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The Dosage Breeding Theory for Horse Racing Predictions
by Marshall Gramm and William T. Ziemba

The link at the bottom launches a pdf file (requiring a pdf reader) of the full text of the above Chapter 15 from "Handbook of Sports and Lottery Markets", edited by D. B. Hausch and W.T. Ziemba (published by Elsevier B.V. (2008) and available at amazon.com and other online booksellers), an academic study of the success of Dosage theory in the Triple Crown races.  Dr. Gramm is on the faculty of the Department of Economics and Business, Rhodes Collegein  Memphis, Tennessee, and Dr. Ziemba is on the faculties of the Sauder School of Business, UBC, Vancouver, Canada, and the Mathematical Institute, Oxford University, and the ICMA Centre, University of Reading in the UK.  Below is a summary of their conclusions.  In the summary, BHZ refers to the previous publication: Bain, R., D. B. Hausch, and W. T. Ziemba. 2006. An Application of Expert Information to Win Betting on the Kentucky Derby, 1981–2005, European Journal of Finance 12, 283–301.  GZ refers to the previous publication: Gramm, M., and W. T. Ziemba. 2008. A Test of Semi-Strong Form Market Efficiency: The Triple Crown Races Betting Markets. Working Paper. University of British Columbia, Vancouver, British Columbia, Canada.

"The racetrack is a useful financial market for testing market efficiency and considerable evidence exists in support of the track’s win market being weak-form efficient. This chapter, however, summarizes the work of BHZ and GZ that show the win market is not semi-strong efficient.  BHZ and GZ focused on a particular aspect of the Kentucky Derby and Belmont Stakes, whose distances of 1 1/4 and 1 1/2 miles are typically farther than any entrant has ever raced, and the Preakness Stakes, which is run between these two races at 1 3/16 mi. This lack of direct evidence of an entrant’s stamina for this race has motivated the search for indirect evidence. Dosage theory, which analyzes a horse’s pedigree, has been offered as such evidence but it has also been controversial, both in general and in its relation to the Kentucky Derby. Other evidence that has been offered includes well-publicized rankings of horses and results from recent high-caliber races.  BHZ did not evaluate the criticisms or the justifications offered for the dosage concept and for the ranking of two-year-olds, nor did they attempt to refine their application to the Kentucky Derby. Instead, they simply merged this publicly available information with the public’s win odds to establish “adjusted” win probabilities. They then tested these win probabilities within a betting system based on the optimal capital growth model and showed statistically significant profits.  GZ applied this procedure to the 1 1/2 mi Belmont Stakes, which is run five weeks after the Kentucky Derby. From the 1980s to the mid-1990s when the dual qualifiers were having very good success in the Derby, GZ’s results in the Belmont were not as good. However, in recent years the situation has reversed with superior results in the Belmont than the Derby. The betting systems discussed here are two of many strategies used by bettors. In the 1 3/16 Preakness, the dosage breeding theory is less of a factor, which is understandable given that the race is shorter than the Kentucky Derby, and thus evidence of a horse’s stamina exists. Even so, a positive return on dual qualifiers exists from 1981–2006. The procedure outlined shows that given the pools from a set of races for which the strategy is applicable, the simple model given in Equation (6) can be used to test the validity of the strategy."   

The Dosage Breeding Theory for Horse Racing Predictions