Bookmaker Margins and Favourite-Longshot Bias in Football Prediction Markets
27 Pages Posted: 15 Sep 2017 Last revised: 29 Sep 2017
Date Written: September 12, 2017
In this article we discuss bookmaker margins embedded in odds for "1X2" bets in the European football betting markets operated by bookmakers. Bookmaker margins are adjustments applied to fair odds, for the purpose of ensuring profits and compensation for risks undertaken, and to cover overall operational costs. They are observable on a per match basis as the excess of the sum of the reciprocals of odds over one, which is popularly referred to as overround. In this article we study the margins from a risk point of view. We derive the expression for the expected variance of a portfolio of bets, in order to study risk-based determinants of margins. Risk of a portfolio of bets is shown to be particularly sensitive to the presence of low probability bets (longshots). We propose a new, risk-based measure for quantifying balancedness of a match. Using this measure along with the standard entropy measure, we investigate variations of overrounds between matches of different levels of balancedness. Our analysis shows that there is no a convincing empirical evidence that overall overrounds are dependent on the match balancedness. Similarly, the study of variations of overrounds by the levels of disagreement in probabilities between different bookmakers, does not show any significant interdependence. On the other hand, our study confirms the pervasiveness of a well known Favourite-Longshot Bias (FLB) in the European football betting markets. The odds have been more favourable for bets on favourites than for longshots. These conclusions suggest that margins are determined on a match-per-match basis. Long odds on longshots are being adjusted more aggressively downwards than short odds on favourites, while overall margins are being kept roughly at bookmaker-specific target levels. Empirical studies were performed using the historical data on 116,150 football matches, containing results and odds from 13 major bookmakers. The data set covers 19 major European football divisions during the last 17 years. Using this rich and recent data set, we also investigated the time evolution of overall margins, and variations of margins between the different bookmakers and football divisions.
Keywords: football betting, prediction markets, prediction bias, favourite-longshot bias, risk management, odds, overrounds, market microstructure
JEL Classification: G14, C57, C70, C81, C55, C58, C49, G02, L11, Z20
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