Efficiency in pari-mutuel betting markets across wagering pools in the simulcast era.Simulcast wagering wa·ger n. 1. a. An agreement under which each bettor pledges a certain amount to the other depending on the outcome of an unsettled matter. b. A matter bet on; a gamble. 2. , where bets from across the country are taken at tracks, off-track betting off-track betting n. Abbr. OTB A system of placing bets away from a racetrack. facilities, casinos A list of casinos. Antigua and Barbuda
tr. & intr.v. in·ter·re·lat·ed, in·ter·re·lat·ing, in·ter·re·lates To place in or come into mutual relationship. in betting markets comprised of win, place (finishing in the top two), and show (finishing in the top three) wagering are efficiently priced. We find that the increased accessibility and betting volume associated with simulcasting has reduced, but not eliminated, the inefficiencies seen in prior studies. Despite the inefficiencies in these markets, arbitrage arbitrage: see foreign exchange. arbitrage Business operation involving the purchase of foreign currency, gold, financial securities, or commodities in one market and their almost simultaneous sale in another market, in order to profit from price is not profitable because market closing prices are unknown when bets are placed. JEL Classification: G14 1. Introduction Pari-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 A betting pool, sports lottery, or office pool if done at work, is a form of gambling where gamblers pay a fixed price into a pool and make a selection on some outcome, usually related to sport. 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 proliferation /pro·lif·er·a·tion/ (pro-lif?er-a´shun) the reproduction or multiplication of similar forms, especially of cells.prolif´erativeprolif´erous pro·lif·er·a·tion n. 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 Expected Return The average of a probability distribution of possible returns, calculated by using the following formula: 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 Vaughan Williams, Ralph 1872-1958. British composer who was influenced by folk tunes and Tudor music. His works include nine symphonies, the ballet Job (1930), and the opera The Pilgrim's Progress (1951). Noun 1. 1999 for an extensive review of the literature). Thaler THALER. The name of a coin. The thaler of Prussia and of the northern states of Germany is deemed as money of account, at the custom-house, to be of the value of sixty-nine cents. Act of May 22, 1846. 2. and Ziemba (1988) define a weak and strong condition for betting-market efficiency. Weak-form efficiency Weak-form efficiency A pricing theory that the price of a security reflects the past price and trading history of the security. Theory implies that security prices follow a random walk. Related: Semistrong-form efficiency, strong-form efficiency. requires that no bets have positive expected returns. Strong-form efficiency Strong-form efficiency A form of pricing efficiency, that posits that the price of a security reflects all information, whether or not it is publicly available. Related: Weak-form efficiency, semi-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 WAGERS. A wager is a bet a contract by which two parties or more agree that a certain sum of money, or other thing, shall be paid or delivered to one of them, on the happening or not happening of an uncertain event. 2. The law does not prohibit all 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 Empirical studies in social sciences are when the research ends are based on evidence and not just theory. This is done to comply with the scientific method that asserts the objective discovery of knowledge based on verifiable facts of evidence. 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 SWINDLER, criminal law. A cheat; one guilty of defrauding divers persons. 1 Term Rep. 748; 2 H. Blackst. 531; Stark. on Sland. 135. 2. Swindling is usually applied to a transaction, where the guilty party procures the delivery to him, under a pretended and Shaw 1995). Explanations of the bias have included risk preference (Ali 1977; Golec and Tamarkin 1998), information disparities (Hurley Hurley has become the English version of at least three distinct original Irish names: the Ó hUirthile, part of the Dál gCais tribal group, based in Clare and North Tipperary; the Ó Muirthile, based around Kilbritain in west Cork; and the OhIarlatha, from the district of and McDonough 1995, 1996; Terrell and Farmer 1996; Gandar, Zuber, and Johnson 2001), transaction costs Transaction Costs Costs incurred when buying or selling securities. These include brokers' commissions and spreads (the difference between the price the dealer paid for a security and the price they can sell it). (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 formulation /for·mu·la·tion/ (for?mu-la´shun) the act or product of formulating. American Law Institute 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 conditional probability the probability that event A occurs, given that event B has occurred. Written P(AB). 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 Car·rel , Alexis 1873-1944. French-born American surgeon and biologist. He won a 1912 Nobel Prize for his work on vascular ligature and grafting of blood vessels and organs. 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 horse racing, trials of speed involving two or more horses. It includes races among harnessed horses with one of two particular gaits, among saddled Thoroughbreds (or, less frequently, quarterhorses) on a flat track, or among saddled horses over a turf course with in the last decade. From 1985 to 2002, the total wagered on thoroughbred Thoroughbred Light breed of racing and jumping horse descended from three desert stallions brought to England between 1689 and 1724. Thoroughbreds have a delicate head, slim body, broad chest, and short back. Most are bay, chestnut, brown, black, or gray. races in North America North America, third largest continent (1990 est. pop. 365,000,000), c.9,400,000 sq mi (24,346,000 sq km), the northern of the two continents of the Western Hemisphere. increased from $8.25 billion to $15.62 billion, despite the fact that the number of races fell to 59,896 from 75,687 (Davidowitz 2003). Perrace wagering more than doubled over the 17-year period, increasing from $109,000 to $260,000. Adjusting for inflation, total wagering increased by 21%, while per-race wagering increased by 53%. Much of this can be attributed to off-track betting, which accounted for 86% of all bets made in 2002. This article is the first comprehensive study of straight wagers since wagering pools began to be commingled in the mid-1990s. The fact that betting markets are accessible to horseplayers across the country should result in more efficient pricing both within and across wagering pools. We use a large dataset, consisting of all tracks available to subscribers of the TVG TVG TV Guide (magazine) TVG Televisión de Galicia TVG Tierversuchsgegner (German: Antivivisection) TVG Television Games Network TVG Toronto Venture Group TVG Tri Valley Growers TVG Time-Variable Gain network's online racing service, to test whether the interrelated markets of win, place, and show wagering are efficiently priced. All major racetracks are included. Despite increased participation, we find that a favorite-long shot bias still exists in each pool, with the bias being more severe in place and show wagering. Place and show bets on extreme favorites earned a positive return. With evidence of inefficiency, an experiment to arbitrage betting markets was attempted but found to be unprofitable. The method used to try to arbitrage interrelated betting markets was the Dr. Z Dr. Z may refer to:
