JOURNAL OF ECONOMICS AND FINANCE • Volume 29 • Number 3 • Fall 2005 391 ODDS-SETTING EFFICIENCY IN GAMBLING MARKETS: EVIDENCE FROM THE PGA TOUR By Stephen Shmanske* Abstract This paper describes the gambling market for PGA TOUR events for the 2002 season. The extent to which the odds predict the outcome is examined, illustrating how much information is captured in the odds and whether there are any identifiable biases in the odds. The overall implied profit to the casino is calculated as well as the returns to several naive betting strategies. By splitting the sample based on whether or not Tiger Woods is in the tournament, a “Tiger Woods effect” or a “thin market versus thick market effect” can be examined. On the whole, efficient markets propositions hold up, but the overwhelming share of the variation in the tournament outcome remains unexplained. Introduction Economists have examined gambling markets, trying to uncover evidence of profitable opportunities, or if failing to do so, providing evidence of a type of efficient market. In asset markets, Alchian’s (1974) martingales proposition suggests that the current price must be an unbiased predictor of the future price, or else positive profit opportunities would exist. The analogy to gambling markets is that the point spread or odds are like a current price predicting the actual outcome, which is like a future price. If an identifiable bias could be uncovered, the point spread or odds “market” would be inefficient, and a profitable betting strategy could be devised. Studies along these lines have been carried out for all the major team sports and for horse racing and are reviewed in Sauer (1998). This paper will extend this type of research to the odds market for wagering on PGA TOUR events. An interesting, tangential line of inquiry presents itself in golf wagering markets. Demsetz (1968) has studied asset markets, suggesting that the bid-ask spread is a measure of the transactions costs to investors and a measure of profitability to the market makers. The size of the transactions costs is a measure of a type of market efficiency that differs from that which focuses on the predictive information imbedded in a price. The bottom line in this research is the intuitively appealing result that bid-ask spreads shrink when the market volume grows. Thus, thin markets are less efficient in the sense of higher bid-ask spreads and a larger implicit profit margin to the broker. Wagering on golf should be less efficient in this sense than wagering on basketball or football because, for golf, the amount of money wagered is much smaller. This much is obvious, but within golf itself a more subtle natural experiment exists because the overwhelming popularity of Tiger Woods spills over into gambling markets. When Tiger Woods is scheduled to compete, the betting volume goes up, and the implied efficiency of the odds prices in the transactions costs sense (and the predictive sense) can be compared to tournaments in which he is not competing. The next section describes the gambling markets in golf and calculates the implied overall profitability of the casino and the returns to bettors following several naive betting strategies. * Stephen Shmanske, Department of Economics, California State University, East Bay, stephen.shmanske@ csueastbay.edu. Helpful comments were received when the paper was presented in a workshop at California State University, East Bay, and at the Western Economic Association International meetings in Vancouver, July 2004. 392 JOURNAL OF ECONOMICS AND FINANCE • Volume 29 • Number 3 • Fall 2005 Following this, in separate sections, the paper examines the ability of the odds to predict the finish order of contestants in the tournament and the ability of the odds to predict the winner of the tournament. The final section is a brief summary. Wagering on PGA TOUR Golf Background and Implied Prices Wagering on PGA TOUR golf consists of the weekly posting by casinos of odds to win that week’s tournament for a variety of golfers and for the field. Bettors can place bets from the time of completion of the previous tournament up until the Thursday morning start of the current tournament. Table 1 shows how the odds for a typical tournament are listed using the example of the 2002 Advil Western Open.1 This odds sheet is particularly interesting because it shows the odds with and without Tiger Woods due to his late withdrawal from the tournament. For most of the other tournaments during 2002, the odds as originally posted