The best predictors other than the baseline predictors (Intercept, wbfAll, and nHor) were, in order of strength: numLineDiff, blinkon, days2nd, notLasix, speedDiff2, ppOut, pp2 and pp3. The rest of the predictors were trainers, jockeys, and horses bred in France.
The only time sensitive step in the process was the computation of Monte Carlo probability estimates which took around 10 to 25 hours depending on the speed of the computer used. EVs (Expected Value/Profitability) do not always increase directly with increases in Perf. It may be that the improvement in Perfs show up in improved 2nd, 3rd, or 4th place performances.
In an article by Clive Thompson [18] in Wired magazine titled “Advantage: Cyborgs,”
it is pointed out that in a “freestyle” 2005 online chess tournament, where any kind of entrant was allowed, the most successful players were “Cyborgs,” those able to use computers as
“assistants” most efficiently. That principle undoubtedly holds at the racetracks. The system described here has tremendous potential for assisting handicappers. Finding accurate
probabilities should translate into high profitability.
CHAPTER 7 CONCLUSIONS
1. The system works. Table 7.1 shows a comparison of the totals for Overlays versus Underlays. The differences are dramatic even taking into account the differences in distribution by odds ranges.
Table 7.1. Comparison of Overlays and Underlays Totals
Totals of Important Statistics Underlays Overlays
% of Total Horses in Odds Range 0-4 1.1 11.7
% of Total Horses in Odds Range 4-9 5.9 26.9
% of Total Horses in Odds Range 9-27 32.2 38.2
% of Total Horses in Odds Range 27 and UP 60.8 23.2
2. A better comparison is Table 7.2 since it is for the odds range 9-27 and the percentage of total horses in the range is about the same (32.2% to 38.2%). Horses in the 9-27 odds range are longshots, basically overlooked or lightly bet. Although a bettor has to be patient for Overlays and Underlays to happen, they can lead to profitable bets when used in the exotic wagering, especially the exactas, trifectas and superfectas since which horses to bet and which to avoid are clearly identified. To hit a 15 or 20 to one longshot in the correct spot on an exotic bet can really boost the payoff!
Table 7.2. Odds Range 9-27 of Overlays and Underlays Totals
Important Statistics: Odds 9 - 27 Underlays Overlays
Profitability/EV 0.67 1.20
3. The system, though it is in its infantcy stage, works well at identifying a predictive model. Using these regression methods will produce more accurate probabilities on some horses than those reflected from the odds.
4. The system is usable at the racetrack. Once a regression equation is found, new estimated probabilities can be generated and calculations quickly made on any new horse to highlight wagers that are likely to be profitable. This includes not only straight win bets, but perhaps more importantly, the exotic single-race bets such as Exactas, Trifectas, and Superfectas, as well as the multiple-race wagers such as the Daily Doubles, Pick3, Pick4, and Pick 6.
5. Just about any pattern or combination of factors or subset of horses can easily and quickly be turned into a predictor variable and analyzed to see how and if it affects a horses probabilities. The flags covariate (see Section 2.1) is an example of an obscure pattern that we found interesting and wanted to investigate and was able to do so just by making in an indicator type predictor. This is a tremendous tool for handicappers who have often wondered about special situations but had no feasible way to get an accurate answer.
6. Improvements are possible: the Response Variable, Perf and its underlying key statistic, Power Point can both be tweaked for better overall performance. Possible new predictor variables with some appropriate variable number N: weight drops from one race to the next, lowest weight in race by N or more pounds, switching distance type after N or more races at one specific type, new jockey after previous jockey rode N or more times, moving up or down in class, three year old horses in races for ages three and up, adding (or removing) blinkers after N races of not wearing (or wearing) them, are some
possibilities. Others may involve comparing lifetime and current year records for statistics such as average earnings per race, percentages for winning or placing, or showing. The foreign horses could also provide valuable predictors like first race in U.S., 2nd race, etc. or when they switch to dirt or synthetic surface for the first time (many horses from Europe have run only on turf when they come to the U. S.). There are numerous possibilities for new predictors.
BIBLIOGRAPHY
[1] D.A. Harville. Assigning probabilities to the outcomes of multi-entry competitions.
Journal of American Statistical Association, 68:312-316, 1973.
[2] R.J. Henery. Permutation probabilities as models for horse races. Journal of Royal Statistical Society B, 43:86-91, 1981.
[3] H. Stern. Models for distributions on permutations. Journal of American Statistical Association, 85:558-564, 1990.
[4] D.B. Hausch, V.S.Y. Lo, and W.T. Ziembe. Efficiency of Racetrack Betting Markets.
Academic Press, New York, NY, 1994.
[5] J.B. Bacon-Shone, V.S.Y. Lo, and K. Busche. Logistics analyses of complicated bets.
Research Report 11, Department of Statistics, the University of Hong Kong, 1992.
[6] V.S.Y. Lo and J. Bacon-Shone. Comparison between two models for predicting ordering probabilities in multi-entry competitions. The Statistician, 43(2):317-327, 1994.
[7] V.S.Y. Lo and J. Bacon-Shone. Handbook of Investments: Efficiency of Sports and Lottery Markets. Elsevier, London, England, 2008.
[8] M.M.Ali. Probability and utility estimates for racetrack bettors. Journal of Political Economy, 84:803-815, 1977.
[9] P. Asch, B. Malkiel, and R. Quandt. Market efficiency in racetrack betting. Journal of Business, 57:165-174, 1984.
[10] W.T. Ziemba and D.B. Hausch. Dr. Z’s Beat the Racetrack. Morrow, New York, NY, 1987.
[11] J.B. Bacon-Shone and V.S.Y. Lo. Probability and statistical models for racing. Journal of Quantitative Analysis in Sports, 4(2):2-11, 2008.
[12] M.H. Kutner, C.J. Nachtsheim, and J. Neter. Applied Linear Regression Models.
McGraw-Hill Irwin, New York, NY, 2004.
[13] B. Harris. Emotional Bob Baffert heads into Thoroughbred Racing Hall of Fame. Sports News, August 12, 2009.
[14] J. Bossert. Trainers bemoan synthetic tracks as Breeders’ Cup approaches. New York Daily News, October 22, 2008.
[15] Wikipedia. Bob Baffert, 2010. http://en.wikipedia.org/wiki/Bob Baffert, accessed May 2010.
[16] Wikipedia. Kent Desormeaux, 2010. http://en.wikipedia.org/wiki/Kent Desormeaux, accessed May 2010.
[17] Wikipedia. Garrett Gomez, 2010. http://en.wikipedia.org/wiki/Garrett K. Gomez, accessed May 2010.
[18] C. Thompson. Advantage: Cyborgs. Wired Magazine, 42, April 2010.