An empirical examination of the parimutuel sports lottery market versus the bookmaker market.

• Author: Chung, Jaiho
• Position: Symposium

1. Introduction

   Market mechanisms under which sports betting takes place can be categorized into two major types: a bookmaker system and a parimutuel market system. In a bookmaker-based system, the bookmaker posts odds and charges a commission (also called "vigorish" or "juice") for placing a bet. In this type of market, bettors (or "punters") are promised a fixed payoff according to the odds that are posted at the time they make their bets. In the parimutuel betting system, there are no bookmakers, and the payout from a specific outcome is inversely related to the aggregate amount wagered on that outcome relative to the aggregate amount bet across all outcomes. Therefore, the payout will not be determined until all bets are submitted. In this study, we use a unique data set in the parimutuel-type Korean sports lottery market and examine the joint efficiency of the parimutuel sports lottery market and the bookmaker market.

   Sports betting markets have been used in many studies as a way of testing market efficiency (see Sauer 1998; Vaughan Williams 1999; and Paton, Siegel, and Vaughan Williams 2009 for reviews). A widely documented anomaly against market efficiency in the sports betting market is the favorite-longshot bias. The favorite-longshot bias, first shown in the horse race betting market, states that horses with lower odds (higher probability of winning) tend to win more frequently than projected by their odds, while horses with higher odds (lower probability of winning) tend to win less frequently than indicated by their odds. In a parimutuel market structure, this suggests that favorites are underbet while longshots are overbet (see Ziemba and Hausch 1984; Thaler and Ziemba 1988; and Paton, Siegel, and Vaughan Williams 2009 for reviews). (1)

   Most horse tracks in the world operate as a parimutuel system (the system is called the totalisator in the United Kingdom, Australia, and New Zealand), (2) whereas horse tracks in the United Kingdom, Ireland, and Australia also employ bookmaker-based systems. Researchers have examined market efficiency between these two different types of market structures for horse tracks. Gabriel and Marsden (1990, 1991), Bruce and Johnson (2000), and Peirson and Blackburn (2003) compare returns in the British horse track for bets made in the parimutuel ("tote") market and bets made with the bookmaker. Gabriel and Marsden (1990, 1991) examine winning bets in two markets under the situation where tote bettors had restricted information on current odds due to the absence of mechanical or electronic tote boards during the year of their sample period. They find that the level of winnings from successful bets in the parimutuel market is larger than that in the bookmaker market. Bruce and Johnson (2000) examine all bets made in the two markets under full odds information available for the tote bettors and find that the favorite-longshot bias is strong in the bookmaker market but not in the parimutuel market. Peirson and Blackburn (2003) also find similar results in British racetracks and note that profit maximization by bookmakers and efficient behavior by bettors can cause the difference between the two markets.

   For sports betting other than horse racing, most markets are bookmaker based, with the exception of betting pools and some sports lotteries. Therefore, almost all previous studies on sports betting outside of horse racing are based on a bookmaker market, and none of these studies examines efficiencies across different market structures. (3)

   In this study, we use a unique data set in the parimutuel-type Korean sports lottery market to ascertain whether there is a significant difference in winning payoffs between this parimutuel sports lottery market and the bookmaker-based market. In the Korean sports lottery market, odds are determined by the parimutuel method, and current odds are readily available on its website, which allows participants to monitor odds on a real-time basis. Among the various betting opportunities that are offered by the Korean sports lottery system, we focus on "soccer special triple" and "soccer special double," where participants who pick the correct final scores of a predetermined three- or two-game soccer lottery win the share of the betting pool. For instances where the Korean sports lottery features games in the English Premier League, the odds on the final score of these three (or two) games are available on major bookmakers, such as the online betting website of William Hill PLC. Using data from 34 sports lotteries for 86 English Premier League matches between 2005 and 2008, we compare the return on winning bets placed in the parimutuel-type Korean sports lottery market to the corresponding return on a bet placed in the U.K. bookmaker-based market.

