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An Examination of the Empirical Derivatives of the Favourite-longshot Bias in Racetrack Betting
Applied Economics
Abstract
Market efficiency dictates it equally profitable to bet on any racing participant, including the favourite or longshot. However, a well-documented anomaly is that racetrack bettors tend to overbet longshots and underbet favourites. This study presents and tests two theoretical explanations for this favourite-longshot bias. The unparalleled richness of the data allows the exploration of how the bias changes with several key variables. This study finds the most popular current explanation for the bias, the risk preference model, cannot explain the data as well as an information-based model, in which the bias depends on bet complexity and the information possessed by bettors.
... Moreover, we are able to test the influence of noise trader liquidity by analyzing the effect of liquidity on market efficiency for weekend and weekday matches separately. Earlier studies (e.g., Kopelman & Minkin, 1991;Sobel & Raines, 2003) have shown that betting activity at weekend matches is characterized by a higher share of irrational noise bettors than betting activity at weekday matches. ...
... We use betting contracts on 2,227 soccer matches played in the English Premier Earlier studies (Kopelman & Minkin, 1991;Sobel & Raines, 2003;Sung & Johnson, 2007) have shown that the betting activity at weekend matches is characterized by a higher share of irrational noise bettors than betting activity at weekday matches. ...
... Kopelman and Minkin (1991) state that weekend bettors at the racetrack are more casual and choose their bets based on irrelevant factors such as the name or color of the horses, whereas weekday bettors are highly knowledgeable about their pursuits and motivated by the desire for financial gain. Moreover, Sobel and Raines (2003) find that weekend bettors wager a significantly lower amount per person and are less informed. Finally, Sung and Johnson (2007) provide evidence that prices for weekend markets exhibit lower market efficiency than weekday markets because weekend markets are populated by a larger proportion of noise bettors. ...
This paper investigates the impact of the market microstructure on market efficiency based on data from the betting industry. Similar to financial mar- kets, betting markets are characterized by the coexistence of a quote-driven market structure (bookmakers) and an order-driven market structure (betting exchanges). We show that the quote-driven market exhibits lower market effi- ciency than the order-driven market. Taking advantage of the inefficient odds available at the quote-driven market leads to above-average, and in some cases even positive bettor returns.
... There are also additional, more detailed, explanations for the favorite-longshot bias. Many of these can be reduced to our two broad explanations, at least in terms of the implications for equilibrium odds. 1 For example, Ottaviani and Sorensen (2010) and Sobel and Raines (2003) have attributed the favorite-longshot bias to heterogeneity of information. From our point of view, these explanations boil down to observed misperception of probabilities. ...
... The logarithmic weighting functions display an S-shape: the curve is convex for small probabilities and turns concave for large probabilities. The existence of an inflection point is contrary to the implications of the information model advocated by Sobel and Raines (2003) in the context of greyhound racing markets. Their model implies a linear relation π ( p) α + βp between the perceived probability and the objective probability, which would imply either a globally concave or globally convex logarithmic weighting function. ...
... In particular, the linear relation between probabilities implies that d 2 ln π/d ln p 2 αβp/(α + βp) 2 , the sign of which is determined by the product αβ. 5 Our data also display the opposite pattern found in Sobel and Raines (2003) in terms of how bet complexity affects the magnitude of the favorite-longshot bias. We find that the favorite-longshot bias becomes less severe as the bet complexity increases, that is the quinella market odds tend to display less bias than the win market odds. ...
We use a unique data set from Finnish and Swedish horse race betting markets to explain the favorite-longshot bias. The data set includes a complete set of odds for exotic markets. We use the exotic market odds in conjunction with the win market odds and find convincing support for the misperceptions explanation of the favorite-longshot bias rather than the risk-love explanation. Furthermore, our data provide evidence of a specific type of failure to reduce compound lotteries. Namely, it seems that bettors do not assess the exotic market events as simple lotteries but instead consider the race for the first place and the race for the second place in a sequential form.
... Swidler and Shaw (1995) find this opposite bias for a smaller Class II racetrack in Texas, and Busche and Hall (1988) find this opposite bias at a racetrack in Hong Kong that had much higher betting volumes than the US racetracks used in other studies. More recently, Sobel and Raines (2003) have identified a situation in which the bias changes from the regular favorite-longshot bias to an opposite bias, under certain predictable conditions. Gramm and Owens (2005) find that the favoritelongshot bias diminishes for races with larger betting pools and more entrants. ...
... One common aspect in these explanations is the utilization of a representative bettor model in which all bettors are assumed to be acting in one particular manner. However, Sobel and Raines (2003) unambiguously show that this is not the case. The authors analyze nearly 2,800 races at two dog tracks in West Virginia. ...
... In addition, races in which there were ties in the finish were also excluded to avoid problems in computing objective probabilities. Sobel and Raines (2003). The favorite/longshot betting ratio is the average percent of win bets on the favorite divided by the average percent of win bets on the longshot. ...
... Cain et al. (2003) provide additional empirical support consistent with the thesis. Working against the primacy of this interpretation, recent research has looked to explain the observed longshot bias in pari-mutuel gambling as the result of bettor misperception (Sobel and Raines, 2003;Snowberg and Wolfers, 2010) or sequential information release (Ottaviani and Sorenson, 2009). results linking bookie takeout rates with race characteristics are generally as expected, in that these takeouts are higher for races with more ex ante even fields, for races with larger fields, and for late-day races. ...
... Levels and elasticities are interesting side-tests, but our primary concern is the predicted impact of allowing a U.S. pari-mutuel racetrack the flexibility to vary its takeout across races. 22 We address this by considering the converse question of what would happen if our bookmaker cartel were restricted to charge the fixed profit-maximizing takeout 22 These percentage impacts are therefore generally robust to any proportional overstatements that the prior figures may display. ...
... Levels and elasticities are interesting side-tests, but our primary concern is the predicted impact of allowing a U.S. pari-mutuel racetrack the flexibility to vary its takeout across races. 22 We address this by considering the converse question of what would happen if our bookmaker cartel were restricted to charge the fixed profit-maximizing takeout 22 These percentage impacts are therefore generally robust to any proportional overstatements that the prior figures may display. ...
We consider a policy reform relaxing price controls in American pari-mutuel wagering on horse racing by examining bookie behavior in Australia's fixed-odds gambling sector. Descriptive regressions indicate that bookmaker takeouts (the effective prices of races) vary substantially and systematically with race characteristics, though in sometimes counterintuitive ways. Estimates of an explicitly reduced form model of bookie takeout, however, qualitatively match both intuition and prior findings in the literature. Counterfactuals using these estimates suggest that regulatory reform that permits racecourses to alter takeout across races would increase variable profit by 3-6%.
... Evidence supports this belief. Sobel and Raines (2003) analysed decisions made by bettors and bookmakers at two greyhound racetracks and found that more casual bettors wagered on weekend races compared to events during the week. Franck, Verbeek, and Nüesch (2011) provided additional evidence in the professional team sport context by distinguishing between betting market outcomes in weekday and weekend matches in a large number of European football leagues. ...
... Both Franck, Verbeek, and Nüesch (2011) and Sobel and Raines (2003) argued casual bettors have lower opportunity costs of betting on weekends compared to weekdays and wager more on weekends while wagering by informed, financially motivated bettors likely occurs uniformly over time. We assume that, due to the lower opportunity costs, casual bettors primarily bet on weekends, while informed betting occurs throughout the week, since games viewed as attractive by financially motivated bettors should be uniformly distributed over time and not more likely to occur on weekends. ...
