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Pricing Exotic Racetrack Wagers
... Alternatively, we can estimate and directly through logistic modeling, for example, see Lo and Bacon-Shone (1994) and Lo (1994). The effect of this improved probability estimation on betting strategy (e.g., the Dr. Z system proposed by Hausch et al. 1981) may result in better returns, see Lo et al. (1995) and Hausch et al. (1994). We assume that the win bet fraction is a good estimate of the win probability. ...
To predict the ordering probabilities of multi-entry competitions (e.g., horse races), Harville (1973) proposed a simple way of computing the ordering probabilities based on the simple winning probabilities. This simple model is implied by assuming that the underlying model (e.g., running times in horse racing) is the independent exponential or extreme-value distribution. Henery (1981) and Stern (1990) proposed to use normal and gamma distributions, respectively, for the running time. However, both the Henery and Stern models are too complicated to use in practice. Bacon-Shone et al. (1992b) have shown that the Henery and Stern models fit better than the Harville model for particular horse racing datasets. In this chapter, we first give a theoretical result for the limiting case that all the horses have the same abilities. This theoretical result motivates an approximation of ordering probabilities for the Henery and Stern models. We then show empirically that this approximation works well in practice.
... Using a similar optimization algorithm, Lo, Bacon-Shone and Busche (1995) demonstrated the superiority of using the Henery and Stern models in terms of long-term returns in different racetracks. Hausch, Lo, and Ziemba (1994b), however, concluded that the Harville model was slightly better than the Henery model using a small data set in a particular type of bets. For future research, it will be interesting to see whether the above non-constant correlation or non-constant variance structure, while marginally significantly better in terms of fit, will demonstrate a better result in betting. ...
Racing data provides a rich source of analysis for quantitative researchers to study multi-entry competitions. This paper first explores statistical modeling to investigate the favorite-longshot betting bias using world-wide horse race data. The result shows that the bias phenomenon is not universal. Economic interpretation using utility theory will also be provided. Additionally, previous literature have proposed various probability distributions to model racing running time in order to estimate higher order probabilities such as probabilities of finishing second and third. We extend the normal distribution assumption to include certain correlation and variance structure and apply the extended model to actual data. While horse race data is used in this paper, the methodologies can be applied to other types of racing data such as cars and dogs.
This is a survey of efficiency in racing, sports, and lottery markets. The win market is efficient but exhibits a favorite-longshot bias. The place and show markets, which involve more possible finishes, allow inefficiencies by using the win probabilities. These biases are discussed for U.S. and Hong Kong markets. The Kelly capital growth criterion is useful to implement a model to exploit these inefficiencies. Exotic markets involve even more complex sets of bets. Finally, possible inefficiencies in cross-track betting are discussed. Football and basketball betting markets are largely efficient. Lotteries provide interesting markets with one way to potentially exploit them being the use of unpopular numbers.
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