did not change over the course of the week. Table 1 illustrates a tendency that was consistent throughout the 2002 season. The worst odds are always offered on Tiger Woods when he is competing, and if he is not competing, the worst odds are always offered on the “field,” which includes all golfers not listed on the posted odds sheet. Golf wagering differs from the more popular point spread wagering on team sports or pari- mutuel wagering on horse racing.2 With point spread betting the odds are always 10/11 (10-to-11), but the house adjusts the point spread to roughly balance the amount bet on the favorite with the amount bet on the underdog.3 With pari-mutuel betting the odds are recalculated depending on the amount wagered on each horse, with the winning bettors splitting the proceeds of all the bets after the track takes a prespecified percentage (usually about 20 percent) of the pool. With either of these arrangements, the house is acting as more of a broker than a bettor, in that it is paying off the winning bets with the proceeds of the losing bets and incurring no risk. By taking bets at posted odds, the house is actually betting against the customer. Although the house may endeavor to match the proportion bet on each golfer to the odds offered, there is generally no guarantee that the money collected on losing bets will cover the required payout to the winners. Compared to pari- mutuel betting, the house is at greater risk. The greater risk to casinos from posted odds bets, and perhaps also from the comparative thinness of the market, shows up in a higher “price” of placing a bet. At the track, for example, a “portfolio” of bets could be made that would assure that the bettor would win one of them, but because the track takes 20 percent of the pool before proportionately dividing the rest among the winners, it would cost $1.25 to return $1. For point spread gambling, the portfolio includes bets on both the favorite and the underdog guaranteeing a winning bet (except in the case of a tie), but it would cost $1.0476 (= 22/21) to return $1. For the posted odds on PGA TOUR golf tournaments, one could also form such a portfolio, but for the final odds as posted for the tournament in Table 1, the cost would be a whopping $1.5624 to return $1. By adding up the implied probabilities of winning any particular tournament given in the posted odds for the tournament, the implied price of a guaranteed return of $1 can be calculated for each tournament and for subsets of tournaments. In 2002, these prices ranged from a low of $1.359 to a high of $1.812. Over all 36 tournaments in the sample, the average price is $1.5145. Generally speaking, betting on golf is not nearly as advantageous to the bettor as betting on football, basketball, or horse racing. Neither is it as consistent in terms of the house’s take. 1 All the odds used as data were graciously supplied by Pete Korner from the archives of Las Vegas Sports Consultants. 2 See Bassett (1981) for a technical treatment of the incentives in odds betting versus point spread betting. 3 The fudge adverb “roughly” is added because there are some subtle technical issues involved. See Shmanske (1991). JOURNAL OF ECONOMICS AND FINANCE • Volume 29 • Number 3 • Fall 2005 393 Table 1: Odds for 2002 Advil Western Open, Cog Hill Golf and Country Club, July 4–7, 2002. Open (July 1) Current (July 4) Note Tiger Woods 6/5 XXX Withdrew 7/2 Vijay Singh 12/1 10/1 Justin Leonard 18/1 12/1 Davis Love III 20/1 15/1 David Toms 20/1 15/1 Charles Howell III 25/1 20/1 Mike Weir 25/1 20/1 Scott Hoch 25/1 20/1 Stuart Appleby 30/1 25/1 Nick Price 30/1 25/1 Scott Verplank 30/1 25/1 Robert Allenby 30/1 25/1 K. J. Choi 35/1 30/1 Kenny Perry 35/1 30/1 Loren Roberts 35/1 30/1 Jerry Kelly 35/1 30/1 Winner Rocco Mediate 35/1 30/1 Bob Estes 35/1 30/1 Cameron Beckman 40/1 35/1 Steve Flesch 40/1 35/1 Peter Leonard 45/1 40/1 Scott McCarron 45/1 40/1 Lee Janzen 45/1 40/1 Steve Stricker 45/1 40/1 Ian Leggatt 50/1 45/1 Frank Lickliter II 50/1 45/1 Steve Elkington 50/1 45/1 Jeff Sluman 50/1 45/1 Chris Riley 60/1 50/1 Skip Kendall 60/1 50/1 Field 3/1 even Note: Takedown date: July 4, 2002, 4 a.m. Source: Las Vegas Sports Consultants. If greater amounts are wagered on a tournament, it might allow the casino to offer more favorable odds, much as transactions costs, measured by bid-ask spreads, are lowered in thick markets. Tiger Woods competed in 13 of the 36 tournaments in the sample and heightened the interest and betting volume of golf fans for those tournaments.