Sentiment bias, defined as investment decisions made for reasons unrelated to fundamentals and related to popularity, represents a common research topic in finance and economics. Empirical research on sentiment bias frequently uses data from sports betting markets. While research generally finds evidence of sentiment bias, in particular, due to team popularity, the prevalence of this bias among fans and bettors in many sports remains unclear and identification of markets with relatively larger numbers of bettors with sentiment bias poses empirical challenges. We analyse outcomes in betting markets for games played in two North American team sports leagues, the National Basketball Association (NBA) and National Football League (NFL) from the 2012–13 to 2016–17 seasons and investigate how game timing, in terms of games played on weekdays and weekends, may affect the presence of bettors with popularity-based sentiment bias. Probit model estimates explaining the probability that a bet on a team wins indicate patterns consistent with the presence of bettors with sentiment bias in the markets for betting on games in the NFL but not in the NBA, and the presence of more such bettors for NFL games played on weekends.
... Like in Sobel and Raines (2003), I also measure the favoritelongshot bias for weekend and weekday games. A reason for distinguishing between weekend and weekday games is that more casual bettors might place bets on weekends and more serious bettors on weekdays. ...
... A reason for distinguishing between weekend and weekday games is that more casual bettors might place bets on weekends and more serious bettors on weekdays. Sobel and Raines (2003) find a regular favorite-longshot bias on weekends and a reverse favorite-longshot bias on weekdays. In their study, they use data from racetrack facilities where bettors have to be present physically in order to place bets. ...
This paper addresses findings from previous asset pricing research that reveal lottery-like stocks are mispriced. This conclusion, however, relies on asset pricing models which might suffer from the joint hypothesis problem: That is, abnormal returns can reflect market inefficiencies, a bad asset pricing model or both. I contribute to the discussion by examining lottery-type assets on the European betting market. Compared to stock markets, betting markets offer the advantage that no asset pricing model is necessary to test market efficiency because outcomes are observable at a terminal point. I use a unique data set of soccer odds covering both a betting exchange and the bookmaker market. The findings reveal a favorite-longshot bias in both market structures confirming the findings from previous literature that lottery-type assets are mispriced. An expected utility model and a prospect theory model confirm that the favorite-longshot bias on the betting exchange is due to misperception of probabilities rather than risk-love. Although bookmakers also bias odds there is evidence that bookmakers are rational in protecting themselves from adverse selection and/or in increasing their turnover. This conclusion is supported by further analysis on the tennis betting market.
... (Vaughan Williams and Paton (1997), Snowberg and Wolfers (2007)). Like the favourite-longshot bias itself, our S-shaped pattern in returns could be due to investors having preferences for certain types of bets (Rosett (1965)), or investors making mistakes in estimating probabilities (Schmidt and Berri (2001), Snowberg and Wolfers (2007), Smith, Paton and Vaughn Williams (2006), Sobel and Raines (2003)). Finally, an alternative explanation lies in the belief aggregation model of Ottaviani and Sørensen (2009), which predicts a favourite-longshot bias and momentum (but not reversals) in prices after news events. ...
... Under this theory, costs of information acquisition cause some investors to bet randomly between different outcomes (such as horses in a race), causing favourites to be under-bet, and long-shots to be over-bet. (Smith et al (2006), Sobel and Raines (2003)). The prevalence of the favourite-longshot bias is thus linked to the information-related transaction costs in the market. ...
for their helpful comments and suggestions. All remaining errors are our own.
... The 2 p-values for win percentages in both the training and test data sets is <0.001. A feature of these results is that no hint of favourite-longshot bias (i.e., overvaluing longshots and undervaluing favourites; Sobel & Raines, 2003) or other forms of bias appears in either data set. To avoid issues related to bias from the presence of few winners relative to many losers, the training data set was 'up-sampled' using bootstrap resampling so that the number of winners exceeded 40 per cent of the data used to train each model, where the number of observations (individual runners) increased from 85,540 to 147,170. ...
The established view for horse race handicapping and staking strategies is to model them as a classification problem using factors describing horse, jockey, trainer, and racing history coupled with public odds, solved via a logistic regression. Logistic regression probabilities are then normalised, and bets filtered by threshold, or anomalous pricing. However, published algorithms do not show systematic profitability, nor do machine learning approaches using algorithmic betting strategies. This deficiency is due to three factors. First, wins are rare and racing data are thus imbalanced. Second, racing factors are multicollinear. Third, the number of factors needed for accurate prediction is very large. We show that alternative methods using variants from principal component analysis produces sustainable profitability regardless of staking strategy through a reduction of factors to fundamental drivers. We apply a partial least squares regression methodology to Australian thoroughbred racing. This approach is shown to outperform logistic regression and machine learning methods in classifying winners for a profitable trading strategy. This method can be applied to multiple betting domains.
... These explanations are based on bettors' "risk loving" behavior, or the so called "fans' sentiment". More recently, several explanations based on the behavioral characteristics of market makers (Shin, 1991(Shin, , 1992(Shin, , 1993, or structural characteristics of the markets, such as the cost of acquiring information relevant to the outcomes (Hurley and McDonough, 1995;Sobel and Travis Raines, 2003) have become common. ...
... Something extra is needed to explain the empirical observations that some sports betting markets, such as soccer, can display both favorite and longshot biases. It has been hypothesized that, in a horse racing context, longshot bias occurs if uninformed bettors dominate, and vice versa favorite bias if informed bettors dominate (Sobel and Raines 2003). Vaughan Vaughan provide a model with two groups of bettors, transaction costs, and an added utility benefit if informed bettors win on favorites. ...
A large body of literature on the favorite–longshot bias finds that sports bettors in a variety of markets appear to have irrational biases toward either longshots (which offer a small chance of winning a large amount of money) or favorites (which offer a high chance of winning a small amount of money). While early studies in horse racing led to an impression that longshot bias is dominant, favorite bias has also now been found in a variety of sports betting markets. This review proposes that the evidence is consistent with both biases being present in the average sports bettor. Sports betting markets with only two potential outcomes, where the favorite therefore has a probability >0.5 of happening, often produce favorite bias. Sports betting markets with multiple outcomes, where the favorite’s probability is usually <0.5, appear more consistent with longshot bias. The presence of restricted odds ranges within any given betting market provides an explanation for why single studies support, at most, one bias. This literature review highlights how individual sports bettors might possess biases toward both highly likely, and highly unlikely, events, a contradictory view that has not been summarized in detail before.
... Furthermore, we contributed to the evaluation of the overall integration of prediction markets and Delphi studies by supporting the claim of that an algorithm for selecting experts on the basis of trading behaviour is possible. In addition to this, our results may also be helpful for researchers that intend to improve prediction market forecasts by giving experts more weight or try to distinguish informed from uninformed traders to reduce biases, e.g. the favourite-longshot bias (Sobel & Raines 2003). ...
Purpose
The selection of experts for Delphi studies is crucial for the quality of the forecast results and the information taken into account. In the past, this has usually been done by selecting participants according to their reputation, although this approach is questionable in terms of reaching the most knowledgeable participants having new, relevant and valid information. In this context, this paper aims to propose to operate a prediction market alongside Delphi studies and select participants based on their trading behaviour in the market for the Delphi study.
