![]() The average loss rates across all bets are higher than suggested by the usual calculation of the bookmaker’s margin, based on the sum of the inverses of the odds. We also document another market inefficiency. Figure 1 shows a pronounced pattern of favourite-longshot bias, supporting previous evidence for European soccer with a smaller dataset presented by Angelini and De Angelis (2019). We then sort the data into deciles of this estimated probability and then calculate the average payoff on a €1 bet for each set of bets. We use this method to estimate the probability of winning for 252,690 bets placed on 84,230 European soccer matches played between 20. If the margin has been applied equally across all bets, we can ‘normalise’ the probabilities to get the true probabilities as 50% for an Arsenal win, 20% for a draw, and 30% for a Chelsea win. But these probabilities sum to 105% this is due to the bookmaker’s profit margin. In this case, Arsenal would have a 52.5% probability of winning, Chelsea a 31.5% probability of winning, and there would be a 21% chance of a draw. ![]() If bookmakers are not expected to make profits on average, you can calculate the probabilities of the outcomes as the inverse of these odds. For example, suppose you are betting on Chelsea versus Arsenal and the amounts you will get back with a winning €1 bet will be €1.90 if you bet on Arsenal to win, €4.76 if you bet on the draw, and €3.17 if you bet on Chelsea to win. Under the null hypothesis that all bets are priced with the same profit margin, it is easy to extract the implied odds and the bookmaker’s margin from these markets. These bookmakers are known to engage in various restrictive practices, limiting how much can be placed and banning serial winners. This is how the ‘high street’ European bookmakers take most of their bets on soccer. The traditional way to bet on soccer is to back one of the three possible outcomes. Here, we summarise our evidence and discuss its implications for understanding the key factors underlying favourite-longshot bias. For the same set of matches, we find one market shows a strong pattern of favourite-longshot bias while the other does not. In a recent paper (Hegarty and Whelan 2023a), we compare two different fixed odds markets for betting on European soccer. 2017) while others have not (Paul and Weinbach 2005). Some studies have found favourite-longshot bias in fixed-odds markets (Berkowitz et al. If a bettor accepts this offer, their odds are not changed by subsequent actions of other bettors. Instead, it features fixed odds set by bookmakers, who make offers like “You take back €3 if your pick wins and lose your €1 bet otherwise”. Modern online sports betting does not use the pari-mutuel structure. ![]() Explanations for this pattern include people being unable to judge small probabilities correctly (Thaler and Ziemba 1988) and some bettors enjoying taking riskier bets (Quandt 1986). Money placed on the favourites loses less than money placed on longshots. Research has shown that pari-mutuel betting on horses – where the money placed is pooled and paid back to those who picked the winners minus a fraction that goes to the operator – features a ‘favourite-longshot’ bias (Snowberg and Wolfers 2008). This raises the question of what happens to the money being gambled. Over 30 US states have now legalised sports betting and huge sums are being spent on marketing by new bookmaking firms to attract new clients. Online betting on sports has grown substantially in the last decade and is projected to become a huge market in the US after the Supreme Court abolished federal restrictions on sports betting in 2018.
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