The following gives an outline of how the simulator works. To understand this, requires an understanding of three steps: First, how each team is assigned a dynamically adjusted rating, to estimate its strenght relative to its opponents. Second, how historial ratings and match outcomes provides a basis for predicting outcomes of a single match. Third, how predictions for matches are combined to predict the final league table.
The strenght of each team is estimated through ratings. The ratings used are based on the work of Arpad Elo (Elo, 1978), which originally was used in the context of chess. Several adaptations of this rating has been proposed, and the Football League Simulator adopts the variant given by Hvattum and Arntzen (2010), where rating adjustments are influenced by the victory margins and not just whether a match ends in a home win, draw, or away win.
Before a given match, the home team and the away team both have a rating. Using lots of historical data, one can look at how the match results vary depending on the difference in ratings between the teams. In the Football League Simulator (and in Hvattum and Arntzen, 2010), ordered logit regression (Greene, 1999) is used to estimate probabilities of possible outcomes (home win, draw, or away win) as a function of the rating difference. It can be shown that this way of obtaining probabilities works fairly well, though not quite as well as relying on market odds.
However, being able to create probabilities for the outcomes of any future fixture while relying only on a single number (the rating) has the advantage of being very simple to use for simulating the final league table. In the Football League Simulator, an efficient Monte Carlo simulation is built to take care of this: given a current rating for each team, probabilities are generated for each remaining match of the league and a random number generator provides the required input so that the league can be simulated with a large number of repetitions (the current version of the Football League Simulator relies on using 200,000 repetitions).
While the odds for a single match is hugely affected by specific issues such as injuries, suspensions, and the number of rest days between fixtures, these issues may tend to cancel out during the course of a full season. Hvattum (2013) presented recent research on the betting market for league winners, and found indications that a basic version of the procedure outlined above creates better probabilities than that of the betting market. In particular, over two seasons and five different leagues, a betting procedure based on the model staked about 219 units for a profit of about 28 units.
There is one limitation of the current version of the simulator (to be improved in later updates), regarding how goal differences are handled. The model predicts match results, and only an ad hoc producedure is added to handle the number of goals scored. Therefore, whenever the league standings are based on using goal differences as the primary tie-break when two or more teams have the same number of points, one could expect that the predictions may be of poorer quality near the end of the season (in particular with only one or two rounds left).
A. E. Elo. The rating of chessplayers, past and present. New York: Arco Publishing, 1978.
W. H. Greene. Econometric analysis (4th ed.). Upper Saddle River, NJ: Prentice Hall, 1999.
L. M. Hvattum and H. Arntzen. Using ELO ratings for match results prediction in association football. Internation Journal of Forecasting, 26:460-470, 2010.
L. M. Hvattum. Analyzing information efficiency in the betting market for association football league winners. The Journal of Prediction Markets, 7:55-70, 2013.