Design/methodology/approach
Based on more than three years of historical prediction market trading data, the authors verify attributes that indicate insightful trades, as previously discussed in the finance literature, by using regression and classification trees.
Findings
The paper contributes attributes of trading behaviour that are theoretically derived from literature and potentially related to informed traders. These are tested and evaluated on historical prediction market data. Especially, the trading volume, the spread at the moment of trading and the market maker attribute seem to predict informed traders the best.
Originality/value
Algorithms based on identified attributes can be used to objectify the selection of experts for Delphi studies with potential gains in terms of the amount of information considered.
... Forrest & McHale (2005),Sobel & Travis Raines (2003) andCain et al. (2003) andWoodland & Woodland (1994) find a positive FLB in a variety of sports betting markets such as baseball, tennis, boxing and horse racing, whileForrest & Simmons (2008) underline the presence of the negative FLB in American team sport betting. ...
The prices offered by the fixed-odd bookmakers in the tennis betting market are biased because of the favourite-longshot phenomenon. How to derive unbiased implied probabilities underlying the published odds is the focus of this study. This paper proposes a new normalization procedure that yields unbiased probabilities, regardless of the presence of heavy underdogs. In-sample, the proposed normalization has a superior forecasting ability than the other methods. Moreover, it enables betting strategies which produce superior returns than those obtained from the Bradley-Terry type model.
... Like in Sobel and Raines (2003), I also measure the favorite-longshot bias for weekend and weekday games. A reason for distinguishing between weekend and weekday games is that more casual bettors might place bets on weekends and more serious bettors on weekdays. ...
This paper addresses findings from previous asset pricing research that lottery-like stocks are overpriced because investors overweight the probability of large positive returns. I examine lottery-type assets on the European soccer betting market because market efficiency tests on the betting market do not rely on potentially incorrect or incomplete asset pricing models. I use a unique data set, which covers odds from both a betting exchange and the bookmaker market, and find that market participants on the betting exchange misprice odds for extreme favorites and extreme longshots severely. An expected utility model confirms the previous findings and suggests that misperception of probabilities is driving the results. Although bookmakers also bias odds there is evidence that bookmakers are rational and engineer the favorite-longshot bias to protect themselves from insiders or to increase turnover.
... In a market characterized by FLB, bettors are biased at estimating the probability of extreme events by overstating and undervaluing the likelihood of "long shots" and favorites respectively. Various theories have been proposed to explain FLB, including inaccurate estimation (Sobel and Travis Raines 2003), probabilistic misperception (Snowberg and Wolfers 2010), and risk-seeking behavior. Since in the corporate context, forecasters are selected by managers rather than individuals who volunteer for entertainment purposes, there is no reason why the former would be intrinsically motivated by risk-seeking preferences. ...
Prediction is an important activity in various business processes, but it becomes difficult when historical information is not available, such as forecasting demand of a new product. One approach that can be applied in such situations is to crowdsource opinions from employees and the public. Our paper studies the application of crowd forecasting in operations management. In particular, we study how efficient crowds are in estimating parameters important for operational decisions that companies make, including sales forecasts, price commodity forecasts, and predictions of popular product features. We focus on a widely adopted class of crowd-based forecasting tools, referred to as prediction markets. These are virtual markets created to aggregate crowds' opinions and operate in a way similar to stock markets. We partnered with Cultivate Labs, a leading company that provides a prediction market engine, to test the forecast accuracy of prediction markets using the firm's data from its public markets and several corporate prediction markets, including a chemical company, a retail company and an automotive company. Using information extracted from employees and public crowds, we show that prediction markets produce well-calibrated forecasting results. In addition, we run a field experiment to study the conditions under which groups work well. Specifically, we explore how group size plays a role in the accuracy of the forecast and find that large groups (e.g., 18 participants) perform substantially better than smaller groups (e.g., 8 participants), highlighting the importance of group size and quantifying the right sizes needed to produce a good forecast using such mechanisms.
... There are at least two caveats in assessing our results: with any other paper on betting, we first share the problem that bettors are un- Sobel and Raines (2003)). Boulier, Stekler, and Amundson (2006) find no significant impact of odds on returns. ...
We extend the literature on risk preferences of a representative bettor by including
odds-dependent bet sizes in our estimations. Accounting for different bet
sizes largely reduces the standard errors of all coefficients. Substituting the coefficients
from the model with equal bet sizes into the model with odds-dependent
sizes leads to a sharp decline in the likelihood which shows that accounting for
different amounts is important. Our estimations strongly reject the hypothesis that
the overbetting of outcomes with low probabilities (favorite-longshot bias) can be
explained by risk-seeking bettors. Depending on the exact specification within cumulative
prospect theory, the data can best be described by an overweighting of
small probabilities which is more pronounced in the gain domain. Models allowing
for two parameters for probability weighting each in the gain- and in the loss
domain are superior.
... When we define favorites as the bottom fifty percent lowest odds placed and longshots as the other fifty percent, losses with longshots are on average almost 90 % higher than those with favorites. The FLB has proven to be largely robust with respect to sports, countries and the estimation method (Ottaviani and Soerensen 2008;Forrest and McHale 2007;Winter and Kukuk 2006), and only a few papers find a reversed FLB (Woodland andWoodland 1994, Sobel andTravis Raines 2003). The main focus of the existing empirical literature on wagering is to investigate the explanatory power of different theories on behavior under risk for the FLB. ...
With a unique data set from New Zealand which allows us to assign each bet to individual bettors, we analyze the impact of experience on behavior and success in non-parimutuel (fixed odds) sports betting markets. We find that experienced bettors bet more on favorites than inexperienced bettors do. Average returns, which we use as success measure, increase with experience even after controlling for odds. This means that the higher return of experienced bettors cannot only be attributed to betting more on favorites. To get a more detailed picture, we divide the data set into ten equally large subgroups, sorted by experience. We find that odds decrease from subgroup to subgroup, while success consistently increases. This shows that the positive impact of experience is not mainly driven by professional bettors.
... When we define favorites as the bottom fifty percent lowest odds placed and longshots as the other fifty percent, losses with longshots are on average almost 90 % higher than those with favorites. The FLB has proven to be largely robust with respect to sports, countries and the estimation method (Ottaviani and Soerensen 2008;Forrest and McHale 2007;Winter and Kukuk 2006), and only a few papers find a reversed FLB (Woodland andWoodland 1994, Sobel andTravis Raines 2003). The main focus of the existing empirical literature on wagering is to investigate the explanatory power of different theories on behavior under risk for the FLB. ...
With a unique data set from New Zealand which allows us to assign each bet to individual bettors, we analyze the impact of experience on behavior and success in non-parimutuel (fixed odds) sports betting markets. We find that experienced bettors bet more on favorites than inexperienced bettors do. Average returns, which we use as success measure, increase with experience even after controlling for odds. This means that the higher return of experienced bettors cannot only be attributed to betting more on favorites. To get a more detailed picture, we divide the data set into ten equally large subgroups, sorted by experience. We find that odds decrease from subgroup to subgroup, while success consistently increases. This shows that the positive impact of experience is not mainly driven by professional bettors.
