I know, I’ve been mega quiet on the blog front, hopefully this will start to make up for things. I’m just throwing out some random things I’m looking at.
Many people have tried to model goals in football (soccer matches) accurately and I appreciate I may be going over old ground to some. What I’m doing is throwing out what I’m currently working on, and also putting it, I hope, into an easier to digest example than many of the research papers.
Poisson distribution is the random distrubuiton of events, in our case goals. The are many great sources of reference for this but wikipedia, as always, would be a great starting point. Should you wish to read some research papers for a more in depth knowledge these can also be found online.
To calculate poisson distrubition, in Excel in our case, we need to first calculate the averge number of events in the given time frame.
I’ve pulled together the results of the premier league from 1996 onwards quickly from the wonderfully useful Football Data.
By quickly adding together all of the goals scored we can find a rounded average of 2.6 goals per game. By using this, and the information in the Excel help file, we can then model the probable distribution of goals within a footbal match.
Poisson probabilities based on an average 2.6 events (goals), please note these numbers are rounded…
|Poisson probabilities based on an average 2.6 events (goals)|
By now knowing what our given poisson distrubition is we can model the number of games in the Premier Leage we believe will have this number of goals, which is fairly accurate
By putting this information in a graph we can visualise this much better, and it certainly appears that goals within the premier league do follow the poisson distrubition.
We can test the effectiveness of this prediction by using the chi-square test. In this case our chi-square test result is 0.00078, which passes with flying colours.
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