Determinants of betting market efficiency

Applied Economics Letters, 2005, 12, 181 185 Determinants of betting market efficiency Marshall Gramm a * and Douglas H. Owens b a Department of Economics and Business, Rhodes College, 2000 North Parkway, Memphis, TN 38112-1690, USA b Welch Consulting, 111 University Drive East, Suite 205, College Station, TX 77840, USA Previous studies of efficient markets in parimutuel betting isolated only one race characteristic, determining efficiency by comparing subjective to objective probabilities of different groupings. By incorporating regression analysis and looking at a wide range of race specific variables, this study is able to isolate various factors which influence efficiency. Using a data set of 5020 races at 18 US racetracks, a standard favourite longshot bias was found, which diminishes for races with larger pools and more horses in a field, and increases for races with higher quality fields and maiden races. When track-specific characteristics are factored out, similar results occur and it is also found that races on grass reduce the bias. I. Introduction Betting markets have been studied by social scientists as a perceived controlled repeated experiment of asset markets and behaviour (see Sauer, 1998, for an overview). This experiment is repeated numerous times daily around the world in parimutuel betting markets such as horse or dog racing. The unique aspect of parimutuel betting is that the track acts only as an intermediary or market maker who extracts a certain amount (14 20%, called the take) from the betting pool and then redistributes the rest to the holders of the winning tickets. Odds are displayed for each betting interest in a race. Efficient markets with perfect information and bettors who choose bets to maximize their expected wealth would imply the expected return on any unit bet would equal one minus the track take. Previous studies have shown that racetrack betting markets are not efficient (see Thaler and Ziemba, 1988; Vaughan Williams, 1999, for an overview). In some studies favourites were underbet and longshots were overbet resulting in a higher expected return for low odds horses (Ali, 1977; Asch et al., 1982). Other studies have found a reverse favourite longshot bias (Busche and Hall, 1988; Swindler and Shaw, 1995). More recent empirical work in the area has focused on single factors that influence efficiency, including breakage (Busche and Walls, 2001; Walls and Busche, 2003), which is the rounding of payoffs to the nearest nickel or dime, the track s take (Vaughan Williams and Paton, 1998), the volume of wagering (Busche and Walls, 2000; Walls and Busche, 2003), the quality of the race participants (Sobel and Raines, 2000), whether the race was the first or last of the day (Busche and Walls, 2000), and whether the race was on a weekend or weekday (Sobel and *Corresponding author. E-mail: gramm@rhodes.edu Applied Economics Letters ISSN 1350 4851 print/issn 1466 4291 online # 2005 Taylor & Francis Group Ltd 181 http://www.tandf.co.uk/journals DOI: 10.1080/1350485042000314352