... In particular, bookmakers are believed to exploit this behaviour and increase profitability by offering more-than-fair odds for 'safe' outcomes, and less-than-fair odds for 'risky' outcomes. This phenomenon is observed in many different markets (Ali M. , 1977;Quandt, 1986;Thaler & Ziemba, 1988;Shin H., 1991, Shin R. E., 1992Shin H., 1993;Woodland & Woodland, 1994;Vaughn Williams & Paton, 1997;Golec & Tamarkin, 1998;Jullien & Salanie, 2000), and various theories exist, such as risk-loving behaviour, on why people are willing to bet on such uncertain propositions (Sobel & Raines, 2003;Snowberg, 2010). In order to investigate the degree of this bias we simulate bets for each potential betting outcome that follows the standard form of a football match {p(H), p(D), p(A)} and record the resulting cumulative returns. ...
A gambling market is usually described as being inefficient if there are one or more betting strategies that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This paper evaluates the efficiency of the Association Football betting market. In contrast to earlier studies, we primarily show that: a) the accuracy between bookmakers is extremely consistent and bookmaking accuracy has not improved over the last decade; b) profit margins have been dramatically reduced over the last decade and can be statistically significant between bookmakers; implying that the published odds of one bookmaker cannot be considered as representative of the overall market; c) profit margins per distinct match can be significant even when considering only one bookmaker and one football division; d) there are some arbitrage opportunities; e) both systematic and significant adjustments of published odds occur at least daily. In many cases the changes cannot be explained by rational qualitative factors and hence may be due to betting volumes. We conclude that the football betting market is deliberately inefficient in an attempt to accomplish commercial objectives but that this inefficiency can only be exploited by a very limited number of bettors.
... It has been suggested that weekday bettors usually attend racetracks with financial ambitions and invest a considerable amount of time, effort and money in analysing the past performances of horses, jockeys and the condition of track (Kopelman and Minkin, 1991). This view is supported by the fact that the average amount bet per person is larger on weekdays than at weekends (McGlothlin, 1956;Sobel and Raines, 2003) and the proportion of large stake bets declines at weekends (Filby and Harvey, 1988). It is argued that the majority of individuals who participate in weekend or Bank holiday betting markets (many are employed at other times) treat betting and attendance at the racetrack as a leisure pursuit. ...
This study explores the origins and strength of the weekend effect by examining a market for state contingent claims where this phenomenon has not been previously explored; the UK horserace betting market. Conditional logit models are developed for weekend and weekday markets and prices are shown to be an inferior guide to race outcome at weekends. Evidence is provided that weekend markets are populated by a larger proportion of noise traders and that their inaccurate judgements cause the effect. It is demonstrated that the effect is sufficiently pronounced to enable abnormal returns to be earned in weekend markets.
... This phenomenon is not only observed in football but also in many different markets [1,31,38,33,35,34,41,39,18,23,6]. Various theories exist, such as risk-loving behaviour, on why people are willing to bet on such uncertain propositions [37,36]. ...
We present a Bayesian network (BN) model for forecasting Association Football match outcomes. Both objective and subjective information are considered for prediction, and we demonstrate how probabilities transform at each level of model component, whereby predictive distributions follow hierarchical levels of Bayesian inference. The model was used to generate forecasts for each match of the 2011/2012 English Premier League (EPL) season, and forecasts were published online prior to the start of each match. Profitability, risk and uncertainty are evaluated by considering various unit-based betting procedures against published market odds. Compared to a previously published successful BN model, the model presented in this paper is less complex and is able to generate even more profitable returns.
... Ali M. , 1977; Quandt, 1986; Thaler & Ziemba, 1988; Shin H., 1991, Shin R. E., 1992; Shin H., 1993; Woodland & Woodland, 1994; Vaughn Williams & Paton, 1997; Golec & Tamarkin, 1998; Jullien & Salanie, 2000), and various theories exist, such as risk-loving behaviour, on why people are willing to bet on such uncertain propositions(Sobel & Raines, 2003; ...
Researchers have witnessed the great success in deterministic and perfect information domains. Intelligent pruning and evaluation techniques have been proven to be sufficient in providing outstanding intelligent decision making performance. However, processes that model uncertainty and risk for real-life situations have not met the same success. Association Football has been identified as an ideal and exciting application for that matter; it is the world's most popular sport and constitutes the fastest growing gambling market at international level. As a result, summarising the risk and uncertainty when it comes to the outcomes of relevant football match events has been dramatically increased both in importance as well as in challenge.
A gambling market is described as being inefficient if there are one or more betting procedures that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This study exhibits evidence of an (intended) inefficient football gambling market and demonstrates how a Bayesian network model can be employed against market odds for the gambler’s benefit. A Bayesian network is a graphical probabilistic model that represents the conditional dependencies among uncertain variables which can be both objective and subjective. We have proposed such a model, which we call pi-football, and used it to generate forecasts for the English Premier League matches during seasons 2010/11 and 2011/12. The proposed subjective variables represent the factors that are important for prediction but which historical data fails to capture, and forecasts were published online at www.pi-football.com prior to the start of each match.
6
For assessing the performance of our model we have considered both profitability and accuracy measures and demonstrate that subjective information improved the forecasting capability of our model significantly. Resulting match forecasts are sufficiently more accurate relative to market odds and thus, the model demonstrates profitable returns at a consistent rate.
... Due to the favourite-longshot bias observed over the previous seasons many have suggested that this bias was due to bookmakers taking dynamic positions against the presumed tendency of the bettors to underbet on favourites and to overbet on risky outcomes (Rossett, 1971;Snyder, 1978;Ali M. M., 1979;Asch et al., 1984;Levitt, 2004;Graham & Stott, 2008). On the basis of this assumption, which was also the case in various other gambling markets, a mixture of theories have been formulated such as risk-loving behaviour on why people are willing to bet on such uncertain propositions (Sobel & Raines, 2003;Snowberg, 2010). If the assumption of having bookmakers taking positions against bettors for maximising profit is correct, then bookmakers' odds are prices published with the intention of maximising profit, which would also support the above assumptions. ...
A gambling market is usually described as being inefficient if there are one or more betting strategies that generate profit, at a consistent rate, as a consequence of exploiting market flaws. This paper examines the online European football gambling market based on 14 European football leagues over a period of seven years, from season 2005/06 to 2011/12 inclusive, and takes into consideration the odds provided by numerous bookmaking firms. Contrary to common misconceptions, we demonstrate that the accuracy of bookmakers' odds has not improved over this period. More importantly, our results question market efficiency by demonstrating high profitability on the basis of consistent odds biases and numerous arbitrage opportunities.
... This phenomenon is due, according to Fox and Clemen (2005), to the fact that Ôpeople anchor their judgements on equal probabilities for each event in the specified partition (the ignorance prior distribution) and adjust insufficiently to account for their beliefs about how the likelihood of the events differÕ. Sobel and Raines (2003) propose an information model in which Bayesian bettors begin with an ignorance prior (equal probabilities) and update the prior according to private information. As a result, longshots are overestimated and favourites underestimated. ...
This article presents new theoretical and empirical evidence on the forecasting ability of prediction markets. We develop a model that predicts that the time until expiration of a prediction market should negatively affect the accuracy of prices as a forecasting tool in the direction of a ‘favourite/longshot bias’. That is, high‐likelihood events are underpriced, and low‐likelihood events are over‐priced. We confirm this result using a large data set of prediction market transaction prices. Prediction markets are reasonably well calibrated when time to expiration is relatively short, but prices are significantly biased for events farther in the future. When time value of money is considered, the miscalibration can be exploited to earn excess returns only when the trader has a relatively low discount rate.
