Aim: Chance, risk and uncertainty are expressed in various formats for decision-makers in everyday-life. In the sports-betting market the probabilities for different outcomes (e.g., Barcelona FC will beat Arsenal FC, Lee Westwood will win the 2011 Open Championship) are reflected by odds, which also determine the amount of money that consumers of betting products (henceforth punters) will receive if their bets turn out to be successful. Typically, odds are fixed and set in advance by betting firms that have proven to be extremely accurate in this task (Forrest et al., 2005; Deschamps, 2008). In Europe odds are generally expressed in either decimals (e.g., 1.61) or fractional numbers (e.g., 8/13), where the latter format is restricted to be used in the UK and Ireland. As odds can be easily converted into implicit probabilities, they may be seen as rare examples of highly predictive probabilistic forecasts. Punters are an ideal group to study when it comes to learn about how people understand and consider quantitative measures of chance, because they are not only exposed to probabilistic information but also they put their own money at stake when making decisions and, accordingly, they should be motivated to avoid judgmental biases. Surprisingly, there is limited research on the ability of punters. Thus, the aim of this paper is to empirically address the questions: Do punters realistically perceive odds? Does the presentation format affect how realistically odds are perceived?
Method: 68 punters responded to a web-based questionnaire where they evaluated two randomly presented sets of 10 bets involving different odds. The sets were identical except for the format (= within-subjects design): set A had bets with decimal-odds, while set B had bets with fraction-odds. The odds reflected 10 different levels and were sampled from a season of English Premier League Football matches. For each of the 20 bets, the participants were asked to imagine 100 such bets and estimate how many that would come true. In connection, they also reported their confidence on a 7-points scale and provided an interval for the given estimate.
Results: Across the ten different bets, the estimates of the mean participant were somewhat realistic, although there were systematic deviations from the true implicit probabilities. The deviations were linked to the presentation format in that the participants, on average, tended to underestimate bets with odds expressed as decimals and overestimate bets with odds as fractional numbers (M=-3.69 vs. 4.49). Greater confidence was also associated with the former format.
Conclusions: Consistent with prior research on the perception of probabilistic information (e.g., Gigerenzer 2002), the perception of the odds was affected by the presentation format. Though the difference between the formats could be due to psychometrical aspects, we attribute it to the fact that the Swedish punters are more familiar with the decimal-format. The most surprising finding was that the punters underestimated the probabilities when odds were presented as decimals. We see three tentative explanations for this finding: (1) punters truly underestimate probabilities, (2) our participants deliberately adjusted their probability estimates so that they included the take-out-rate of the betting firms (betting firms adjust their odds so that they will make a profit of x%), (3) our participants assessed probabilities that were well calibrated to their prior experiences but failed to understand that the prior experience is biased by the take-out-rate of the betting firms. The questions of (i) whether or not the format-difference is caused by familiarity and (ii) why probabilities are underestimated with the decimal format are explored in two follow up studies with similar designs.
Twenty-third bi-annual meeting of the European Association for Decision Making (SPUDM) in Kingston Upon Thames (UK).