Longshot Bias Research Articles

Risk aversion and favourite–longshot bias in a competitive fixed‐odds betting market

AbstractResearch on sports betting has generally found a favourite–longshot bias: bets on longshots lose more than bets on favourites. Existing research focuses largely on pari‐mutuel betting, but favourite–longshot bias is also evident in fixed‐odds online betting markets of the type that are growing rapidly around the world. Explanations for this bias in previous work on pari‐mutuel markets cannot explain why it would be a feature of competitive fixed‐odds betting markets. We show how disagreement among gamblers and risk aversion on the part of bookmakers in a competitive market can produce a pattern of favourite–longshot bias resembling the empirical evidence.

Prospect Theory and the Favorite Long-Shot Bias in Baseball

We provide new evidence of a favorite long-shot bias for bets placed on baseball games. Our analysis uses the difference of mean run differentials as an observable proxy for the probability of a team to win. When baseball is viewed through this proxy, we see that bettors believe favorites are less likely to win than they actually are and long-shots more likely. This result is consistent with prospect theory, which suggests that large and small probabilities are poorly estimated when making decisions with risk.

A Decision Theoretic Foundation for Noise Traders and Correlated Speculation

Noise traders are a central idea in the modern theory of asset markets, yet there is not a standard model of such agents in contrast to the well-established representation of rational agents as expected utility maximizers. We propose the Hurwicz criterion, a classical criterion in decision analysis for choice under uncertainty, as a foundation for noise traders in asset markets. Hurwicz agents trade on optimism and pessimism and do not trade on information. A binary asset market is introduced with asymmetric information and heterogeneity both in rationality and in ambiguity attitudes. In this environment, noise trader behavior is endogenously positively correlated, the market is more efficient in low sentiment periods, and the favorite-longshot bias holds in equilibrium. The analysis demonstrates that aggregate market properties such as positive trading volume and the favorite longshot bias can be derived from the micro behavior of individual agents that have an axiomatic foundation.

The Longshot Bias Is a Context Effect

In nearly every betting market, gamblers overvalue the riskiest bets. This “longshot bias” is usually explained by a tendency to overweight low-probability events. We offer a novel explanation: contrast effects enhance the attractiveness of longshots because gambles presented in terms of their payoffs are easier to compare along the payoff dimension than along the probability dimension. Our analysis of historical betting odds suggests that contrasts between gamble payoffs can explain the longshot bias. Laboratory experiments confirm those contrast effects and show that the longshot bias disappears when gamblers consider bets in isolation or when winning probabilities are easier to compare. This paper was accepted by Manel Baucells, behavioral economics and decision analysis. Funding: The authors thank the University of Chicago’s Center for Decision Research and Richard Thaler for funding. Supplemental Material: The online supplement and data are available at https://doi.org/10.1287/mnsc.2023.4684 .

The Longshot Bias is a Context Effect

The Longshot Bias is a Context Effect

Are Sports Bettors Biased toward Longshots, Favorites, or Both? A Literature Review

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.

Do Individual Investors Overpay the Lottery-type Stocks?

The stock market has often been compared to gambling. Using daily return and volume data from January 1st, 2001 until December 31st, 2012 for all common shares listed on KOSPI and KOSDAQ in the Korea stock market, we examine the role of extreme positive returns in the cross-sectional pricing of stocks. Our argument rests on the idea that individual investors, like racetrack punters, overvalue assets with lottery-like payoff. Retail investors tend to hold poorly diversified portfolio and more susceptible to longshot bias than institutional investors. If individuals have stronger preference for lottery-type stock than institutions participating in the stock market, then stock return is related to the extreme events observed in the past, and investor overpay these stock with dreaming jackpot winners. By testing several hypotheses, We find that individual investor overpay the lottery-type stocks. This investors' tendency increases gambling inclinations in market. Unlike previous studies, we find that racetrack punters do not tend to gamble during an economic downturn. Also, there is the strong intersection effect between maximum return portfolio and volatility, and between maximum return portfolio and skewness on the preference for gamble stocks. And, there are significantly stronger with lottery stock demanded by individuals than that of institutions.