... Another point of view is to place betting in terms of Stock Market Efficiency. In this approach it is argued that betting on favorites should be as profitable as betting on longshots (Sobel and Raines, 2003). However, this is not the case which leads to a bias towards longshot odds. ...
In this paper we investigate the role of machine learning within the domain of Greyhound Racing. We test a Support Vector Regression (SVR) algorithm on 1,953 races across 31 different dog tracks and explore the role of a simple betting engine on a wide range of wager types. From this we triangulated our results on three dimensions of evaluation: accuracy, payout and betting efficiency. We found that accuracy and payouts were inversely linked, where our system could correctly predict Wins 45.35% of the time with a betting efficiency of 87.4% (return per bet) for high accuracy low payout, or predict Superfecta Box wagers with 6.45% accuracy and a 2,195.5% return per bet, corresponding to low accuracy high payout. This implied that AZGreyhound was able to correctly identify longshot dogs and we investigate the reasons why as well as the system's performance.
... Despite a full spectrum of results concerning the favorite-long shot bias, models have emerged that can predict the movement of biases based upon predictable factors. By assuming heterogeneous pools of bettors, as opposed to the typical homogenous pool of identical " representative bettors, " biases can be estimated due to race specifications that determine the characteristics of the bettors' pool (Sobel and Raines 2003). Biases are generated by uninformed bettors skewing the information gleaned from posted odds. ...
This paper is an analysis of the demand for thoroughbred racetrack wagers, examining evidence that would support the existence of two types of bettors: the risk-averse informed bettor versus the uninformed bettor. Looking at 12 major racetracks over the fall of 2002, we undertake an empirical examination of the determinants of bettors' preferences for particular wagers on specific races. The goal is to try to determine what individual aspects of a race (conditions, surface, participants, etc.) will encourage increased wagering dollars. With the advent of simulcasting, the competition for the wagering dollar is fierce, as the bettor can choose from more than 100 races daily, each race offering numerous betting options. We find for most wagers that higher quality participants, larger and more competitive fields, and turf races increase betting volume while higher pari-mutuel takeout, poor track conditions, and other races run concurrently reduce volume. However, more competitive fields reduce betting volume in the show and trifecta pools. Optimal field size is determined to be between 10 and 12 betting interests. Overall, we find support for the existence of a significant share of risk-averse informed bettors.
... Second, investors may view games as more uncertain than they actually are. (Schmidt and Berri (2001), Smith et al (2006), Sobel and Raines (2003)). When a team gets ahead, investors may think it has a lower probability of winning than it actually does, and returns are higher than the price indicates.) ...
Examining NFL betting contracts at Tradesports.com, we find mispricing consistent with the disposition effect, where investors are more likely to close out profitable positions than losing positions. Prices are too low when teams are ahead and too high when teams are behind. Returns following news events exhibit short-term reversals and longer-term momentum. These results do not appear driven by liquidity or non-financial reasons for trade. Finding the disposition effect in a negative expected return gambling market questions standard explanations for the effect (belief in mean reversion, prospect theory). It is consistent with cognitive dissonance, and models with time-inconsistent behaviour.
... betting exchanges, spread betting and significant reconfiguration of regulatory arrangements in relation to betting. Each of these has prompted new and wider research into efficiency characteristics across a broad range of geographical and sporting contexts (see, for example, Gander et al (2001) (New Zealand horseracing); Sobel and Raines (2003) (American greyhound racing); Dare and Holland (2004) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 Whilst the volume and range of work in the area of betting market efficiency is clearly extensive, therefore, there is a reasonable consensus around two themes. First, there are established biases in betting markets in terms of patterns of misalignment between subjective and objective probabilities which appear generally (though not universally) robust to different market and national contexts. ...
This article offers a new perspective on efficiency in betting markets by examining the degree to which finishing order in horse races corresponds to probabilities inherent in odds across different categories of horse race. The application of an exploded logit procedure reveals a significantly greater degree of ordinal efficiency in higher relative to lower-class races. Explanations for the phenomenon include differences in prize-related incentives, cross-market distinctions in information markets and differential opportunity/incentive for market manipulation.
Recent findings in behavioral economics have shown that an individual may not always act optimally and rationally in their decision-making. However, these findings have come mainly from laboratory conditions, and as such, they need to be verified under real circumstances. This paper examines the presence of heuristics in the environment of fantasy sports. The data come from a fantasy league based on the National Hockey League in the season of 2015–16. Its users come mainly from the Czech Republic. The results show a moderately strong presence of representativeness. Nevertheless, there are also manifestations of not always prioritizing point-maximizing strategies, for example in the higher demand for hockey players of the same nationality as that of the users. However, the main factor influencing the demand is still the athletes’ performance. This study’s findings hold implications for fantasy sports, prompting fantasy sports participants to strategically adjust squad selection. For platforms, it suggests user experience enhancements and algorithmic adjustments to guide optimal decision-making, enriching overall engagement. Additionally, the research contributes to decision-making theory by validating behavioral economics in the real world, emphasizing context-specific biases, and advocating for an integrated understanding of heuristics and rational factors in decision environments.
Previous literature has established the need to separate insider from expert trading in both financial and betting markets. This type of separation proves difficult to achieve because experts and insiders co-exist in most market settings. Utilizing novel betting markets in which expert skill bettors are unable to use their expert knowledge, this study uncouples insider from expert betting, and allows more direct measurement of insider trading than in previous empirical tests. Evidence is presented in favor of some predictions from the highly cited Shin model of insider trading. Price setters charge an extra premium in markets with high proportions of insiders when compared to equivalent markets. The insiders accurately predict event outcomes, and their presence exacerbates a well known bias in betting market prices whereby returns on betting favorites is higher than for bets on longshots.
Many laboratory-based studies provide evidence that temperature can influence how people make decisions, by affecting their risk preferences and propensity to make cognitive errors. However, the role of temperature on the quality of decisions made in real-world settings it is not well-understood. A strand of literature in financial markets has attempted to explore this, but the results have been inconclusive: some studies suggest that temperature does not affect financial decisions, whilst others reach contrasting conclusions – some suggesting that higher, and others that lower temperatures, reduce the quality and economic value of financial decisions. We design an empirical experiment to overcome the limitations of previous studies in order to shed new light on the role of temperature in financial decisions. The study employs data from a time-limited market for state-contingent assets, namely an event-driven prediction market. We assess the extent to which prediction market participants’ subjective judgments of event probabilities deviate from the actual probability of the event occurring, as a result of temperature-induced cognitive errors and risk-taking. The results demonstrate that higher temperatures are associated with lower decision quality. We also found that temperature differentially influences the decisions of those with different decision profiles, with the largest influence observed on individuals whose decisions are based on logic, objectivity and skilful cognitive evaluations of alternatives.
Simulcast wagering, where bets from across the country are taken at tracks, off‐track betting facilities, casinos, by phone or online and incorporated into the same mutuel pool, has contributed to a large increase in betting volume on American horse races since the mid‐1990s. This article investigates betting‐market efficiency in the simulcast era focusing on whether the interrelated 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 is not profitable because market closing prices are unknown when bets are placed.