Probabilities that are determined subjectively (for example, on the basis of judgment rather than statistical sampling). , can be a good approximation approximation /ap·prox·i·ma·tion/ (ah-prok?si-ma´shun) 1. the act or process of bringing into proximity or apposition. 2. a numerical value of limited accuracy. of a horse's actual probability of winning. Harville introduced methods to calculate the probability of finishing in the top two or three based on the win probabilities of the horses in a race. A good place (show) bet may exist when a horse's probability of finishing in the top two (three) is much greater than the amount bet on the horse in the place (show) pool would justify. Unfortunately for the arbitrageur Arbitrageur A type of investor who attempts to profit from price inefficiencies in the market by making simultaneous trades that offset each other and capture risk-free profits. , the amount bet on each horse is typically not fully known until after the race has begun, making applications of the Dr. Z system a challenge at the racetrack. While arbitrageurs may wait until the last minute to have the best projection of the final odds, they run the risk of getting shut out at the betting window. These last frantic minutes often involve making quick but somewhat complex calculations to determine how much to bet on which horse or horses. The analysis also shows that, based on the final odds, arbitraging these betting markets using the Dr. Z system could be profitable. However, because our dataset contains final pool totals, the question still remained as to whether profits could be made in an actual betting scenario. To test this in practice, we placed bets on 203 races from February through April of 2003. Our bets fit the criteria of the Dr. Z system and were made online at the last possible moment that betting was allowed. Even so, only about 60% of the final pool totals are recorded when the betting windows close. The results show that the market becomes more efficient in the minutes leading up to the race, meaning that profitable bets at post time become poor plays once the final pool totals are revealed. Overall, the experiment resulted in a small net loss. 2. Empirical Results Data Overview The authors have collected a comprehensive dataset including all races available to the TVG network TVG Network is an American digital cable network that specializes in horse racing. The company broadcasts from Los Angeles, California and is available in the United States on Dish Network and DirecTV as well as select cable companies. online subscribers from October 9 to December 31 of 2002. This includes 96,275 betting interests (1) in 11,361 races over 84 days at 36 racetracks. All major tracks are included. Of the 36 tracks studied, 23 hosted thoroughbred racing, 10 harness, and 3 were mixed (including thoroughbreds, quarterhorses, arabians, and even mules). Both the overall size of the dataset and the number of racetracks included make it one of the largest to be used in a betting-market efficiency study. Table 1 summarizes the dataset by race meet. The number of horses and races are included in the table, with an overall average of 8.47 betting interests per race. The track take varies from a low of 14% at the New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of tracks to 20.5% at Pompano pompano (pŏm`pənō), common name for fishes of the genus Trachinotus, and for Palometus simillimus, members of a large and important family of mackerellike fishes, abundant in warm seas around the world. Park in Florida. Pool size is the average total bet on straight wagers per race. With more than $400,000 per race, Arlington Park Arlington Park is a horse race track in the Chicago suburb of Arlington Heights, Illinois. Horse racing in the Chicago region has been a popular sport since the early days of the city in the 1830s, and at one time Chicago had more horse racing tracks (six) than any other major has the highest average bet, mainly due to hosting the Breeders' Cup The Breeders' Cup World Championships is an annual series of Grade I thoroughbred horse races operated by Breeders' Cup Limited, a company formed in 1982 by a consortium of North American racing organizations, led by the National Thoroughbred Racing Association. World Thoroughbred Championships. Prairie prairie Level or rolling grassland, especially that found in central North America. Decreasing amounts of rainfall, from 40 in. (100 cm) at the forested eastern edge to less than 12 in. Meadows, one of the small tracks in the study, had just over $1000 bet per race during their harness meet. Average purse PURSE. In Turkey the sum of five hundred dollars is called a purse. Merch. Dict. h.t. size gives an indication of how important the track is, and once again, Arlington Park ranks at the top due to the $13 million in purses at the Breeders' Cup. Favorite-Long Shot Bias The favorite-long shot bias can be detected by grouping horses by favorite position and comparing the subjective probability with the objective probability Objective probability The true unobservable underlying odds that something is so. . The subjective probabilities are what the bettors in aggregate feel the horses' chances are, as revealed by the odds. Objective probabilities, on the other hand, are defined as the actual percentage of winners in the group. A significant difference between subjective and objective probability for a group indicates mispricing and market inefficiency. The total amount bet to win on all horses in a race can be expressed as W, with w denoting the amount bet to win on an individual horse, so that [[summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) ].sup.n.sub.i=1] [w.sub.i] = W, where i indexes the n individual horses in a race. The odds on a horse to win are equal to [(1 - t)W/[w.sub.i]] - 1, where t is the track take. The odds are updated every minute and payouts are based on the odds when the pools close (when the horses start running and thus the tellers stop taking bets). A horse's subjective probability of winning is [psi PSI - Portable Scheme Interpreter ] = [w.sub.i]/W = (1 - t)/([Odds.sub.i] + 1). The return on a $1 win bet is [(1 - t)W - [w.sub.i]]/ [w.sub.i] = [Odds.sub.i] if horse i wins and-1 otherwise. The objective probability, [zeta], is the percentage of winners in each observed group. To determine whether there is a significant difference between the objective and subjective probabilities for a given group, the number of wins can be viewed as a binomial