Efficiency in Pari-Mutuel Betting Markets across Wagering Pools in the Simulcast Era

Abstract

1. IntroductionPari-mutuel wagering has been much studied in economics and finance because it functions as a controlled repeated experiment of an asset market (see Sauer 1998 for an overview). Through pari-mutuel betting, the public collectively establishes a price on each betting interest, and these prices have been found to be fairly accurate in representing the true value of the bet. The track acts as a market maker, extracting a fixed percentage (14-20%) from betting pools and redistributing the rest to the holders of the winning tickets. Because the market is repeated numerous times daily at tracks across the world, an abundance of data exists on betting markets. Furthermore, with the proliferation of simulcasting races, participation in the pari-mutuel market is no longer restricted to just those attending the races.In a speculative market, efficiency dictates that the expected return on an asset should equal the return on the entire market. Betting-market efficiency requires that no betting strategy generates above-market returns after accounting for costs (see Vaughan Williams 1999 for an extensive review of the literature). Thaler and Ziemba (1988) define a weak and strong condition for betting-market efficiency. Weak-form efficiency requires that no bets have positive expected returns. Strong-form efficiency requires all bets to have the same expected return equal to one minus the track take. Therefore, under strong-form efficiency, the probability of a horse winning a race would be equal to the percentage of money bet on that horse.This article is an empirical analysis of straight wagers, which are bets on a horse to win, place (finish in the top two), or show (finish in the top three). Numerous empirical studies have found the existence of a bias on win wagers such that favorites were underbet relative to long shots, resulting in a higher expected return for low-odds horses (Ali 1977; Asch, Malkiel, and Quandt 1982). However, other studies have found a reverse favorite-long shot bias (Busche and Hall 1988; Swindler and Shaw 1995). Explanations of the bias have included risk preference (Ali 1977; Golec and Tamarkin 1998), information disparities (Hurley and McDonough 1995, 1996; Terrell and Farmer 1996; Gandar, Zuber, and Johnson 2001), transaction costs (Hurley and McDonough 1995, 1996; Vaughan Williams and Paton 1998a, b), and market size (Busche and Walls 2000). Previous studies on place and show betting have found even more pronounced biases, and these findings have led to the formulation of profitable betting strategies, the most prominent being Ziemba and Hausch's Beat the Racetrack (Ziemba and Hausch 1984; Asch, Malkiel, and Quandt 1984, 1986; Asch and Quandt 1986; Hausch, Ziemba, and Rubinstein 1981; Hausch and Ziemba 1985). There have been few articles on betting simulations and efficiency, the most notable being Goodwin (1996), who uses forecasts of conditional probabilities to earn above-market returns.The proliferation of simulcast wagering has created an environment where relatively few betting patrons attend the races anymore, and those that do are more likely to be found in front of a television carrel watching races from around the country, rather than in the grandstand. Previously, tracks would simulcast only major races a few times a year and have their own separate betting pools for these races. A betting pool at a given track for a given race would be comprised of money from people at the track and in some instances, from off-track betting sites or phone accounts, both within the track's home state. Today, simulcast wagering allows bettors to play a multitude of races at many tracks across the country, from their home track, casino, off-track betting hub, by phone, or online, and their bets are commingled into the same pool as those made at the host track. This development has resulted in an explosion in the dollar volume wagered on horse racing in the last decade. …