Surprised by the Parimutuel Odds?

This paper analyzes the role of private information in parimutuel (also known as pool betting) markets, a method commonly adopted to determine betting odds for horse races and other sporting events. According to the parimutuel system, the amount wagered on all outcomes is redistributed to the bets placed on the winning outcome. Given the frequent observation of the realized outcomes (which are not affected by the market process) and the absence of book makers (who could induce biases), parimutuel betting markets offer an ideal testbed for theories of information aggregation and market efficiency. The efficient market hypothesis asserts that the fraction of money wagered by the market on an outcome is an unbiased estimate of the outcome’s empirical frequency. Beginning with Richard M. Griffith (1949), empirical studies have established that market probabilities of favorites (i.e., outcomes with short odds) tend to underpredict their empirical probabilities; conversely, longshots are overbet and yield lower expected returns at the final odds. The favorite-longshot bias (FLB) is perceived as a systematic deviation from the efficient market hypothesis. In this paper, we argue that one should expect the FLB to result when a large number of privately informed bettors take simultaneous positions just before post time. Our resolution of the FLB is based on the identification of the empirical probability of an outcome with the outcome’s posterior probability derived by Bayes’s rule to incorporate the information revealed by the bets placed in equilibrium. Using the equilibrium structure to compute the Bayesian posterior probability associated with any realized market probability, we show that the ex post realization of a high market probability indicates favorable information about the outcome’s likelihood—and the opposite for longshots. The FLB is present because in a Bayes-Nash equilibrium bettors are not allowed to revise their positions to incorporate the surprise revealed by the final odds. The bias would instead be eliminated in a rational expectations equilibrium.