binomial (bī'nō`mēəl), polynomial expression (see polynomial) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth power of a binomial (x+ statistic statistic, n a value or number that describes a series of quantitative observations or measures; a value calculated from a sample. statistic a numerical value calculated from a number of observations in order to summarize them. . For a sample of n horses, a z-statistic can be computed as z = ([psi] - [zeta])[square root n/[zeta](1 - [zeta])] (see Busche and Walls 2001). Z-statistics that are significantly different from zero provide evidence of inefficiency. A positive (negative) z-score indicates that a group is overbet (underbet) relative to its true probability. For this analysis, subjective probabilities for place and show wagers are calculated using the Harville formulas: Probability that i is first and j is second - [q.sub.i][q.sub.j]/ (1 - [q.sub.i]) Probability that i is first, j is second, and k is third = [q.sub.i] [q.sub.j][q.sub.k] (1 - [q.sub.i])(1 - [q.sub.i] - [q.sub.j]), where q represents the probability that the horse wins the race. Summing all the probabilities involving a horse either finishing first or second will yield its probability of placing, and summing the probabilities for finishing first, second, or third will yield the probability of showing. However, using subjective win probabilities for q fails to take into account what Hausch, Ziemba, and Rubinstein (1981) dubbed dub 1 tr.v. dubbed, dub·bing, dubs 1. To tap lightly on the shoulder by way of conferring knighthood. 2. To honor with a new title or description. 3. the Silky Sullivan Silky Sullivan (February 28, 1955 – November 18, 1977) was an American thoroughbred race horse, considered by many to be the come-from-behind runner of come-from-behind runners, the closer of closers. problem after the great western closer. Silky Sullivan (2) and horses of his ilk were all or nothing; they either won or finished out of the money. Therefore, Harville formulas overestimate o·ver·es·ti·mate tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates 1. To estimate too highly. 2. To esteem too greatly. these horses' probabilities of placing and showing. There are other horses (handicap horse Perfect Drift Perfect Drift, (foaled April 29, 1999 in Kentucky) is an American thoroughbred gelding racehorse. He is sired by the leading stud,Dynaformer, out of the Naskra mare, Nice Gal. This makes Perfect Drift a half-brother to 2006 Kentucky Derby winner, Barbaro. comes to mind) that finish second and third on many occasions but rarely visit the winner's circle win·ner's circle n. pl. winners' circles An enclosed area at a racetrack where the winning horse and jockey are brought for awards and publicity. Noun 1. . In those instances, the probability that the horse placed or showed would be underestimated. Therefore, we use an adjusted version of the Harville formulas in this study. For place wagers, [q.sub.i] is estimated by [p.sub.i]/P, where [p.sub.i] is the amount bet on horse i to place and P is the total amount wagered in the place pool. For show wagers, [q.sub.i] is estimated by [s.sub.i]/S, where [s.sub.i] is the amount bet on horse i to show and S is the total amount wagered in the show pool. These adjustments allow the place and show subjective probabilities to reflect the bettors' intentions by including the amount bet in the place and show pools, as opposed to constructing them from subjective win probabilities estimated from the win pool. Because we would like to look at inefficiencies across betting pools, it is preferable to isolate isolate /iso·late/ (i´sah-lat) 1. to separate from others. 2. a group of individuals prevented by geographic, genetic, ecologic, social, or artificial barriers from interbreeding with others of their kind. all calculations involving a horse's probability of finishing in the top two to the place pool (and likewise all calculations involving a horse's probability of finishing in the top three to the show pool). The return on a place bet depends on whether horse i finishes in the top two and which other horse finishes in the top two with it. The return on a $1 place bet if horse i finishes in the top two with horse j is [(1 - t)P - [p.sub.i] - [p.sub.j]]/2[p.sub.i]. Similarly for show wagering, the return on a $1 show bet if horse i finishes in the top three with horses j and k is [(1 - t)S - [s.sub.i] - [s.sub.j] - [s.sub.k]]/3[s.sub.i]. Thus, while the odds that a horse will win the race are publicly available, the public does not know the probable payoff of place and show wagers. The public is able to view how much is bet on each horse in place and show pools but not probable payoffs because the probable payoffs are determined in part by who the other top two or three finishers are. The more money bet on horse j to place reduces the place payoff on horse i if horses i and j are the top two finishers. Likewise, the more money bet on horses j and k to show reduces the show payoff on horse i if horses i, j, and k are the top three finishers. Establishing the existence and the direction of a favorite-long shot bias involve comparisons of the subjective and objective probabilities between groups of horses. One method of grouping involves ranking the horses in each race from most favored (lowest odds) to least favored (highest odds). The horses are divided into nine groups by their favorite position in the race from 1 (most favored, lowest odds) to 9-14 (least favored, odds rankings of ninth and above). The 9th through 14th favorites were combined because of the (relatively) small number of observations. The results axe summarized in Table 2. Note that fewer horses could be bet on in the place and show pools because some races with small fields do not allow show betting and, in rare instances, do not allow place betting. Differences in the size of the groups is due to variation in the number of horses in each race and because horses with the same odds were given the same odds ranking. The column labeled Raw in Table 2 is the raw return from betting all horses in the odds grouping not accounting for any takeout Takeout A financing to refinance or take out another loan. ; in other words Adv. 1. in other words - otherwise stated; "in other words, we are broke" put differently , if the track returned 100% of all pools. The Take and Breakage return column is the actual payout pay·out n. 1. The act or an instance of paying out. 2. A percentage of corporate earnings that is paid as dividends to shareholders. to the bettor accounting for the track take (typically 14-20%) and any breakage (rounding payouts down to the nearest nickel nickel, metallic chemical element; symbol Ni; at. no. 28; at. wt. 58.69; m.p. about 1,453°C;; b.p. about 2,732°C;; sp. gr. 8.902 at 25°C;; valence 0, +1, +2, +3, or +4. or dime). In win, place, and show bets, the standard favorite-long shot bias was evident. The difference in returns between the lowest and highest odds horse was much greater in the place (-8 to -38%) and show pool (-7.5 to -42.5%) than in the win pool (-16.5 to -24%). The differences between objective