The past several decades have witnessed a growing enthusiasm to implement the market as an information aggregation tool. However, some deep-rooted pricing anomalies frequently observed in various markets loom large, questioning the rationality of such eagerness. One of these anomalies is the favorite-longshot bias, and sometimes its opposite, the reverse favorite-longshot-bias. We propose an equilibrium model consisting of bettors with cumulative prospect theory-based utility and heterogeneous beliefs to explain these two anomalies in a unified framework. Unlike existing results that mostly focus on one aspect of the underlying model, our model enables us to isolate and analyze the impacts of probability weighting, loss aversion, belief concentration, and belief tailedness. We show how these parameters jointly determine the properties of the equilibrium price. Empirical results also suggest this model has adequate flexibility to explain the behavior of actual historical data.
This paper presents a systematic literature review using HistCiteTM in the context of gambling. After several iterations of data cleaning, the final dataset comprised 265 articles. Four key themes are identified: profiling gamblers; gambling markets; gambling motivation and fallacies; and societal effects. Further, this study identifies four key emerging research themes and associated directions for future research: adolescent gambling, health conditions and problem gambling, dark nudging. Gambling is economically and socially significant, both in Australia and globally. Whilst gambling taxes are utilised by governments for the social good, the academic literature largely focuses on the issue of problem gambling.
Testing the impact of profitable investment strategies is often hampered by the practical difficulties of determining who knew what, and when. This study examines the impact of the publication of a profitable wagering strategy on the Major League Baseball wagering market. While standard measures of market efficiency characterized the Major League Baseball win–loss moneyline market to be efficient, previous works shows that wagering on underdogs early in the season can generate persistent profits. Though the overall efficiency of the baseball wagering market remained after publication, these profitable opportunities dissipated. Bettor behaviour is found to play varying roles across different wagering strategies; up to half of the drop in returns can be attributed to wagering market participant behaviour.
Legal disputes are often negotiated under the backdrop of an adjudicated award. While settlements are common, they are not universal. In this paper, we empirically explore how uncertainty in adjudicated awards impacts settlement negotiations. To do so, we develop an experimental design to test how increases in variance and positive skewness of the award distribution impact negotiations and settlement rates. We find increases in variance decrease settlement rates, while increases in skewness generally increases settlement rates. We also gather individual measures of risk aversion and prudence, and incorporate these measures into the analysis to test for heterogeneous treatment effects. Overall, our results suggest that highly variable adjudicated awards can contribute to the excess use of inefficient litigation, while more positively skewed awards can reduce the use of inefficient litigation.
This chapter examines the idea of weak form information efficiency as it has been applied to betting markets, and reviews the concepts, distinctions and tests which are associated with this concept. It has been shown in chapter 1 that weak form information efficiency is the notion that current prices incorporate all the information available from a study of past prices and price movements. In consequence, in a financial market which is weakly efficient it should not be possible to earn abnormal returns through a strategy of predicting future prices from past information on prices. Indeed, any such strategy should on average yield the same return. Many studies of weak form information in betting markets have adapted this idea to examine the possibility for earning differential (or even abnormal) returns in the future, from betting on the basis of past information about the yield to bets at identified prices. In a betting market, these prices take the form of ‘odds’. Odds of 3 to 1 laid against an outcome, for example, imply a return to a successful bet of three times the initial stake, plus the initial stake returned. An unsuccessful bet loses the entire stake. The theoretical point is that in a betting market which is weak form efficient the expected return to betting at any identified odds or odds grouping should be identical, unless there are differential costs or risks associated with betting at the various prices.
We demonstrate that there is a considerable variation in bookmaker margins across matches, time and bookmakers. Our results imply that using match, tournament and players’ characteristics explains the variations in margins hence, they can be helpful in managing intermediation cost in a market of state-contingent assets: fixed-odds betting markets. We also provide evidence that bookmakers protect themselves by increasing odds on the favourite player, thus attracting more bettors to the favourite player, while deterring bettors from betting on the underdog by reducing the odds. By that process, bookmakers are possibly sacrificing a portion of their margin.
This paper compiles and summarizes the theoretical literature on the favorite-longshot
bias, an anomaly that has been found in sports betting markets for over half a century.
Explanations of this anomaly can be broken down into two broad categories, those
involving preferences and those involving perceptions. We propose a novel test of these
two classes of models that allows us to discriminate between them without parametric
assumptions. We execute these tests on a new dataset, which is an order of magnitude
larger than any used in previous studies, and conclude that the perceptions model, in
which bettors overestimate the chances of small probability events, provides a better fit
to the data.
We consider a policy reform that would relax price controls in American pari-mutuel wagering on horse racing by examining bookie behavior in Australia's fixed-odds gambling sector. Descriptive regressions indicate that bookmaker takeouts (the effective prices of races) vary substantially and systematically with race characteristics, though in sometimes counterintuitive ways. Estimates of an explicitly reduced form model of bookie takeout, however, can qualitatively match both intuition and prior findings in the literature. Counterfactuals that use these estimates suggest that regulatory reform that permits racecourses to alter takeout across races would increase variable profit by about 5 %.
The chapter is primarily concerned with the information efficiency of exchanges. Their operation and functionality are discussed, along with some of the initial impacts they have had on betting markets, including the hostile response from some traditional bookmakers. Previous empirical studies concerning information efficiency in exchanges are outlined, although they are few at this relatively early stage of the development of the exchanges. New evidence about the degree of odds bias in exchange horse race markets is then presented. This evidence is found to be consistent with previous studies showing a much smaller degree of favorite-longshot bias in the exchanges than exists in traditional bookmaker markets.
Racing prediction schemes have been with mankind a long time. From following crowd wisdom and betting on favorites to mathematical methods like the Dr. Z System, we introduce a different class of prediction system, the S&C Racing system that derives from machine learning. We demonstrate the S&C Racing system using Support Vector Regression (SVR) to predict finishes and analyzed it on fifteen months of harness racing data from Northfield Park, Ohio. We found that within the domain of harness racing, our system outperforms crowds and Dr. Z Bettors in returns per dollar wagered on seven of the most frequently used wagers: Win 2.30, Show 19.24, Quiniela 3.56 and Trifecta Box $21.05. Furthermore, we also analyzed a range of race histories and found that a four race history maximized system accuracy and payout. The implications of this work suggest that an informational inequality exists within the harness racing market that was exploited by S&C Racing. While interesting, the implications of machine learning in this domain show promise.
This study explores the extent of mispricing in a market for state contingent claims that is commonly believed to be efficient, the UK horserace betting market. We develop conditional logit models for weekend and weekday markets and show that prices are inefficient at weekends when the presence of a larger proportion of less informed bettors results in mispricing. A Kelly investment strategy focused on high probability outcomes in such markets yields considerable positive returns. We identify the need for research exploring the implications for information suppliers and users, regulators and operators in wider financial markets.
This paper examines decision making in a special case of risk and uncertainty that is similar to pari-mutuel betting. Specifically, this paper examines following issues: the presence of a longshot bias; the strategies participants adopt in making a priori selections; the effect of these strategies on total payoff; and the association of these strategies with participants' demographics. By examining decision strategies, the paper provides evidence of a longshot bias – participants bet on underdogs with an expectation to win big although in reality such a strategy usually correlates with lower total returns. The paper also shows the presence of risk zone where risky strategies significantly lower total returns. Interestingly, participants in the risk zone tend to bet more on longshots than on favourites. The paper offers economic explanations for the observed longshot bias in office pools and possible resolutions to mitigate this bias.
