Explaining the Favorite–Long Shot Bias: Is it Risk-Love or Misperceptions?

Abstract

The favorite-long shot bias describes the long-standing empirical regularity that betting odds provide biased estimates of the probability of a horse winning: long shots are overbet whereas favorites are underbet. Neoclassical explanations of this phenomenon focus on rational gamblers who overbet long shots because of risk-love. The competing behavioral explanations emphasize the role of misperceptions of probabilities. We provide novel empirical tests that can discriminate between these competing theories by assessing whether the models that explain gamblers' choices in one part of their choice set (betting to win) can also rationalize decisions over a wider choice set, including compound bets in the exacta, quinella, or trifecta pools. Using a new, large-scale data set ideally suited to implement these tests, we find evidence in favor of the view that misperceptions of probability drive the favorite-long shot bias, as suggested by prospect theory. We thank David Siegel of Equibase for supplying the data, and Scott Hereld and Ravi Pillai for their valuable assistance in managing the data.

Estimating Risk Preferences in the Field

“…66 In each case, the estimate θ ̂ a is not far from what is obtained for the EU model, the probability weighting function for gains is slightly convex but not significantly so, but the probability weighting function for losses is highly and significantly concave, leading to a clear rejection of EU. Snowberg and Wolfers (2010) revisit the favorite-longshot framing of the data as in Griffith (1949) and Weitzman (1965), and investigate whether it is driven by risk love (increasing marginal utility) or by risk misperceptions (probability distortions). As in Ali (1977), either model can fully explain data on win bets.…”

“…First, Snowberg and Wolfers (2010) use race results to estimate how the win probability depends on the odds. They pursue an approach similar to Weitzman (1965), first calculating the empirical frequency of winners for each value of odds R observed in the data, and then using Lowess smoothing to estimate a function p ̂ (R) .…”

“…Next, Snowberg and Wolfers (2010) separately fit the EU model and the risk misperception model to the estimated p ̂ (R) function. For the EU model, they assume that bettors' beliefs correspond to p ̂ (R) , in which case, the market equilibrium condition implies…”

“…Finally, in step 3, having established that either model can perfectly fit data on win bets, Snowberg and Wolfers (2010) turn to compound bets. They (and we) outline their approach only for exacta bets (in which the bettor wagers that horse A will come in first and horse B will come in second); analogous approaches are used for quinella and trifecta bets.…”

“…In particular, the assumption of unidimensional heterogeneity that 76 This step is analogous to the approach in Weitzman (1965) and Snowberg and Wolfers (2010), except that they estimate how the probability of horse i winning depends on the full vector of odds R , as opposed to merely depending on R i . 77 Here, they do not pursue a maximum-likelihood approach as in Jullien and Salanié (2000) and Gandhi and Serrano-Padial (2015).…”