Every year I study and bet on the Triple-Crown races. We had a very good run in the 1970s, 80s, 90s into the 2000s. You could use the Dosage Index to basically eliminate most runners in these races, especially the mile-and-a-quarter Kentucky Derby held on the first Saturday in May at Churchill Downs in Louisville, Ky., and the Belmont Stakes’ mile-and-a-half held five weeks later at Belmont Park on Long Island.
The Dosage Index is basically speed divided by stamina. The idea, which is still useful, has several parts. Some horses have never run this distance before, so handicapping information on them is hard to come by. Then, there is speed versus stamina in that comes from a horse’s pedigree.
The index itself is compiled by noting the presence of certain influential sires, known as chefs-de-race (French for "chiefs of racing," or, more esoterically, "masters of the breed") in the first four generations of a horse's pedigree. Based on what distances the progeny of the sires so designated excelled in during their racing careers (the distance preferences displayed by the sires themselves while racing being irrelevant), each chef-de-race (the list released in the early 1980s identified 120 such sires, and 85 more have been added as of April 2005) is placed in one or two of the following categories, or "aptitudinal groups": Brilliant, Intermediate, Classic, Solid or Professional, with "Brilliant" indicating that the sire's progeny fared best at very short distances and "Professional" denoting a propensity for very long races on the part of the sire's offspring, the other three categories ranking along the same continuum in the aforementioned order. If a chef-de-race is placed in two different aptitudinal groups, in no case can the two groups be more than two positions apart; for example, Classic-Solid or Brilliant-Classic are permissible, but Brilliant-Solid, Intermediate-Professional and Brilliant-Professional are not.
Certain stallions breed consistent characteristics in their offspring, such as speed, stamina and the quality of the horse. There is much research in using these to determine how far a horse can go in terms of winning a race. Steve Roman took it up in a 1981 Daily Racing Form column. Roman has continued this research since then as have I since the 1984 Derby, and there is a section on it in Ziemba and Hausch (1987). Steve's work can be found here where you will find very good useful information on many relevant topics.
This results in a Dosage Profile consisting of five separate figures, listed in order of Brilliant-Intermediate-Classic-Solid-Professional. Secretariat, the 1973 Triple Crown winner, for example, had a Dosage Profile of 20-14-7-9-0. To arrive at the Dosage Index, the first two figures plus one-half the value of the third figure are added together, and then divided by one-half of the third figure plus the sum of the last two figures. In this case, it would be 37.5 (20 + 14+ 3.5) divided by 12.5 (3.5 + 9 + 0), giving Secretariat a Dosage Index of exactly 3.00 (the figure almost always being expressed with two places to the right of the decimal point and rounded to the nearest .01).
Now to the script in those salad days. Steve Roman found that from 1940 to 1990 no horse with a dosage above 4.00 actually won the Kentucky Derby. Moreover those horses, called dual qualifiers with DIs below 4.00 but within 10 pounds of the highest rated 2-year-old on the EXP rating, have special advantage. Here’s a good example: three horses were the lone doasge quatients (DQ), then had terrible 3-year-old years and did poorly in the Derby and skipped the Preakness two weeks later, then ran in the Belmont and won at huge odds. These include Birdstone (36-1 in 2004) and Lemon Drop Kid (29.75-1 in 1999).
In 2012 Union Rags was the lone DQ and won at odds of 2.75-1 and in 2015 Carpe Diem, a horse I own part of, was the lone DQ for the Belmont won by triple crown winner American Pharaoh, who was not a DQ. But Carpe got injured and did not run in the Belmont. Another is Althea, the Derby favorite in 1984 after a 107 new record in the 1 and 1/8th Arkansas Derby against the males. Her high dosage suggested trouble in the Derby and indeed she was first after one mile but 19th at the finish. The last 1/8 of a mile of the Derby is one of the greatest tests of thoroughbred stamina.