probability and subjective probability were significant in three positions for win wagers, six positions for place wagers, and seven positions for show wagers. To jointly test the difference in actual and expected returns across all odds groupings, we use a chi-square test chi-square test: see statistics. equal to the sum of the squared z-scores from each odds grouping. The statistic is 31.70 for win bets, 87.61 for place bets, and 185.52 for show bets, each greater than the 1% critical value of 21.67. Thus, it can be concluded that the place and show pools exhibit a more pronounced favorite-long shot bias than the win pool. Even so, strictly betting favorites to place or show will result in a negative return. If the Harville formulas are correct and win, place, and show wagers are equally efficient, then the percentage bet on a particular horse should be the same across win, place, and show wagers. As shown in Table 3, this is clearly not the case. Of all the money bet on race favorites, 68.1% is to win, 21.5% is to place, and 10.4% is to show. Moving lower in the odds ranking, there is less bet to win as a percentage (down to 56.2%) and more bet to place (up to 25.8%) and show (up to 18.0%). When people bet long shots, they tend to back them in the place and show pools while favorites are backed more heavily in the win pool. This is further demonstrated by the percentage of the win, place, and show pools bet on each horse. Of all win bets, 34.7% are on the race favorites, while only 30.7% of the place bets and 29.6% of the show bets on race favorites. The least favorite horses receive only 1.9% of all money bet in the win pool, but 2.3% of the place pool and 3.1% of the show pool. These results are strong evidence of inefficiencies across the three wagering pools. There have been a number of betting-market studies conducted over the years, and it is insightful to compare efficiency under different conditions. To compare betting-market efficiency between different datasets, a simple regression Noun 1. simple regression - the relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x) regression toward the mean, statistical regression, regression of the subjective probability for each favorite grouping can be regressed on the objective probability as follows: (3) [Subjective.sub.i] = [[beta].sub.0] + [[beta].sub.1] [Objective.sub.i] + [u.sub.i], where i indexes favorite position groups. If [[beta].sub.0] = 0 and [[beta].sub.1] = 1, then the market is efficient. A standard favorite-long shot bias exists when [[beta].sub.1] < 1 and a reverse favorite-long shot bias when [[beta].sub.1] > 1. Regression regression, in psychology: see defense mechanism. regression In statistics, a process for determining a line or curve that best represents the general trend of a data set. results for win wagers for this data as well as five previous studies are shown in Table 4. Chronologically chron·o·log·i·cal also chron·o·log·ic adj. 1. Arranged in order of time of occurrence. 2. Relating to or in accordance with chronology. , Ali (1977) looked at harness races in New York; Asch, Malkiel, and Quandt (1982) at horse races Flat races Argentina
Area, 24,181 sq mi (62,629 sq km). Pop. . Each dataset involved pari-mutuel wagering and grouped participants by favorite position. The t-statistics given are for tests against a null A character that is all 0 bits. Also written as "NUL," it is the first character in the ASCII and EBCDIC data codes. In hex, it displays and prints as 00; in decimal, it may appear as a single zero in a chart of codes, but displays and prints as a blank space. where [[beta].sub.0] = 0 and [[beta].sub.1] = 1, respectively. Only the two studies focusing on foreign racing (Busche and Hall 1988; Gandar, Zuber, and Johnson 2001) had slope coefficients that were not significantly different from one. Both Hong Kong and New Zealand racing have characteristics that differentiate them from American racing American Racing Equipment Inc. is a high performance after-market wheel manufacture started during the American muscle car era. History American Racing was founded by Romeo Palamides, a drag racer, J.O. . In Hong Kong, the amount wagered per race is much bigger than in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. . Busche and Hall point out that per-race handle in Hong Kong, when their study was undertaken, was $5.6 million as compared with only $87,000 for the United States (Busche and Hall 1988). New Zealand racing is overseen by the Totalisator totalizator, totalisator a computer-driven, machine-operated betting system which eliminates the bookmaker in the betting industry which surrounds horse and dog racing. Called also parimutuel. Agency Board, which, in the duration of Gandar, Zuber, and Johnson's study, had a large national off-track presence including telephone accounts and wagering hubs in retail stores and pubs. Ninety percent of the betting volume on New Zealand racing was done off track (Gandar, Zuber, and Johnson 2001). The American studies either predate simulcasting (Ali 1977; Asch, Malkiel, and Quandt 1982) or have a small percentage of betting volume generated off track (Sobel and Raines 2003). Each of these studies reveals inefficient betting markets, with Sobel and Raines' greyhound greyhound, breed of tall, swift, sight hound developed nearly 5,000 years ago in Egypt. It stands about 26 in. (66 cm) high at the shoulder and weighs about 65 lb (29.5 kg). races having a reverse favorite-long shot bias. Our data exhibit the standard favorite-long shot bias despite the increased bettor participation through simulcasting. Looking at the magnitude of the slope coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int) 1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities. 2. , domestic betting markets have become only slightly more efficient over time, despite increased bettor participation through simulcasting. Arbitrage Given that inefficiencies exist between win, place, and show pools, can a profitable wagering rule be established? This was a question that was addressed by Ziemba and Hausch in their 1984 book, Beat the Racetrack (also see Hausch, Ziemba, and Rubinstein 1981; Ziemba and Hausch 1984; and Hausch and Ziemba 1985). Dr. Z's system, as it came to be known, involved calculating the expected return to place and show based on the amounts wagered on a horse in the three betting pools. (4) E(RE[T.sub.PLACE]) [approximately equal to] 0.319 + 0.559 [w.sub.i]/ W/[p.sub.i]/P + (2.22 - 1.29 [w.sub.i]/W) (1 - t - 0.829) (5) E(RE[T.sub.SHOW]) [approximately equal to] 0.543 + 0.369 [w.sub.i]/ W/[s.sub.i]/P + (3.60 - 2.13 [w.sub.i]/W) (1 - t - 0.829) Formulas 4 and 5, Ziemba and Hausch's empirical estimates of the expected return for place and show wagers, are used to initially screen for horses that might be underbet in the place and show pools. If the expected return to place (show) on a horse is 1.15, then a place (show) bet will earn a predicted 15% return. Dr. Z's betting strategy involves betting horses to place or show if their expected return is above a minimum criterion and if these horses are not long