Favorite-longshot Bias Research Articles

Comparing Two Methods for Testing the Efficiency of Sports Betting Markets

Sports betting markets can be considered strongly efficient if expected returns on all possible bets on an event are equal. If this form of efficiency holds, then there is a direct mapping from betting odds into probabilities of outcomes of sporting events. We compare two regression-based methods for testing this form of efficiency that have been used in previous research: One that uses normalized probabilities as the explanatory variable for event outcomes and one that uses the inverse of the decimal odds. We show that the normalized probability method produces good tests of the null hypothesis of strong market efficiency but that the inverse odds method does not, with results biased against finding favorite-longshot bias. We illustrate this finding using large datasets of bets and outcomes for tennis and soccer and also with realistic simulations.

Re-examining the bias and market inefficiency in eSports betting markets: On the application of multivariate regression model

Favorite-longshot and reverse favorite-longshot biases have become widespread in various traditional sports betting markets in recent years. However, there is a limited number of investigations that have been conducted on the eSports betting market or the bettors that operate within it. In the present research, we have made efforts to re-examine the bias and market inefficiency in four typical eSport games: League of Legends, Counter-Strike: Global Offensive, Dota 2, and King of Glory. Due to the natural characteristics of e-sports, we analyze the reasons for the market biases from 4 aspects: commission, region, match format, and tournaments. We find that both the favorite-longshot and reverse favorite-longshot bias occur in eSports. Moreover, the distribution of these betting biases is completely different among different eSports game titles and tournaments. The results of the weighted linear regression model reveal that long match format is the important factor of long-short bias, while regional tournaments are the important factor of reverse long-short bias in League of Legends.

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.

Calcutta auctions

ABSTRACT This analysis is the first study to examine an emergent wagering market: the Calcutta auction. Participants in Calcutta auctions bid for entrants that compete to earn a pre-determined percentage of an unknown total pot size. Utilizing 13-year data from an in-person Calcutta auction of NCAA men’s basketball tournament teams, evidence exists of a traditional favourite-longshot bias, of lower overall returns existing for teams in the middle of the team quality distribution and of auction participants being unable to correctly identify (through higher bids) teams that ultimately win more games after their quality is taken into account.

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.

What drives biased odds in sports betting markets: Bettors’ irrationality and the role of bookmakers

In sports betting markets, bookmakers may take speculative exposures to the game outcomes when they can assess the probabilities better than others. We propose a simple model of fixed-odds betting markets in which bookmakers tilt their odds to maximize their own speculative profits. They do so by accommodating bettors’ irrationality, thereby reinforcing systematic biases in betting markets. In European football betting markets, the Favorite-Longshot Bias and the Hot-Hand Bias persist despite the increased competition. This is difficult to explain only by bettors’ irrationality but consistent with the predicted odds-setting behavior of bookmakers. We discuss the implications for financial market anomalies.

Liquidity, Favorite-Longshot Bias, and the Return of Lottery-Like Stocks

Liquidity, Favorite-Longshot Bias, and the Return of Lottery-Like Stocks

Betting market efficiency and prediction in binary choice models

Implied winning probabilities are usually derived from betting odds by the normalization: inverse odds are divided by the booksum (sum of the inverse odds) to ensure that the implied probabilities add up to 1. Another, less frequently used method, is Shin’s model, which endogenously accounts for a possible favourite-longshot bias. In this paper, we compare these two methods in two betting markets on soccer games. The method we use for the comparison is new and has two advantages. Unlike the binning method that is used predominantly, it is based on match-level data. The method allows for residual favourite-longshot bias, and also allows for incorporation of match specific variables that may determine the relation between the actual probability of the outcome and the implied winning probabilities. The method can be applied to any probabilistic classification problem. In our application, we find that Shin’s model yields unbiased estimates for the actual probability of outcome in the English Premier League. In the Spanish La Liga, implied probabilities derived from the betting odds using either the method of normalization or Shin’s model suffer from favourite bias: favourites tend to win their matches more frequently than the implied probabilities suggest.