   We find notable differences in the realized return between these two markets. For example, a $1.00 bet on the final score of 1:0, 2:0, and 0:3 for matches between Bolton and Manchester United, Arsenal and Wigan, and Middlesbrough and Aston Villa, played on November 25, 2007, paid an amount of $6605.20 in the Korean sports lottery market, compared to $2028.00 in the U.K. bookmaker market. However, another $1.00 bet on the final score of 2:l, 1:1, and 1:2 for matches between Arsenal and Tottenham, Fulham and Wigan, and Middlesbrough and West Ham on December 22, 2007, paid only $92.90 in Korea's sports lottery market, compared to $585.00 in the U.K. bookmaker-based market. These discrepancies in winning payouts between two markets are surprising since current odds on both markets are accessible to participants in the Korean sports lottery market. We find that for low-payout outcomes (games that turn out as many have expected), the Korean sports lottery market returns lower payouts compared to the corresponding payoffs in the bookmaker-based market. The reverse relationship is found for high-payout outcomes (games that do not turn out as many have expected). Overall, our results suggest that the two markets are not jointly efficient.

   Our main contributions are twofold. First, to the best of our knowledge, this is the first study to provide an empirical examination of a parimutuel sports lottery market relative to a bookmaker market. (4) Some sports lotteries, such as Pro-line, operated by the Ontario Lottery and Gaming Corporation in Canada, are organized as bookmaker-based, fixed-odds systems and do not have a corresponding parimutuel market to compare against. For parimutuel-type sports lotteries such as The New Football Pools or Brittens National Pools in the United Kingdom or Sports Action in the United States, the lack of information on current odds or on the final payoff data make it impossible to compare the return against a bookmaker-based market. (5) The sports lottery market in Korea, which provides current odds information to all participants and ex post payout information for their events, provides a unique opportunity for us to examine the parimutuel-type sports lottery market against the bookmaker market.

   Second, given that the sports lottery, which we investigate, operates as a parimutuel market, this is also the first study to empirically test the joint efficiency of the parimutuel market and bookmaker-based market outside the realm of horse tracks. (6) In horse racing, studies (for example, Crafts 1985 and Shin 1992) note that private inside information is believed to be prevalent, and Shin (1991, 1992) argues that the bookmakers worsen the odds for longshots to guard against bettors with inside information, thereby causing the favorite-longshot bias in the bookmaker market. In comparison to horse race betting, betting on the final score of a soccer game would see many fewer cases of insider traders. For example, even if someone has inside information on a player's physical condition, the insider trader is unlikely to predict the final score of the game with high accuracy because of the larger proportion of the unpredictable component ("luck") present in the correct score betting. Therefore, it is interesting to see whether the favorite-longshot bias would still exist in the bookmaker market relative to the parimutuel market when bookmakers are faced with less threat of privately informed bettors. Our results suggest that the bias still exists in the bookmaker market.

   Our study is not without limitation. Since we compare the parimutuel market and the bookmaker market on the basis of only winning bets, we do not intend to test the market efficiency in each of the two markets. Rather, we test the joint efficiency of these two markets and look only for the relative extent of bias across these two markets.

   The article is organized as follows: Section 2 introduces the Korean sports lottery market and the U.K. bookmaker market. Section 3 explains the different market structures and mechanisms between the two markets, while section 4 compares the payoffs from the Korean sports lottery market against those from the U.K. bookmaker-based market. Section 5 analyzes these results with respect to the existence of the favorite-longshot bias. Section 6 provides some additional analyses, including the comparison against betting exchanges and tests of alternative specifications of the model, and section 7 concludes the article.

2. The Korean Sports Lottery Market and the U.K. Bookmaker Market

   Korean Sports Lottery Market

   In Korea, the only government-sanctioned and legalized sports betting markets outside of on-track betting are Sports Toto, which is structured as a parimutuel market, and Sports Proto, which is structured as a bookmaker market. (7) In this study, our reference to Korean sports lottery refers to the parimutuel-type Sports Toto.

   Participants in the Korean sports lottery can make their bets offline through licensed betting offices, which are equipped with online terminals, or directly purchase online through the Korean sports lottery website (www.betman.co.kr). (8) To bet online...