shots. Ignoring any horse going to the post at greater than 8:1 odds and using 1.15 as the minimum expected return, the methodology yields a 14.87% profit using our data. Wagering opportunities were sparse sparse - A sparse matrix (or vector, or array) is one in which most of the elements are zero. If storage space is more important than access speed, it may be preferable to store a sparse matrix as a list of (index, value) pairs or use some kind of hash scheme or associative memory. , with only 3.03% of all betting interests exhibiting an expected return above the set threshold but below the odds cut off. Even so, this would imply a few bets a day at any given racetrack, just as indicated in Beat the Racetrack. While the profitability of the system may seem enticing, it is important to remember that we are looking at returns on bets using final pool totals. The pool totals and odds are updated every minute and continue to be updated even after the horses leave the starting gates starting gate n. Sports 1. A series of stalls with interconnected doors that open simultaneously at the beginning of a race. 2. and the betting windows have closed. No one has the benefit of applying a system to the final pool totals, so we tested the profitability of the Dr. Z system in real time. Despite the positive return of these mythical myth·i·cal also myth·ic adj. 1. Of or existing in myth: the mythical unicorn. 2. Imaginary; fictitious. 3. bets, the greatest difficulty with the Dr. Z system is in its implementation. Bettors have to watch the tote board tote board n. A large, usually electrically operated board that displays changing numerical information, such as betting payoffs or voting results. and make calculations while trying not to get shut out at the betting window. With the evolution of online wagering, monitoring pool totals and making calculations using Dr. Z's formulas are much easier. For the purposes of evaluation, Dr. Z system bets were made on 203 races at 34 tracks in February through April of 2003. A $2 wager was made on horses with an expected return on a place (show) wager at or above 1.15 and with win odds less than or equal to 8:1. (3) Furthermore, any races likely to create a minus pool, where so much money is bet on one horse that tracks pay the minimum 5% and lose money on the race, were not considered (see Chapter 15 of Ziemba and Hausch 1984). Betting was postponed until the last possible moment but could be done quickly through the author's online wagering account. Expected returns from Equations 4 and 5 could be found quickly with a computer. Bets were made at the last possible moment (save a few instances when the author was shut out) to get the closest approximation of the final odds and expected returns. Unfortunately, on average, only 57% of the final pool totals are viewable on the tote board when betting on a race ends. Much of the betting occurs in the last few minutes and posted pool totals change when betting is closed. Overall, 319 $2 bets were made on 203 races. There were 113 place wagers and 206 show wagers, and the net result was a $91.80 loss (-12.8%). While these bets looked attractive when made, the late money often lowered their expected return below 1.00. A $45.70 profit (7.2%) would have been made had we received the payouts based on pool totals when the wager was made. Only 90 of the original 319 wagers meet the criterion both at the time of wager and in the final total. These bets returned $9.30, or 5.2%. Using final pool totals, 134 wagers (43 place and 91 show) met the criteria and returned $31.40, or 11.8%. The data from the arbitrage experiment exhibited the same favorite-long shot bias found in previous studies when final pool totals are examined. Thus, it is likely that the negative returns were not an aberration. We find that late money eliminates the opportunity to arbitrage betting pools. Table 5 shows the results of analyses that lead to this conclusion. Two subjective probabilities were calculated, one with final pool totals and another using the pool totals when wagers were made or the post time (PT) pool totals. In each case, late money flows to the favorites in all pools. The subjective probability increases for the top two favorite positions in all pools, including a five percentage point increase for place and show wagers. The subjective probability falls for positions four and higher in the win and place pools and five and higher in the show pool. These changes in probabilities demonstrate that late money shifts the odds toward the true win probabilities. The increased efficiency reduces the number of optimal bets from 319 to 134. Figure 1 contains graphs of the estimated return line for each betting pool by favorite position. The three lines designate des·ig·nate tr.v. des·ig·nat·ed, des·ig·nat·ing, des·ig·nates 1. To indicate or specify; point out. 2. To give a name or title to; characterize. 3. estimated returns using the TVG data (solid line) and data from the betting experiment, both post time (dotted line) and final (dashed dash 1 v. dashed, dash·ing, dash·es v.tr. 1. To break or smash by striking violently. 2. To hurl, knock, or thrust with sudden violence. 3. and dotted line) pool totals. All estimated return lines are downward sloping, with the TVG data being the most flat. In each pool, the estimated return flattens from post time to final pool totals, indicating that the market becomes more efficient. [FIGURE 1 OMITTED] 3. Conclusion This article finds that, despite increased accessibility and participation due to the proliferation of simulcast wagering, betting markets continue to inefficiently in·ef·fi·cient adj. 1. Not efficient, as: a. Lacking the ability or skill to perform effectively; incompetent: an inefficient worker. b. price outcomes, a result that holds across wagering pools. The win pool exhibits a favorite-long shot bias where favorites are underbet relative to long shots. The size of the bias is smaller than previous studies of American racing but much greater than foreign countries where simulcast wagering is prevalent. Expanding the analysis to the place and show pools, we find an even more pronounced bias continues to exist. Data used in the study were comprised of a large number of races over numerous racetracks and included nearly all races simulcast in the fall of 2002. The variation in return was much larger for place and show wagers. Based on final betting pool totals, a small positive profit could be earned betting extreme favorites (odds on) to place and show. However, betting extreme long shots (40:1 or greater) would result in a 34% loss on win wagers, 46% loss on place wagers, and 50% loss on show wagers. Despite strong evidence of inefficiencies between wagering pools, methods used to arbitrage betting markets resulted in a net loss. Using a modification of the Dr. Z system described in Beat the Racetrack resulted in a net loss of 13% from bets on 319 horses in 203 races in the winter of 2003. This was despite the fact that it was generally possible through online wagering to make bets in the last seconds before the races began. A positive expected return at post time disappeared as late money reduced or eliminated the inefficiencies that had appeared exploitable. References Ali, Mukhtar Mukhtar, meaning "chosen" in Arabic, refers to the head of a village or mahalle (urban district) in many Arab countries. The name refers to the fact that mukhtars are usually selected by some consensual or participatory method, often involving an election. M. 1977. Probability and utility estimates for racetrack bettors. Journal of Political Economy 85:803-15. Asch, Peter, Burton G. Malkiel, and Richard E. Quandt Richard E. Quandt is a Guggenheim Fellowship winning economist who analyzed the results of the Judgment of Paris wine tasting event with Orley Ashenfelter. [1] Quandt serves as a professor of economics at Princeton University.