The implied volatility of a sports game

Abstract

In this paper we provide a method for calculating the implied volatility of the outcome of a sports game. We base our analysis on Stern's stochastic model for the evolution of sports scores (Stern, H. S. 1994. "A Brownian Motion Model for the Progress of Sports Scores." Journal of the American Statistical Association 89:1128-1134.). Using bettors' point spread and moneyline odds, we extend the model to calculate the market-implied volatility of the game's score. The model can also be used to calculate the time-varying implied volatility during the game using inputs from real-time, online betting and to identify betting opportunities. We illustrate our methodology on data from Super Bowl XLVII between the Baltimore Ravens and the San Francisco 49ers and show how the market-implied volatility of the outcome varied as the game progressed.