stock.
3. Only three winners of the Kentucky Derby since 1940 (Strike the Gold, Real Quiet and Charismatic), and only three winners of the Belmont Stakes over the same time frame (Damascus, Conquistador Cielo, and Creme Fraiche) have had a DI above 4.00. This is in direct contrast to dirt stakes winners in general, of which about one-fourth to one-third have a DI greater than 4.00 and for which the average DI is slightly below 4.00. The combination of Dosage and our observation that 21 of the 28 winners of the Kentucky Derby since 1972 were ranked as a juvenile within 10 pounds of the high weight on the Experimental Free Handicap or were named juvenile champion in another country has become an especially powerful tool in isolating the true classic contenders. In the seven races where a "dual qualifier" (i.e., DI and two-year-old form) failed to win, three finished second, and in four of those races, a qualifier subsequently won either the Preakness or Belmont Stakes. The implications of this result are that a pedigree suited to distance, along with a demonstration of high-class, early maturity are more important for classic performance than other factors such as form in the pre-Derby preps at distances less than ten furlongs. Over the past 29 years, an average of only three and a half starters per Derby have met both criteria, including longshot winners Genuine Risk, Gato del Sol, Ferdinand, Alysheba, Unbridled, Sea Hero, Go for Gin, and Thunder Gulch. In addition, the "dual qualifiers" have accounted for 9 exactas and 5 trifectas. Thirty-four percent of all "dual qualifiers" won at least one classic race.
4. The average DI of juvenile stakes winners steadily decreases throughout the season, indicating a larger speed component in the pedigree of winners early in the year relative to winners later on. This phenomenon parallels the need for greater stamina as the distances of races for two-year-olds increase through the year.
5. The DI of many steeplechase champions since 1972 exceeds the classic guideline figure of 4.00 despite the long distances associated with steeplechase racing. This result suggests that the pace of these races is well within the ability of speed-bred runners and that their quickness over the jumps can be a more important factor for success. The remainder of steeplechase champions has had a DI close to 1.00 or less, more typical of expectations for competitors at very long distances. Surprisingly, there are few steeplechase champions with a DI in the range of middle distance flat racers.
6. The average DI of stakes winners at tracks favoring speed is higher than the average DI of stakes winners at tracks where speed is less favored. This result is consistent with the observation that brilliantly bred runners often carry their speed further on the speed-oriented surface.
7. Turf stakes winners have, on average, a lower DI than stakes winners on dirt. Furthermore, the turf runners have a significantly greater representation of Solid and Professional chefs in their pedigree. This result is consistent with the observation that turf races are run at a longer average distance than are races on dirt.
The studies described here are based on large populations that reflect statistically significant trends. The Dosage user must recognize, however, that within these populations there is great variation. Accordingly, Dosage figures for an individual may not conform to those of the whole population. Greater accuracy and increased predictability depends in large part on a continual modification and refinement of the chef-de-race list, guided by the principle of a better description of reality.
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