[2]. . 1982. Racetrack betting and informed behavior. Journal of Financial Economics 10:187-94. Asch, Peter, Burton G. Malkiel, and Richard E. Quandt. 1984. Market efficiency in racetrack betting. Journal of Business 57:165-75. Asch, Peter, Burton G. Malkiel, and Richard E. Quandt. 1986. Market efficiency in racetrack betting: Further evidence and a correction. Journal of Business 59:157-60. Asch, Peter, and Richard E. Quandt. 1986. Racetrack betting: The professors' guide to strategies. Dover: Auburn Auburn (ô`bərn). 1 City (1990 pop. 33,830), Lee co., E Ala.; inc. 1839. The city's economy centers around Auburn Univ.; there is some manufacturing. 2 City (1990 pop. 24,309), seat of Androscoggin co. House. Busche, Kelly, and Christopher D. Hall. 1988. An exception to the risk preference anomaly Abnormality or deviation. Pronounced "uh-nom-uh-lee," it is a favorite word among computer people when complex systems produce output that is inexplicable. See software conflict and anomaly detection. . Journal of Business 61:337-46. Busche, Kelly, and W. David Walls David Walls (born November 22, 1986 in Leeds, England) is a professional footballer who has played for Huddersfield Town and Farsley Celtic. . 2000. Decision cost and betting market efficiency. Rationality and Society 12:477-92. Busche, Kelly, and W. David Walls. 2001. Breakage and betting market efficiency: Evidence from the horse track. Applied Economics Letters Economics Letters is a scholarly peer-reviewed journal of economics that publishes concise communications (letters) that provide a means of rapid and efficient dissemination of new results, models and methods in all fields of economic research. Published by Elsevier. 8:601-4. Davidowitz, Steve. 2003. The American racing manual 2003. New York: DRF DRF Daily Racing Form (horse racing) DRF Dansk Ride Forbund (Danish) DRF Deafness Research Foundation DRF Disaster Relief Fund DRF Data Recovery Field DRF Demat Request Form DRF Dose Reduction Factor Press. Gandar, John M., Richard A. Zuber, and R. Stafford Johnson. 2001. Searching for the favourite-longshot bias  This article or section may be confusing or unclear for some readers.Please [improve the article] or discuss this issue on the talk page. down under: An examination of the New Zealand pari-mutuel betting market. Applied Economics 33:1621-9. Golec, Joseph, and Maurry Tamarkin. 1998. Bettors love skewness Skewness A statistical term used to describe a situation's asymmetry in relation to a normal distribution. Notes: A positive skew describes a distribution favoring the right tail, whereas a negative skew describes a distribution favoring the left tail. , not risk, at the horse track. Journal of Political Economy 106:205-25. Goodwin, Barry K. 1996. Semiparametric (distribution-free) testing of the expectations hypothesis expectations hypothesis The explanation that the slope of the yield curve is attributable to expectations of changes in short-term interest rates. The yield curve relates bond yields and maturity lengths. in a parimutuel gambling market. Journal of Business and Economic Statistics 14:487-96. Harville, David A. 1973. Assigning as·sign tr.v. as·signed, as·sign·ing, as·signs 1. To set apart for a particular purpose; designate: assigned a day for the inspection. 2. probabilities to the outcomes of multi-entry competitions. Journal of the American Statistical Association Established in 1888 and published quarterly in March, June, September, and December, the Journal of the American Statistical Association (JASA) has long been considered the premier journal of statistical science. 69:446-52. Hausch, Donald B., and William T. Ziemba. 1985. Transactions costs Transactions costs The time, effort, and money necessary, including such things as commission fees and the cost of physically moving the asset from seller to buyer. Transcations costs should also include the bid/ask spread as well as price impact costs (for example a large sell , extent of inefficiencies, entries and multiple wagers in a racetrack betting model. Management Science 31:381-94. Hausch, Donald B., William T. Ziemba, and Mark Rubinstein Mark Edward Rubinstein is the Paul Stephens Professor of Applied Investment Analysis at the Haas School of Business of the University of California, Berkeley. He is a leading finance academic, focusing on derivatives, particularly options, and is probably best known for his . 1981. Efficiency of the market for racetrack betting. Management Science 27:1435-52. Hurley, William, and Lawrence McDonough. 1995. A note on the Hayek hypothesis and the favorite-longshot bias in parimutuel betting parimutuel betting (păr'ĭmy  `tyĕl), system of cooperative wagering invented (c.1870) in France by Pierre Oller. .
American Economic Review 85:949-55.
Hurley, William, and Lawrence McDonough. 1996. The favourite-longshot bias in parimutuel betting: A clarification of the explanation that bettors like to bet longshots. Economics Letters 52:275-8. Sauer, Raymond D. 1998. The economics of wagering markets. Journal of Economic Literature 36:2021-64. Sobel, Russell S Russell, English noble family. It first appeared prominently in the reign of Henry VIII when John Russell, 1st earl of Bedford, 1486?–1555, rose to military and diplomatic importance. ., and S. Travis Raines. 2003. An examination of the empirical derivatives derivatives In finance, contracts whose value is derived from another asset, which can include stocks, bonds, currencies, interest rates, commodities, and related indexes. Purchasers of derivatives are essentially wagering on the future performance of that asset. of the favourite-longshot bias in racetrack betting. Applied Economics 35:371-85. Swindler, Steve, and Ron Shaw. 1995. Racetrack wagering and the uninformed bettor: A study of market efficiency. Quarterly Review of Economics and Finance 35:305-14. Terrell, Dek, and Amy Farmer. 1996. Optimal betting and efficiency in parimutuel betting markets with information costs Information costs Transactions costs that include the assessment of the investment merits of a financial asset. Related: Search costs. . Economic Journal 106:846-68. Thaler, Richard H., and William T. Ziemba. 1988. Anomalies: Parimutuel betting markets: racetracks and lotteries United Kingdom
