Constant Bet Size? Don't Bet on It! Testing Expected Utility Theory on Betfair Data

Abstract

I analyze the risk preferences of bettors using data from the world's largest betting exchange, Betfair. The assumption of a constant bet size, commonly used in the current literature, leads to an unrealistic model of bettors' decision making as a choice between a high return - low variance and low return - high variance bet, automatically implying risk-loving preferences of bettors. However, the data show that bettors bet different amounts on different odds. Thus, simply by introducing the computed average bet size at given odds I transform the bettor's decision problem into a standard choice between low return - low variance and high return - high variance bets, and I am able to correctly estimate the risk attitudes of bettors. Results indicate that bettors on Betfair are either risk neutral (tennis and soccer markets) or slightly risk loving (horse racing market). I further use the information on the average bet size to test the validity of Expected utility theory (EUT). The results suggest that, when facing a number of outcomes with different winning probabilities, bettors tend to overweight small and underweight large differences in probabilities, which is in direct contradiction to the linear probability weighting function implied by EUT.