On Two Regression Methods for Testing Efficiency in Betting Markets

Betting markets are efficient if expected payouts on all possible bets on an event are equal. We compare two regression-based methods for testing for efficiency that have been used in previous research: One that uses normalized probabilities as the explanatory variable for payouts and one that uses the inverse of the decimal odds. We show that the normalized probability method produces good tests of the null hypothesis but that the inverse odds method does not, with results biased against finding favorite-longshot bias. We illustrate this finding using regression with data on odds and outcomes from betting on tennis and European soccer and also with bootstrapped simulations