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.