Poisson distribution for modelling football scores
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i am trying to write code for a poisson model which calculates the probability of multiple score outcomes in a match given a teams attack score and defence score. the issue is i have no values for attack and defence scores and have been told that i need to use paramaters mu and lambda with values alpha(attack strength) and beta(defence strength) for either the home or away team, to do this i need to calculate the loglikelihood and use fmincon but i have no idea where to even start with this
Image Analyst on 18 Dec 2020
Why do you think it's Poisson? If I were you, I'd get a list of thousands of game scores and do a scatterplot of winning scores vs. losing scores. Then use that to get a probability distribution. Maybe it's Poisson, maybe it's not. You can either use the actual emprical distribution, or try to model it to a reasonable function. Do you have a list of such scores?
Raunak Gupta on 18 Dec 2020
For the specific football model, I will recommend referring the literature either in some standard book or in a research paper to get the mathematical model. For using the Poisson distribution, you may refer to poissrnd and some relevant examples mentioned here. For setting up optimization problem and solving it you can read the fmincon documentation.