An Effective Approach for Exploiting the Inefficiencies of the Italian Football Betting Market

In this paper, the author analyses the main inefficiencies of the Italian Serie-A betting market: in particular, using previous findings on the favourite-long shot bias, the team scoring home advantage and the league winner scoring advantage, a strategy aimed to outperform the market will be presented. By testing the betting scheme over the past 19 seasons, it was possible to obtain an average return per bet of 9.31%, with 16 of the 19 years resulting in positive financial returns. In order to verify the computations, different betting odds databases were used. The results obtained are particularly significant for two reasons: firstly all computations were performed on market average coefficients, leaving on the table an additional 3-4% of profit, which could be obtained by using best coefficients among bookmakers and secondly compared to market benchmarks and other betting strategies, the net profit is considerably higher. In particular other three strategies were used as a benchmark: the first one uses the favourite-long shot bias, the second one the Home factor and the third one the league favourite team advantage. All these betting schemes performed more poorly, with the second best strategy scoring on average 6% worse. After analysing possible future improvements, in the final section the author describes how the findings of this paper may be applied to other betting markets, such as different football leagues, basketball, hockey and tennis.

On prices and returns in commercial prediction markets

The Commodity Futures Trading Commission (CFTC) has recently licensed a commercial prediction market to operate in the US. With regulatory restrictions lifted, these markets can now play the important role that has been often envisaged for them. For example, investors can use them to hedge various event-related risks directly rather than indirectly via portfolios expected to move a certain way if events occur. Commercial prediction markets charge fees, an element that has not been incorporated into previous theoretical work on these markets. We examine the impact of fees on prediction market prices and returns by introducing them to a model in which the market price equals the true probability when there are no fees. We find that existing fee models mean contract prices for low probability outcomes are below the true probability but the impact of fees means prediction markets feature a form of favorite-longshot bias: Post-fee loss rates depend negatively on the probability of the event being backed. We show this result holds even if prediction market operators set a fee structure that is more generous to contracts with a low probability of success.

Market efficiency and the Greek fixed-odds betting market

PurposeThe purpose of this study is to empirically examine the efficiency of Greek fixed-odds (offline) betting market as offered by OPAP for the period 2016–2019.Design/methodology/approachUsing a four-year data sample of OPAP's opening and closing odds for football matches from all over the world and applying linear probability and probit models, the market efficiency is examined and the existence of possible anomalies is investigated.FindingsThe main findings of research suggest that although the odds are dominated primarily by favorite-longshot bias and secondarily by draw bias, this mispricing cannot prove profitable. However, the opening odds, the margin levels and the market structure provide information that is not fully captured by the closing odds, giving bettors profit opportunities. Thus, findings show that the semi-strong market efficiency is questionable. Finally, competition reduces commissions leading to more efficient odds.Practical implicationsThe conclusions of this study are useful for football betting market and, particularly, for government authorities, bookmakers and bettors. Findings can be extended in future research to prediction tasks.Originality/valueTo the best of the authors’ knowledge, this is the first study about the Greek football betting market. The contribution to the literature lies on the one hand in the examination of a monopolistic land-based betting market, which is being squeezed and threatened by the more competitive online betting market, and on the other hand in the simultaneous examination of the opening and closing odds.

Informational efficiency and behaviour within in-play prediction markets

Studies of financial market informational efficiency have proven burdensome in practice, because it is difficult to pinpoint when news breaks and is known by some or all the participants. We overcome this by designing a framework to detect mispricing, test informational efficiency and evaluate the behavioural biases within high-frequency prediction markets. We demonstrate this using betting exchange data for association football, exploiting the moment when the first goal is scored in a match as major news that breaks cleanly. There are pre-match and in-play mispricing and inefficiency in these markets, explained by reverse favourite-longshot bias (favourite bias). The mispricing tends to increase when the major news is a surprise, such as a goal scored by a longshot team late in a match, with the market underestimating their chances of going on to win These results suggest that, even in prediction markets with large crowds of participants trading state-contingent claims, significant informational inefficiency and behavioural biases can be reflected in prices.

