ABSTRACT
There are two distinct strands of empirical literature on modelling the outcomes of matches in association football (soccer). The first approach involves modelling the numbers of goals scored and conceded directly. Forecasts of win-draw-lose match results can be derived indirectly, by aggregating the estimated probabilities assigned to appropriate permutations of goals scored and conceded by the two teams. The second approach involves modelling win-draw-lose results directly, using discrete choice regression models such as ordered probit or logit. Using data on English league football, Goddard (2005) has recently drawn comparisons between the forecasting performance of statistical models based on each of these two approaches. The models are estimated using the same data, and are used to produce forecasts for the same set of matches. The difference in forecasting performance between the
two types of models turns out to be rather small. This finding may explain why both goals-based and results-based models have been used in the recent applied statistics and econometrics literatures, with neither of these two approaches seeming to dominate the other. In this chapter, we present a similar analysis based on data on Scottish league football. Accurate forecasting is important primarily to bookmakers and bettors, who may
have a significant financial interest in being able to assess accurately prior probabilities for football match results. Research concerning the relationship between the odds set by bookmakers for bets on the outcomes of sporting contests, and the probabilities associated with these outcomes, forms a subfield within the literature on financial market efficiency. Although much of this literature focuses on racetrack betting, the market for fixed-odds betting on match outcomes in professional football has also attracted some attention. A divergence between the bookmakers’ odds and the true probabilities implies a violation of the condition for the efficiency of the fixed-odds betting market, and creates opportunities for sophisticated bettors to extrapolate from historical data on match outcomes (or other relevant information), in order to formulate a betting strategy that yields either a positive return, or (at least) a loss smaller than would be expected by an unsophisticated or indiscriminate bettor due to the loading contained in the odds that allows for the bookmaker’s costs and profit. Much of the literature on the efficiency of the fixed-odds betting market focuses on betting on English football. This chapter extends the range of evidence that is available in this literature, by presenting for the first time an analysis of the efficiency of the fixed-odds betting market for Scottish league football. This chapter is structured as follows. Section 6.2 reviews the previous academic
literature on modelling goal scoring and match results in association football (soccer). Section 6.3 specifies the models that are estimated in this study. Section 6.4 describes the Scottish league football match results data set, and presents and interprets the estimation results for the goal-based and results-based models. Section 6.5 presents an analysis of the efficiency of the market for fixed-odds betting on Scottish league football. Finally, Section 6.6 summarizes and concludes.