182 M. Gramm and D. H. Owens Raines, 2003). This paper explores these factors and others collectively through regression analysis using a sample of 5020 horse races at major American tracks in the fall of 2002. ( 1 for a non-winner and the odds for a winner). Another advantage of regression analysis is that we can look at the partial effect of a number of variables and determine whether they increase or decrease efficiency. The following equation is estimated II. Empirical Analysis NR ij ¼ 0 þ 1 Odds ij þ 2 Odds 2 ij þ k Odds ij Race Factors j þ " ð1þ The data used in the study is comprised of thoroughbred races run at 18 racetracks in the USA during the months of October, November, and December of 2002. Included were the major racing circuits of New York (Belmont and Aqueduct), Kentucky (Keeneland, Churchill Downs, Turfway Park), and California (Santa Anita, Hollywood Park), as well as mid-major circuits in Maryland, Louisiana, and Florida, and a number of minor tracks. Table 1 lists the tracks, as well as provides information on their take, per race average size of the win pool, per race average purse, and track take. One way to analyse betting data for efficiency is to use regression analysis as suggested by Vaughan Williams and Paton (1998). Many previous studies divide horses into groups based on favourite position or odds categories and compare subjective probabilities, what the general public feels the horses chances are as revealed by the odds, to objective probabilities, the actual percentage of winners in the group. Vaughan Williams and Paton argue this method results in measurement error bias which can be eliminated by using information on individuals betting interests, their respective odds, and actual returns where NR ij is the actual net return to a unit win bet on the ith horse in the jth race and Odds ij are the odds on the ith horse in the jth race. If 1 <0 then a traditional favourite longshot bias exists where the returns are greater for lower odds horses. A quadratic term is included for odds and odds is interacted with k race-specific factors. The interaction term allows us to determine effects of the race specific factors on efficiency. If the coefficient on an interaction term is estimated to be positive (negative) then increases in that factor increase (decrease) net returns for longer odds horses and therefore reduce (increase) a standard favourite longshot bias. The race factors analysed are summarized in Table 2. Breakage is the expected rounding per dollar payout and is calculated by multiplying the horse s subjective probability (amount bet to win on a horse divided by total amount bet into the win pool) with the amount of rounding that would occur should the horse win. The Class variable is a rating of the quality of participants in a race produced by Equibase, the official database for racing, and called TrackMaster Class Ratings. The ratings, ranging from 50 to 100, are equalized across tracks so that a given number Table 1. Racetracks Track City State Horses Races Take (%) Average pool size ($) Average purse ($) Aqueduct Ozone Park NY 3447 403 14.00 210 607 45 022 Arlington Arlington Heights IL 940 118 17.00 252 455 122 000 Belmont Elmont NY 512 65 14.00 227 589 51 542 Calder Miami FL 5044 618 18.00 79 696 23 845 Churchill Downs Louisville KY 2280 244 16.00 146 463 39 598 Fair Grounds New Orleans LA 1366 157 17.00 96 126 27 322 Hollywood Park Inglewood CA 2175 296 15.43 184 202 42 233 Hoosier Anderson IN 3453 372 18.00 23 794 14 902 Keeneland Lexington KY 622 70 16.00 154 198 44 800 Laurel Park Laurel MD 3945 493 18.00 47 615 21 296 Louisiana Downs Bossier City LA 1401 171 17.00 38 077 11 388 Moutaineer Chester WV 3330 357 17.30 25 747 18 076 Retama Selma TX 1028 116 18.00 21 946 11 521 Sam Houston Houston TX 2798 307 18.00 35 556 18 002 Santa Anita Arcadia CA 1269 150 15.43 193 200 42 970 Suffolk Downs East Boston MA 3225 360 19.00 25 169 14 314 Turf Paradise Phoenix AZ 4275 507 20.00 23 383 7521 Turfway Park Florence KY 2136 216 17.50 49 244 14 240 43 246 5 020

Determinants of betting market efficiency 183 Table 2. Race factor variables Variable Definition Pool Size Dollars bet into the win pool Average $85 141 Takeout Track s share of the pool Range 14 20% Breakage Expected breakage per dollar Average $0.05 Horses Number of betting interests Average 9 Range 4 14 First Race First race on the card 9.2% of all races Last Race Last race on card 11.7% of all races Weekend Race on a weekend/holiday 36.7% of all races Class TrackMaster class ratings Avg 74, Range 50 100 Maiden Race for non-winners 31.8% of all races State Bred Race for horses bred in state 11.3% of all races Fillies Race for fillies and mares 41.6% of all races Juvenile Race for 2 year-olds 24.0% of all races Off Track Race on an off track 25.5% of all races Grass Race on the grass 10.5% of all races Route Race at a mile or greater 38.7% of all races Table 3. Regression results Model I: Standard Model II: Fixed effects Coefficient Slope z-stat Coefficient Slope z-stat Odds 0.6299 0.0544 22.99 0.6125 0.0522 11.81 Odds 2 0.0035 0.0003 14.04 0.0037 0.0003 12.60 Interactions Pool Size 0.0014 0.0001 3.05 0.0013 0.0001 2.27 Takeout 0.0168 1.87 Breakage 0.0102 0.99 0.0101 0.99 Horses 0.0209 0.0018 2.87 0.0198 0.0017 2.70 First Race 0.0396 0.93 0.0338 0.78 Last Race 0.0182 0.54 0.0218 0.62 Weekend 0.0319 1.23 0.0253 0.99 Class 0.0073 0.0006 2.78 0.0076 0.0006 2.94 Maiden 0.1182 0.0102 3.47 0.1301 0.0111 3.85 State Bred 0.0636 1.63 0.0540 1.27 Fillies 0.0411 1.50 0.0389 1.44 Juvenile 0.0111 0.39 0.0299 1.08 Off Track 0.0085 0.28 0.0226 0.69 Grass 0.0956 1.91 0.1056 0.0090 2.19 Route 0.0197 0.64 0.0157 0.54 Constant 13.7867 27.16 represents the same quality at any track. A number of the race specific factors are dummy variables and the percentage of races satisfying the conditions are reported. Since the data is censored at 1, a Tobit regression is preferred. Horses within races are interdependent, therefore observations are clustered within races and assumed independent across races. Two regressions, standard and fixed-effects, are estimated. The standard regression is a clustered tobit with the leftcensored dependent variable of net return and independent variables including odds, the squared odds (to capture increasing or decreasing marginal effects), and race specific interaction terms. The fixed effects regression is the same as the standard model, with the exception that the track specific factors are partialled out by interacting odds with dummy variables for each track. Efficiency would dictate that the expected return on a dollar bet would be the same no matter what the odds were. Thus, the partial effect of odds on net return would be zero should no bias exist. A negative partial effect would be evidence of the standard favourite longshot bias. The results in Table 3 report the coefficient on