Betting market equilibrium with heterogeneous beliefs: A prospect theory-based model

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.

Changes in risk preferences: Evidence from Swedish harness horse racing data

We measure the time variation of risk preferences in real market data. We utilize data on Swedish tote-betting on horse races for the period 1995 to 2015 and show that risk preferences among horse-race bettors change with economic conditions. More specifically, we extract a measure of risk-aversion based on the favorite-longshot bias (FLB) and provide evidence that the computed measure follows the consumer-confidence index. In addition, we show by an application that the FLB-based risk-preference measure sharpens the predictions of a simple forecasting model for Swedish industrial production. Furthermore, we show that risk-aversion consistently increases following shocking news on disastrous events, including non-economic events such as natural disasters and terrorist attacks. We argue that emotions, such as fear, are the likely explanation for this variation.

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.

What Can Betting Markets Tell Us About Investor Preferences and Beliefs? Implications for Low Risk Anomalies

An empirical puzzle in financial markets, known as the low-risk anomaly, is that riskier assets earn lower risk-adjusted returns than less risky assets. Theories for this phenomenon focus either on market frictions, such as leverage costs, or non-traditional preferences for lottery-like payoffs. We relate the low risk anomaly to the Favorite-Longshot Bias in betting markets, where returns to betting on riskier longshots are lower than returns to betting on favorites, and provide novel evidence to both anomalies. Synthesizing the evidence, we study the joint implications from the two settings for a unifying explanation. Rational theories of risk-averse investors with homogeneous beliefs cannot explain the cross-sectional relationship between diversifiable risk and return in betting markets. Rather, we appeal to models of non-traditional preferences or heterogeneous beliefs. We find that a model with reference-dependent preferences, featuring probability weighting and diminishing sensitivity, two features of Cumulative Prospect Theory, best fits the data, and is able to capture the choice and the amount to bet. Calibrated parameter values for probability weighting and diminishing sensitivity that capture financial markets facts can simultaneously explain the betting market facts. However, explaining the choice to bet is at odds with loss-aversion, a feature of Cumulative Prospect Theory often used in financial markets applications.

Implications of Belief Distribution and Loss Aversion for Betting Market Anomalies

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 traders 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 impact of probability weighting, loss aversion, belief concentration, and belief tailedness. We show how these parameters jointly determine the property of the equilibrium price. Empirical results also suggest this model has adequate flexibility to explain the behavior of actual historical data.

Informational Efficiency and Price Reaction Within In-Play Prediction Markets

Studies of financial market informational efficiency have proven burdensome in practice, because it is difficult to pinpoint when news breaks and is known by some or all the participants. We overcome this by designing a framework to detect mispricing, test informational efficiency and evaluate the behavioural biases within high-frequency prediction markets. We demonstrate this using betting exchange data for association football, exploiting the moment when the first goal is scored in a match as major news that breaks cleanly. There are pre-match and in-play mispricing and inefficiency in these markets, explained by reverse favourite-longshot bias (favourite bias). The mispricing tends to increase when the major news is a surprise, such as a goal scored by a longshot team late in a match, with the market underestimating their chances of going on to win. These results suggest that, even in prediction markets with large crowds of participants trading state-contingent claims, significant informational inefficiency and behavioural biases can be reflected in prices.

Parimutuel betting on the eSports duels: Evidence of the reverse favourite-longshot bias

Abstract We analyse betting behaviour patterns of the visitors of the specialized betting website dedicated to the popular eSports game Counter-Strike: Global Offensive. The reverse favourite-longshot bias is found, which is rather unusual for parimutuel betting markets, where favourite-longshot bias is more common. We define simple betting strategies based on the bets on underdogs and show that these strategies make a sufficiently large positive profit both on the in-sample and out-of-sample datasets, which is a sign of market inefficiency. In matches with popular underdogs, the sentiment bias decreases the market inefficiency caused by the reverse favourite-longshot bias. At the same time, the role of the geographical location of teams in the reverse favourite-longshot bias is only marginal.