Managing losses in exotic horse race wagering

Abstract

We consider a specialized form of risk management for betting opportunities with low payout frequency, presented in particular for exotic horse race wagering. An optimization problem is developed which limits losing streaks with high probability to the given time horizon of a gambler, which is formulated as a globally solvable mixed integer nonlinear program. A case study is conducted using one season of historical horse racing data.

Appendix

1.1 Estimating win probabilities

A number of factors and their logarithms were considered, displayed in Table 2 below. The domain of each factor is listed in brackets, but all were normalized to be between 0 and 1 for statistical use. The first six factors are from CompuBet (2014), with the other two from the race program and result.

Table 2 Win probability considered factors

Systematically removing the least significant factor with a p-value greater than 0.05 resulted in the factors in Table 3.

Table 3 Win probability factors

The McFadden (1974) $R^2$ goodness of fit measure was used to compare the public’s implied winning probabilities to the model’s, where $R^2=1$ implies perfect predictive ability and $R^2=0$ means predictability is no better than random guessing. Using the last $30\%$ of the racing data, $R^2_{\pi _h}=0.218077$ and $R^2_{\pi ^m_h}=0.214455$. We see the model has a small positive edge of $\Delta R^2=R^2_{\pi _h}-R^2_{\pi ^m_h}=0.0036$ over the general public.

1.2 Estimating superfecta probabilities

Below are the results of estimating the $\lambda ^{i}$ parameters Table 4.

Table 4 Superfecta probability parameters

1.3 Estimating public’s superfecta probabilities

Below are the results of estimating the $\theta ^{i}$ parameters Table 5.

Table 5 Superfecta probability parameters