184 M. Gramm and D. H. Owens each independent variable along with the estimated slope for statistically significant variables. Regression results indicate that a traditional favourite longshot bias exists. In the standard regression, the partial effect of odds on return is found to be dependent on odds, pool size, number of horses, class, and the maiden dummy; NR ¼ 0:0544 þ 0:0006 Odds þ 0:0001 Pool Size Odds þ 0:0018 Horses 0:006 Class 0:0102 Maiden ð2þ Both Odds and Odds 2 are significant, and the signs on the estimates indicate that odds on a horse have a negative but diminishing effect on net return. The partial effect of odds on net return is found to be 5.44. However, the longer the odds on the horse, the smaller this inefficiency becomes, decreasing by 0.06 for every dollar increase in the odds. The turning point from a negative to positive partial effect of odds on net return occurs at 90 1, an extreme longshot only represented by 1% of the sample. A one thousand dollar increase in pool size increases the marginal effect of odds on return by 0.01. Therefore, increased bettor participation, measured by dollars bet into the win pool, will increase efficiency, but the effect is very small. The greater the number of horses in a race, the more options bettors have, and this is found to increase efficiency. A surprising finding is that a higher quality field is less efficiently priced. Stakes races, which typically have a class rating in the 90s, will increase the bias by 1.2 for every dollar increase in the odds when compared to a mid-level claiming race with a class rating in the 70s. A maiden race increases the predicted bias by about 1 for every dollar. Sobel and Raines, looking at dog races, found that the public tended to overbet favourites in high grade races (a class measure for dog racing) and underbet favourites in low grade and maiden races. They argued in those markets with the least prior information available to bettors that the bias is most heavily skewed towards a regular favourite-longshot bias (p. 380). In our data we find the exact opposite to be true. Perhaps this can be explained by differences between dog and horse racing or because of omitted variable bias in their study, which only compares subjective and objective probabilities by grade of race. The results are very similar in the fixed effects regression, with the exception that the grass race dummy variable is now statistically significant, and grass races are estimated to increase efficiency. The partial effect of odds on return is described by NR ¼ 0:0522þ0:0006Oddsþ0:0001Pool Size Odds þ0:0017horses 0:006Class 0:0111Maiden þ0:0090grass ð3þ Note that takeout was dropped from the fixed effects regression because it does not vary within tracks. The slopes on the significant independent variables are not very different from the standard regression, but all are still significantly different from zero, despite accounting for track specific differences. The only variable whose statistical significance was affected by using the fixed effects regression was the dummy variable for a race on the grass, which is found to reduce the favourite longshot bias by 0.9 for every dollar increase in the odds. Certain factors had no influence on efficiency in either regression model. Neither the first nor the last race had a significant impact on efficiency, which is consistent with previous studies (Busche and Walls, 2000). There was also no difference found between weekend or weekday races, contrary to the findings of Sobel and Raines, who found a standard favourite-longshot bias on weekends and a reverse favourite longshot bias on weekdays. Takeout was not significant in the standard regression, which runs counter to previous explanations of increased transactions cost reducing efficiency. However, the p-value was 0.061 indicating that one could reasonably consider takeout significant. A one percentage point increase in takeout would increase the bias by a predicted 0.15. Unlike studies conducted by Busche and Walls using Asian race data, this study found the bias to be unaffected by breakage. In addition to those factors previously analysed by others, the bias was also found to be unaffected by races open only to fillies and mares (female horses), horses bred in the state where the track is located, or for juveniles. Track conditions (muddy, sloppy, etc) or the distance of the race did not effect efficiency. III. Conclusions By incorporating regression analysis and looking at a wide range of race-specific variables, we are able to isolate some of the determinants of efficiency in parimutuel betting markets for thoroughbred horse races. Previous studies isolated only one race factor and determined efficiency by dividing horses into groups and comparing subjective to objective probabilities. Using a data set with 43 246 betting interests, numerous factors are examined simultaneously

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