Vaughan Williams, Leighton. 1999. Information efficiency in belting markets: A survey. Bulletin of Economic Research 51:307-37. Vaughan Williams, Leighton, and David Paton David Paton (born 29 October 1949, Edinburgh, Scotland) is a bass and guitar player, most notably with three different bands: Pilot, Alan Parsons Project, and Camel. He has also worked as a solo artist, session musician, and sometime vocalist. . 1998a. Why are some favorite-longshot biases positive and some negative? Applied Economics 30:1505-10. Vaughan Williams, Leighton, and David Paton. 1998b. Do betting costs explain betting biases? Applied Economics Letters 5:333-5. Ziemba, William T., and Donald B. Hausch. 1984. Beat the racetrack. San Diego San Diego (săn dēā`gō), city (1990 pop. 1,110,549), seat of San Diego co., S Calif., on San Diego Bay; inc. 1850. San Diego includes the unincorporated communities of La Jolla and Spring Valley. Coronado is across the bay. : Harcourt, Brace, and Jovanovich. (1) Generally, each horse in a race is a separate betting interest. However, in some cases when horses have the same owners or trainer, they are grouped together as one betting interest and are effectively treated as one horse in wagering. References to horses in this article are actually to betting interests and coupled entries are treated as one horse. (2) Silky Sullivan ran in the late 1950s, mainly in California. He generally raced from well off the pace and often closed with a flourish to win. He finished with 12 wins in 27 starts, but ran off the board (outside the top three) in 9 of the remaining 15 starts. (3) Dr. Z's system advocated using the Kelly criterion In probability theory, the Kelly criterion, or Kelly formula, is a formula used to maximize the long-term growth rate of repeated plays of a given gamble that has positive expected value. It was described by J. L. (maximizing expected log wealth) to determine bet size. This replication In database management, the ability to keep distributed databases synchronized by routinely copying the entire database or subsets of the database to other servers in the network. There are various replication methods. did not do so. Marshall Gramm * and Douglas H. Owens ([dagger]) * Department of Economics and Business, Rhodes College Rhodes College is a four-year, private liberal arts college located in Memphis, Tennessee. Founded in 1848, Rhodes enrolls approximately 1,700 students. About one third of Rhodes students go on to graduate and professional school soon after graduation,[1]. , 2000 North Parkway, Memphis, TN 38113, USA; E-mail gramm@rhodes.edu; corresponding author. ([dagger]) Welch Welch , William Henry 1850-1934. American pathologist and bacteriologist who discovered the bacteria that causes gas gangrene. Consulting, 8757 Georgia Avenue Georgia Avenue is a major north-south artery in Northwest Washington, D.C. and Montgomery County, Maryland. Within the District of Columbia, Georgia Avenue is also U.S. Route 29. Both Howard University and Walter Reed Army Medical Center are on Georgia Avenue. , Suite 520, Silver Spring, MD 20910, USA; E-mail dowens@welchcon.com. The authors would like to thank Ramon P. DeGennaro, Robert B. Ekelund, Christopher P. Kilby, and Wayne Strayer stray intr.v. strayed, stray·ing, strays 1. a. To move away from a group, deviate from the correct course, or go beyond established limits. b. To become lost. 2. for comments on the article as well as participants at the Third International Equine equine Any member of the ungulate family Equidae, which includes the modern horses, zebras, and asses, all in the genus Equus, as well as more than 60 species known only from fossils. Equines descended from the dawn horse (see Eohippus). Industry Program Academic Conference. The article also benefited from suggestions by an anonymous referee A judicial officer who presides over civil hearings but usually does not have the authority or power to render judgment. Referees are usually appointed by a judge in the district in which the judge presides. and Dek Terrell. Amanda Godbold helped with data entry. This research was funded in part by a grant from the Rhodes Faculty Development Endowment A transfer, generally as a gift, of money or property to an institution for a particular purpose. The bestowal of money as a permanent fund, the income of which is to be used for the benefit of a charity, college, or other institution. . Received January 2004; accepted March 2005.
Table 1. Racetracks (October 2002 to December 2002)
Track State Type Take (%)
Aqueduct New York Thoroughbred 14.0
Arlington Illinois Thoroughbred 17.0
Balmoral Illinois Harness 17.0
Belmont New York Thoroughbred 14.0
Beulah Ohio Thoroughbred 18.0
Calder Florida Thoroughbred 18.0
Churchill Downs Kentucky Thoroughbred 16.0
Colonial Downs Virginia Harness 18.0
Delta Downs Louisiana Thoroughbred 17.0
Dover Downs Delaware Harness 18.0
Fair Grounds Louisiana Thoroughbred 17.0
Fairmount Park Illinois Thoroughbred 17.0
Fresno Fair California Mixed 16.8
Great Lakes Downs Michigan Thoroughbred 17.0
Harrington Raceway Delaware Harness 18.0
Hollywood Park California Thoroughbred 15.4
Hoosier Indiana Thoroughbred 18.0
Keeneland Kentucky Thoroughbred 16.0
Laurel Park Maryland Thoroughbred 18.0
Lone Star Park Texas Mixed 18.0
Los Alamitos California Mixed 15.6
Louisiana Downs Louisiana Thoroughbred 17.0
Maywood Illinois Harness 17.0
Monticello Raceway New York Harness 18.0
Moutaineer West Virginia Thoroughbred 17.3
Northfield Ohio Harness 18.0
Oak Tree California Thoroughbred 15.43
Pompano Florida Harness 20.5
Prairie Meadows Iowa Harness 18.0
Retama Texas Thoroughbred 18.0
Sam Houston Texas Thoroughbred 18.0
Saratoga Harness New York Harness 18.0
Suffolk Downs Massachusetts Thoroughbred 19.0
Sunland Park New Mexico Thoroughbred 19.0
Turf Paradise Arizona Thoroughbred 20.0
Turfway Park Kentucky Thoroughbred 17.5
Track Horses Races Pool Size ($) Purse ($)
Aqueduct 3447 403 321,428 45,022
Arlington 1103 137 404,221 122,000
Balmoral 4587 493 37,255 7762
Belmont 660 84 356,853 51,542
Beulah 6322 665 25,033 6800
Calder 5233 641 120,388 23,845
Churchill Downs 2280 244 232,216 39,598
Colonial Downs 1452 190 3451 6752
Delta Downs 2312 258 26,927 17,428
Dover Downs 4391 545 13,177 14,676
Fair Grounds 1401 160 151,360 27,322
Fairmount Park 458 60 10,604 6667
Fresno Fair 373 49 43,207 8088
Great Lakes Downs 832 106 13,977 9703
Harrington Raceway 1797 225 10,207 11,811
Hollywood Park 2175 296 289,380 42,233
Hoosier 3786 409 38,787 14,902
Keeneland 622 70 250,352 44,800
Laurel Park 4069 511 72,429 21,296
Lone Star Park 2751 304 21,657 15,771
Los Alamitos 3193 433 26,589 16,057
Louisiana Downs 1722 206 62,207 11,388
Maywood 3067 389 32,565 8851
Monticello Raceway 4011 542 9627 2092
Moutaineer 3788 405 41,689 18,076
Northfield 5388 633 22,891 4368
Oak Tree 1419 168 308,508 42,970
Pompano 3688 457 9860 5348
Prairie Meadows 1284 166 1313 2692
Retama 1085 123 36,327 11,521
Sam Houston 2896 319 60,005 18,002
Saratoga Harness 2079 270 5532 2244
Suffolk Downs 3361 373 40,356 14,314
Sunland Park 2519 264 12,747 21,052
Turf Paradise 4588 547 37,604 7521
Turfway Park 2136 216 76,850 14,240
Balmoral, Fairmount Park, and Maywood all charge a 1% surtax on winning
tickets.