Longshots, overconfidence and efficiency on the Iowa Electronic Market

We study the forecast accuracy and efficiency of popular “binary” prediction markets. Such markets forecast probabilities for future states of the world (e.g., election winners) by paying off $0 or $1 depending on the realized state (e.g., who actually wins). To assess accuracy, forecast probabilities must be compared to realization frequencies, not individual realizations. We use Iowa Electronic Market (IEM) data to test efficiency against two alternative propositions from behavioral finance: the longshot bias and the overconfidence bias (which yield opposing predictions). No longshot bias appears in IEM markets. Nor does overconfidence influence prices at short horizons. However, overconfident traders may bias prices at intermediate horizons. While the markets are efficient at short horizons, non-market data indicate some intermediate-horizon inefficiency. We calculate Sharpe ratios for static trading strategies and document returns for dynamic trading strategies to assess the economic content of the inefficiencies.

Favorite–longshot bias in pari-mutuel betting: An evolutionary explanation

Favorite–longshot bias (FLB) refers to an observed tendency whereby “longshots” are overvalued and favorites are undervalued. We offer an evolutionary explanation for FLB in pari-mutuel betting using a simple market model. A bettor is forced to quit with some probability if his total net gain in one day is negative. Because of a positive track take, the expected returns of any strategy are negative, and so every agent must eventually lose and disappear in the long run. Those who favor longshots have a better chance of getting ahead with rare but large gains, enabling them to survive for longer than those who bet on favorites. This relative advantage results in overvaluation of longshots in the long run.

Adjusting Bookmaker’s Odds to Allow for Overround

Several methods have been proposed to adjust bookmakers’ implied probabilities, including an additive model, a normalization model, and an iterative method proposed by Shin. These approaches have one or more defects: the additive model can give negative adjusted probabilities, normalization does not account for favorite long-shot bias, and both the normalization and Shin approaches can produce bookmaker probabilities greater than 1 when applied in reverse. Moreover, it is shown that the Shin and additive methods are equivalent for races with two competitors. Vovk and Zhadanov (2009) and Clarke (2016) suggested a power method, where the implied probabilities are raised to a fixed power, which never produces bookmaker or fair probabilities outside the 0-1 range and allows for the favorite long-shot bias. This paper describes and applies the methods to three large bookmaker datasets, each in a different sport, and shows that the power method universally outperforms the multiplicative method and outperforms or is comparable to the Shin method.

Towards an Understanding of the Origins of the Favourite–Longshot Bias: Evidence from Online Poker Markets, a Real‐money Natural Laboratory

Evidence of differential returns to bets placed with different probabilities of success has revealed a broadly systematic tendency for low/high‐probability events to be relatively overbet/underbet, a phenomenon known as the favourite–longshot bias. While most of the literature focuses on sports, especially horse racing, we report here the existence of the same phenomenon in online poker games. We find that misperception rather than risk‐love offers the best explanation for the behaviour that we identify. This paper contributes to the more general literature explaining betting behaviour as well as the prevalence of the favourite–longshot bias in betting markets.

Estimating Subjective Win Probabilities from Money Lines

We contribute to the literature on money line betting markets by investigating the relationships between the various methods used to derive subjective win probabilities from money lines. We show that, although the seven methods described appear to be unique, they actually share many common assumptions and that, surprisingly, they reduce to three distinct estimates of bookmaker commission and subjective win probabilities. We also show that among the three distinct estimates, one is biased when money lines suggest a very heavy favorite in a particular sporting event. Thus, it is important to consider the assumptions for each method when deciding which to use in a particular context. Two empirical examples demonstrate how a market inefficiency, such as a long-shot favorite bias, should influence the choice of methodology.

Does Belief Heterogeneity Explain Asset Prices: The Case of the Longshot Bias

This article studies belief heterogeneity in a benchmark competitive asset market: a market for Arrow–Debreu securities. We show that differences in agents' beliefs lead to a systematic pricing pattern, the favourite–longshot bias (FLB): securities with a low-pay-out probability are overpriced, whereas securities with high probability pay-out are underpriced. We apply demand estimation techniques to betting market data, and find that the observed FLB is explained by a two-type population consisting of canonical traders, who hold virtually correct beliefs and are the majority type in the population (70%); and noise traders exhibiting significant belief dispersion. Furthermore, exploiting variation in public information across markets in our data set, we show that our belief heterogeneity model empirically outperforms existing preference-based explanations of the FLB.