This paper describes an experiential learning case that uses the horse race betting markets as a vehicle to understand the process of decision making. In horse racing the spectator is also a decision maker. The experiment consists of using the class as a mini-simulcast centre whereby races are simulcast to the class from the internet and projected onto a big screen. The students also have access to individual terminals where they can access the real time wagering (betting) pools of a particular race and use Excel spreadsheets to monitor the results of their decisions.
The recent expansion of prediction markets provides a great opportunity to test the market efficiency hypothesis and the calibration of trader judgements. Using a large database of observed prices, this article studies the calibration of prediction markets prices on sporting events using both nonparametric and parametric methods. While only minor bias can be observed during most of the lifetime of the contracts, the calibration of prices deteriorates very significantly in the last moments of the contracts’ lives. Traders tend to overestimate the probability of the losing team to reverse the situation in the last minutes of the game.
Previous studies have found some degree of inefficiency in betting markets. However, it is difficult to implement a strategy to take advantage of these biases. This article investigates and attempts to arbitrage interrelated betting markets by undertaking three betting simulations using two datasets comprised of parimutuel pools from US horse races. Two of the betting simulations are positive returns, but in the most realistic real-time simulation the losses are substantial. Profitable betting opportunities disappear due to last minute wagers which change the odds and increase market efficiency.
Economists have given great attention to stock markets in their efforts to test the concepts of market efficiency and rationality. Yet wagering markets are, in one key respect, better suited for testing market efficiency and rationality. The advantage of wagering markets is that each asset (bet) has a well-defined termination point at which its value becomes certain. The absence of this property is one of the factors that has made it so difficult to test for rationality in the stock market. Since a stock is infinitely lived, its value today depends both on the present value of future cash flows and on the price someone will pay for the security tomorrow. Indeed, one can argue that wagering markets have a better chance of being efficient because the conditions (quick, repeated feedback) are those which usually facilitate learning. However, empirical research has uncovered several interesting anomalies. While there are numerous types of wagering markets, legal and otherwise, this column will concentrate on racetrack betting and lotto-type lottery games.
Many racetrack bettors have systems. Since the track is a market similar in many ways to the stock market one would expect that the basic strategies would be either fundamental or technical in nature. Fundamental strategies utilize past data available from racing forms, special sources, etc. to "handicap" races. The investor then wagers on one or more horses whose probability of winning exceeds that determined by the odds by an amount sufficient to overcome the track take. Technical systems require less information and only utilize current betting data. They attempt to find inefficiencies in the "market" and bet on such "overlays" when they have positive expected value. Previous studies and our data confirm that for win bets these inefficiencies, which exist for underbet favorites and overbet longshots, are not sufficiently great to result in positive profits. This paper describes a technical system for place and show betting for which it appears to be possible to make substantial positive profits and thus to demonstrate market inefficiency in a weak form sense. Estimated theoretical probabilities of all possible finishes are compared with the actual amounts bet to determine profitable betting situations. Since the amount bet influences the odds and theory suggests that to maximize long run growth a logarithmic utility function is appropriate the resulting model is a nonlinear program. Side calculations generally reduce the number of possible bets in any one race to three or less hence the actual optimization is quite simple. The system was tested on data from Santa Anita and Exhibition Park using exact and approximate solutions (that make the system operational at the track given the limited time available for placing bets) and found to produce substantial positive profits. A model is developed to demonstrate that the profits are not due to chance but rather to proper identification of market inefficiencies.
Discusses the cognitive and the psychophysical determinants of choice in risky and riskless contexts. The psychophysics of value induce risk aversion in the domain of gains and risk seeking in the domain of losses. The psychophysics of chance induce overweighting of sure things and of improbable events, relative to events of moderate probability. Decision problems can be described or framed in multiple ways that give rise to different preferences, contrary to the invariance criterion of rational choice. The process of mental accounting, in which people organize the outcomes of transactions, explains some anomalies of consumer behavior. In particular, the acceptability of an option can depend on whether a negative outcome is evaluated as a cost or as an uncompensated loss. The relationships between decision values and experience values and between hedonic experience and objective states are discussed. (27 ref)
Much of the information available to participants in speculative markets is in the nature of expert opinion, analysis, professional advice, and so on. Markets discount widely held factual information very well; this paper studies market efficiency with respect to subjective information. We examine the "market" for bets on thoroughbred horse races to determine whether the published forecasts of professional handicappers are completely discounted. A multinomial logit probability model is used to measure the information content of the forecasts, and we find that they do contain considerable information but that the track odds generated by betting discount almost all of it. Within the population of bettors, those betting at the track appear to discount the handicapper information fully, but those betting through New York's off-track betting system do not.
Wagering markets provide a natural laboratory for testing models of market prices and behavior under uncertainty. The literature on wagering, albeit contentious, has established the following. First, prices set in these markets, to a first approximation, are efficient forecasts of outcomes. Second, price changes in these markets are driven by an informed class of bettors and improve prediction. Nevertheless, there are important departures from generic notions of market efficiency. Recent models focusing on diverse information, heterogeneous agents, and transaction costs help to explain these findings.
Gandar, Zuber, and Russo are from the Department of Economics, University of North Carolina at Charlotte. O'Brien is from the Department of Finance, University of Connecticut. The authors are grateful to the finance workshops at the Universities of Connecticut and North Carolina at Chapel Hill and to George Ignatin, Michael Roxborough, Chris Piros, Hal Stern, Steven Swidler, Gene Webb, and an anonymous referee for helpful discussions and comments and to Craig Brown and John Griffith for assistance in data collection and processing
According to most economists, economic behavior is a rational undertaking. It is assumed that we know what we want, strive to get it, and accept the verdict of the market for our effort.
In this profound and provocative work, Richard Thaler challenges the received economic wisdom by revealing many of the paradoxes that abound even in the most painstakingly conducted transactions. He presents literate, challenging, and often funny examples of the various anomalies that confront and confound people in everyday economic life—such as "the winner's curse," a dynamic wherein winners become losers by miscalculating the value of a purchase made in a common value auction. He also demonstrates that markets do not always operate with the traplike efficiency we impute to them.
Thaler argues that recognizing these sometimes topsy-turvy facts of economic behavior will compel economists, as well as those who live by their lights in our jobs and organizations, to adopt a more balanced view of human nature, one reflected in Adam Smith's professed belief that despite our selfishness, there is something within our natures that prompts us to enjoy, even promote, the happiness of others. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This study examines the ability of economists to forecast ten major economic series. The data for this study were provided by J. A. Livingston of the Philadelphia Inquirer, who since 1947 has collected forecasts for the upcoming 6 and 12 months. The results reveal that, in general, for the period from 1947 through 1978, the economists in Livingston's sample did not produce efficient forecasts and were not able to outperform simple statistical models. It should be noted, however, that a substantial and consistent improvement in forecasting performance by economists in Livingston's sample did occur over this same period. These results contain important information for managers who use macro-economic consensus forecasts.
