The Poisson distribution is typically used as a model for goals scored or for goal differences in football. Other distributions provide a better fit. For example, it seems that the bivariate Poisson distribution is the most popular in the trading world – although it has some significant limitations. In any case, Poisson distribution provides a good starting point.
How to calculate expected goals
The article Poisson Distribution: Predict a soccer betting winner provides a step-by-step method on how to apply the Poisson distribution to predict goals scored per team. The technically inclined may wish to read the more academic approach by Maher.
In essence, for each team playing a match, one needs to calculate their predicted average goals to be scored. This is dependent on the average goals scored in the past, their relative attack strength at home/away (that is a 103% would mean that this team scores 3% more at home than a typical team) and the opposing team defence strength.
For two teams that are expected to score 1.25 goals per match, the chance of a draw is 27% while that of a win for either team is 36.5%.
Although short tournaments, such as the Euro, may not have the intricacies of dealing with home and away goals since practically all teams are playing away, they are harder to deal with mainly due to the parameter error.
National teams play less frequently than club teams. Moreover a tournament held over a few days may be more affected by the immediate performance, rather than the performance over months. In Unpredictability in Euro 2016, I suggested that it is more likely to see Wales win the Euro than what Leicester City actually achieved mainly due to random fluctuation.
Hence, we would need to guess, or make presumptions, about the expected goals to be scored per team. In this article I will show how a small fluctuation may greatly affect the final results. In modelling parlance, this would be an exercise of stress testing our model.
Base rate of 1.25 goals per match
Let’s start off with two teams that are expected to score 1.25 goals per match. In this case, the chance of a draw is 27% while that of a win for either team is 36.5% To get the gist of how these values were obtained, refer to the aforementioned article on Poisson Distribution.
What if the goal rate was wrong by just 0.1? Well, if one team has a 1.35 goal rate, their chances of winning would increase by 2.6% to 39.1%, while the chance of a draw drops marginally by 0.6%.
This is assuming the average goal rate for the opposing team stays at 1.25 goals per game. The effects of a 0.1 drop in goal rate are similar, being a decrease of 2.8% chance of winning the match.
Base rate of 2 goals per match
If both teams are high scoring, one would expect a draw to be more unlikely. For example in the case of an average rate of 2 goals to be scored, a draw is only 20% likely.
The difference in a the chances of a draw between using parameters of 2 and 1.25 expected goals per match is from 20% to 27% - an equivalent odd from 5.00 to 3.70.
If one team has a 0.1 higher rate (2.1 goals) or 0.1 lower , the effects on a draw are minimal at a maximum of 1% discrepancy. However, the probabilities of winning or losing changes by 2%. We see more fluctuations at a lower expected rate, partially because 0.1 difference is a larger percentile (8%) in the 1.25 as a parameter than 2 (5%).
One can observe that small changes barely have an effect. The interesting part is if the parameter estimate is more off-track. Consider that the difference in a draw between using parameters of 2 and 1.25 is from 20% to 27% - an equivalent odd from 5.00 to 3.70.
If there is one lesson to be learned here is to examine how a small change in your parameter value may affect results, before blindly trusting results.
See the latest Euro 2016 odds, including method of victory, Asian handicap markets, clean sheet wins much more under the left-hand side menu Bet Options/Specials!
See the latest Euro 2016 odds, including method of victory, Asian handicap markets, clean sheet wins and much more under the left-hand side menu Specials!