Are the odds odd? Positive return evidence in German horse race betting

The article deals with the question, if odds derived from the behavior of bettors in a pari-mutuel setting really reflect the chances of winning for a particular horse in a particular race. Using a unique data set with more than 46,000 race observations from Germany for the years 2001 to 2003 the paper presents evidence on the favorite long-shot bias, evaluates the predictive power of totalizator odds, uses a binary logistic regression model to predict probabilities of winning and finally suggests three wagering strategies that actually yield positive returns in a hold-out oriented analytical setting.

Betting Markets Efficiency: Evidence from European Football

This paper uses data from up to 79 bookmakers in any one match to analyze the efficiency of European football betting markets during the 2005/2006 season. We first examine the empirical derivatives of the longshot bias, and find that the bias is much more pronounced for high-grade matches. This arguably supports the information-based explanation of the longshot bias. We also show that internet betting, by giving access to a large number of bookmakers, improves significantly bettors' potential return. Finally, we find that average odds do not provide the best estimate of the likelihood of a result. Indeed, the best available odds are informative as well, even after controlling for the average odds.

APPLICATIONS OF AN SPRT-LIKE TEST IN PARI-MUTUEL WAGERING

Pari-mutuel wagering functions as a very simple financial market, and has therefore been important in studying market efficiency. In this study, an SPRT-like test reveals that probabilities from the win pool corrected for the favourite longshot bias using Asch and Quandt’s regression equation can be used to exploit the exacta pool, and probabilities obtained from the exacta pool can be used to exploit the win pool. These finding differ from previously published studies that maintain that the win pool is largely efficient. Further, these findings mirror statistical arbitrage strategies utilized by hedge funds, where pricing inefficiencies are exploited between related assets.

EFFICIENCY IN BETTING MARKETS: EVIDENCE FROM ENGLISH FOOTBALL

We analyze the efficiency of English football betting markets between 2002 and 2006. We find evidence of a positive favourite-longshot bias for both home odds and away odds. Draw odds are instead characterized by a negative longshot bias. We also identify a draw bias in the sense that betting at draw odds yields a higher return than betting at home or away odds. Finally, we investigate betting strategies that exploit the variance of odds between bookmakers.

Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences

A large body of evidence has documented that risk preferences depend nonlinearly on outcome probabilities. We discuss the foundations and economic consequences of probability-dependent risk preferences and offer a practitioner's guide to understanding and modeling probability dependence. We argue that probability dependence provides a unifying framework for explaining many real-world phenomena, such as the equity premium puzzle, the long-shot bias in betting markets, and households' underdiversification and their willingness to buy small-scale insurance at exorbitant prices. Recent findings indicate that probability dependence is not just a feature of laboratory data, but is indeed manifest in financial, insurance, and betting markets. The neglect of probability dependence may prevent researchers from understanding and predicting important phenomena.

ARE SURVEYS OF EXPERTS UNBIASED? EVIDENCE FROM COLLEGE FOOTBALL RANKINGS

Policymakers are frequently interested in soliciting unbiased information regarding alternative policies, and expert surveys can be influential. As ranking policies is an often subjective process, there is always the concern of bias, both intentional and not. Expert bias is difficult to discern in the policy world, but surveys of expert opinion are compiled and “tested” for accuracy weekly in college football, allowing for hypothesis testing. Although previous research has used college football rankings to determine the ability of surveys to incorporate relevant information, this article examines the Associated Press and American Football Coaches' Association rankings for evidence of systematic bias. Specifically, more than 1,300 games from the 2003 to 2008 regular seasons are tested for factors that are systematically correlated with upsets. Both polls predict the winner nearly 80% of the time, and although there is evidence of systematic conference bias, correcting the rankings would only improve the accuracy of the polls by about 1%. There is no evidence of a bias favoring “big market” teams, nor teams that have strong journalism programs or are from the East Coast. (JEL D4, L8)

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