The analysis examines the wagering behavior of the “uninformed” bettor. Using data from a second tier racetrack, the high correlation between subjective and objective probabilities suggests an efficient win pool. However, the results fail to demonstrate the public 's tendency to underbet favorites and overbet longshots. Employing computer intensive statistical methods, a second part of the analysis suggests that mispricing does exist in the place and show pooh, although the size of these inefficiencies may be of small economic consequence. Taken as a whole, the results of a small, start-up track mirror those found in earlier studies of major racetracks and support an earlier conjecture that the fast, repetitive feedback in horserace wagering facilitates learning.
In this paper we test the efficiency of the gambling market for Na- tional Football League games. Two efficiency tests are conducted. The first test is derived from the finance literature on market efficiency, while the second test is based on a market's being efficient when the rate of return on any gambling strategy based on publicly available information approximates the bookmaker's commission. While the first test is found to be too weak to establish conclusions about the efficiency of the NFL gambling market, the second test results, showing the existence of profitable betting opportunities, indicate that speculative inefficiencies exist in this market.
Subjective and estimated objective winning probabilities are obtained from 20,247 harness horse races. It is shown that subjectively a horse with a low winning probability is exaggerated and one with a high probability of winning is depressed. Various hypotheses characterizing the bettors' behavior to explain the observed subjective-objective probability relation are explored. Under some simplified assumptions, a utility of wealth function of a decision maker is derived, and a quantitative summary measure of his risk attitude is defined. Attitude toward risk of a representative bettor is examined. It is found that he is a risk lover and tends to take more risk as his capital dwindles.
The following sections are included:INTRODUCTIONPARI-MUTUEL BETTINGBETTING COMBINATIONSTHE THEORETICAL RELATION BETWEEN RETURNS AND PROBABILITIESRACE-TRACK DATATHE EMPIRICAL RELATION BETWEEN RETURN AND THE PROBABILITY OF WINNINGCONCLUSIONSAPPENDIX A LIMITS ON THE p − R RELATIONAPPENDIX B THE PARLAY RELATIONAPPENDIX C THE MARTINGALE RELATION
Studies of horse race betting have empirically established a longshot anomaly; that is, low-probability, high-variance bets (longshots) provide low mean returns and high-probability, low-variance bets provide relatively high mean returns. Because bettors willingly accept low-return, high-variance bets, researchers conclude that bettors are risk lovers. In this study, we show that the data are at least as consistent with risk aversion as they are with risk loving when one explicitly considers the skewness of bet returns. Because the variance and skewness of bet returns are highly correlated, bettors may appear to prefer variance when it is skewness that they crave.
The theory of risk bearing implies risk aversion. In every published study of horse race betting known to the authors, however, investigators reject this implication in favor of "ri sk-loving" behavior. Using the techniques of these studies, the auth ors examine a new data set from Hong Kong and find a rather different result: Hong Kong bettors seem to be either risk neutral or risk ave rse. A striking difference between the Hong Kong data and the previou sly studied North American data is the much larger betting volume per race. Copyright 1988 by the University of Chicago.
Most studies of both pari-mutuel and fixed-odds betting markets have shown a systematic tendency for the expected return to bets at lower odds to exceed those at higher odds. Some work, however, has revealed in certain markets the absence or even reversal of this bias. We present a model which distinguishes two separate types of bettor, and use this to demonstrate how transactions costs, the extent of public information, and consumption benefits of betting can explain the disparities. Our empirical evidence, taken from a fixed-odds market, lends support to our theoretical conclusions.
This paper investigates biases in the perceptions of probabilities using data from the 1989 and 1994 seasons at the Woodlands greyhound park in Kansas City, Kansas. Results reveal consistent evidence that the gambler's fallacy exists. The results also reveal that gamblers overestimate the probability of a win by the favorite and the dog in the "lucky" seven position. However, the comparison also suggests some learning by bettors between the first season of operation in 1989 and the 1994 season.
Copyright 1998 by Kluwer Academic Publishers
The efficiency and profitability of exotic racetrack bets such as exactas and daily doubles are examined. Efficiency is understood to mean that above average returns cannot be made in the long run once risk is appropriately controlled for. The markets in question are found not to be efficient; the inefficiencies, however, are insufficient to permit simple strategies to show a consistent profit. Some evidence of "smart money" exists in that holders of inside information may bet on exactas rather than equivalent standard bets in order to avoid signaling their actions to the betting public. Copyright 1987 by The Review of Economic Studies Limited.
Horse racing data permit interesting tests of attitudes toward risk. The present paper studies a new sample of racetrack results from Atlantic City, New Jersey. The questions examined are: (1) Are the market odds the best data for predicting the order of finish? (2) Do horses go off at odds that reflect their true probability of winning? (3) Is there any evidence that late bettors have better information than early bettors? It is found that market odds predict the order of finish well, but that ‘favorites’ are good bets and ‘long shots’ are poor ones. The data suggest that there does exist an ‘informed’ class of bettors and that bettors are on the whole neither risk neutral nor risk averse.
This paper examines the optimal pricing decision of a bookmaker facing a group of gamblers, some of whom have superior information to the bookmaker. The central result is that the normalized betting odds diverge systematically from the true possibilities of winning. Specifically, it is optimal for the bookmaker to follow a "square root rule" in which the ratio of posted prices is given by the square root of the ratio of winning probabilities. One consequence of this rule is that the betting odds understate the winning chances of the favorites and exaggerate the winning chances of the longshots. This is precisely the bias observed in several empirical investigations of betting markets. Copyright 1991 by Royal Economic Society.
It is well known that the returns on various betting opportunities at a racetrack are determined by a competitive bidding of the bettors in a natural environment of their decision making. In this paper, two simple bets of unknown but identical winning probabilities are identified. An analysis of 1,089 observations shows that the data are consistent with the hypothesis that both bets are identically priced, an implication of an efficient speculative market.
Empirical studies of parimutuel games establish several facts not previously explained by theory. For example, market odds fail to provide accurate predictions of outcomes and longshots earn lower expected values than other bets. This paper outlines a model of parimutuel games in which such outcomes arise as a consequence of the takeout of the track. Bettors may purchase true probabilities of events, and equilibrium entry and wagers of these informed bettors lead to patterns observed in previous studies. A case study of the Woodlands Greyhound Park supplies evidence consistent with the model. Copyright 1996 by Royal Economic Society.
This paper examines the efficiency of the legal gambling market for major league baseball. Weak-form tests of market efficiency within and across odds lines are performed. Surprisingly, the consistently observed favorite-longshot bias in racetrack betting is shown to exist in reverse for baseball bettors. However, these and other deviations from efficiency are shown to be insufficient to allow for profitable betting strategies when commissions are considered. Copyright 1994 by American Finance Association.
Sangamon State University. An earlier version of this paper was presented December 20, 1976 at the Third Conference on Gambling, Las Vegas, Nevada. I am slightly embarrassed at the extent to which I am indebted to others for help of various kinds. Ron Sutherland suggested the framework for this study and provided helpful comments on various drafts. Nancy Jacob and Mark Rubinstein also made several recommendations. H. Fabro, J. Jung, N. Ostroot and J. Rogers gave many tireless hours collecting data. Also, I received the cooperation of the Illinois Racing Board and the Daily Racing Form's statistical editor Don Anderson. But my list would be totally inadequate without expressing my gratitude to J. Miller's T.A. seminar for requiring me to make a “contract” to complete this study.