Table 2. Data Grouped by Favorite Position
Favorite Objective Subjective
Position Runners Winners Probability (%) Probability (%)
Win pool
1 11,365 4126 36.30 34.75
2 11,371 2425 21.33 20.78
3 11,367 1622 14.27 14.63
4 11,362 1137 10.01 10.39
5 11,340 787 6.94 7.39
6 11,063 533 4.82 5.22
7 10,086 331 3.28 3.73
8 8226 209 2.54 2.72
9-14 10,095 191 1.89 1.89
Place pool
1 11,349 6532 57.56 54.56
2 11,357 4746 41.79 40.27
3 11,353 3500 30.83 31.45
4 11,348 2656 23.41 24.02
5 11,330 1998 17.63 18.05
6 11,051 1361 12.32 13.31
7 10,085 922 9.14 9.86
8 8226 547 6.65 7.34
9-14 10,095 461 4.57 5.10
Show pool
1 11,300 7954 70.39 68.93
2 11,308 6462 57.15 55.06
3 11,304 5418 47.93 45.88
4 11,299 4305 38.10 37.62
5 11,309 3541 31.31 30.52
6 11,039 2539 23.00 24.20
7 10,080 1786 17.72 19.19
8 8223 1046 12.72 15.39
9-14 10,092 907 8.99 11.07
Favorite Take and
Position z-Stat Raw (%) Breakage (%)
Win pool
1 -3.45 3.68 -16.43
2 -1.42 1.30 -17.70
3 1.10 -3.28 -21.11
4 1.36 -5.20 -22.43
5 1.88 -8.76 -25.21
6 1.99 -10.85 -26.91
7 2.50 -19.26 -33.82
8 1.01 -8.29 -24.57
9-14 -0.02 -7.80 -24.19
Place pool
1 -6.46 11.81 -8.16
2 -3.27 5.23 -15.94
3 1.44 0.38 -20.24
4 1.54 -3.37 -23.97
5 1.16 -3.69 -24.43
6 3.18 -11.40 -30.75
7 2.51 -13.61 -32.34
8 2.52 -17.05 -34.92
9-14 2.57 -21.63 -38.08
Show pool
1 -3.40 10.74 -7.52
2 -4.49 9.56 -12.63
3 -4.37 8.24 -15.73
4 -1.06 2.19 -21.79
5 -1.81 2.72 -22.49
6 2.99 -7.27 -30.22
7 3.87 -11.22 -33.47
8 7.25 -24.06 -43.14
9-14 7.33 -24.54 -42.73
Table 3. Breakdown of Wagering Pools by Favorite Position
Conditioned on Favorite
Position Conditioned on Wager Type
Favorite
Postion % Win % Place % Show % Win % Place % Show
1 68.1 21.5 10.4 34.7 30.7 29.6
2 66.6 22.9 10.4 20.8 20.1 18.7
3 65.0 23.8 11.1 14.6 15.1 14.4
4 63.6 24.5 11.9 10.4 11.3 11.2
5 62.1 25.0 12.9 7.4 8.3 8.8
6 60.6 25.3 14.1 5.2 6.1 6.8
7 58.8 25.7 15.4 3.7 4.0 5.4
8 57.2 25.8 17.0 2.7 3.3 4.3
9 56.2 25.8 18.0 1.9 2.3 3.1
Table 4. Comparisons of Studies of Betting Markets
Author Races Years
Ali 20,247 1970-1974
Asch, Malkiel, and Quandt 729 1978
Busche and Hall 2653 1981-1987
Gandar, Zuber, and Johnson 10,332 1994-1997
Sobel and Raines 2799 1996-1997
Gramm and Owens 11,365 2002
Intercept
Standard
Author Coefficient Error t-Stat
Ali 0.014 0.004 3.72
Asch, Malkiel, and Quandt 0.008 0.003 2.75
Busche and Hall -0.002 0.003 -0.66
Gandar, Zuber, and Johnson 0.002 0.001 1.34
Sobel and Raines -0.018 0.006 -3.20
Gramm and Owens 0.006 0.002 3.67
Slope
Standard
Author Coefficient Error t-Stat
Ali 0.887 0.023 -4.88
Asch, Malkiel, and Quandt 0.873 0.018 -7.16
Busche and Hall 1.018 0.024 0.75
Gandar, Zuber, and Johnson 0.991 0.012 -0.76
Sobel and Raines 1.143 0.041 3.50
Gramm and Owens 0.948 0.011 -4.94
Table 5. Betting Application Data
Favorite Objective Subjective
Position Runners Winners Probability (%) Probability (%)
Win pool
1 203 72 35.47 34.27
2 203 48 23.65 21.42
3 204 28 13.73 15.23
4 202 18 8.91 10.50
5 203 17 8.37 7.26
6 200 9 4.50 4.98
7 184 6 3.26 3.51
8 145 4 2.76 2.45
9-12 195 1 0.51 1.52
Place pool
1 203 121 59.61 54.16
2 203 86 42.36 39.82
3 204 70 34.31 33.02
4 202 32 15.84 23.68
5 203 42 20.69 18.10
6 200 23 11.50 13.27
7 184 18 9.78 9.87
8 145 10 6.90 6.77
9-12 195 5 2.56 4.50
Show pool
1 203 148 72.91 67.55
2 203 113 55.67 52.61
3 204 101 49.51 47.68
4 202 67 33.17 38.50
5 203 73 35.96 31.24
6 200 48 24.00 24.35
7 184 33 17.93 19.30
8 145 18 12.41 15.11
9-12 195 9 4.62 10.51
Favorite PT Subjective
Position z-Stat Probability (%) z-Stat
Win pool
1 -0.36 32.37 -0.92
2 -0.75 20.83 -0.94
3 0.62 15.25 0.63
4 0.79 10.84 0.96
5 -0.57 7.69 -0.35
6 0.33 5.51 0.69
7 0.19 4.03 0.59
8 -0.23 2.88 0.09
9-12 1.96 1.93 2.76
Place pool
1 -1.58 49.53 -2.93
2 -0.73 38.45 -1.13
3 -0.39 32.51 -0.54
4 3.05 24.51 3.37
5 -0.91 19.48 -0.43
6 0.78 14.51 1.34
7 0.04 11.25 0.67
8 -0.06 7.98 0.51
9-12 1.71 5.50 2.60
Show pool
1 -1.72 62.72 -3.26
2 -0.88 49.83 -1.67
3 -0.52 46.91 -0.74
4 1.61 37.51 1.31
5 -1.4 32.69 -0.97
6 0.11 26.00 0.66
7 0.48 21.81 1.37
8 0.98 17.73 1.94
9-12 3.92 12.75 5.42
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