I could be totally off but when performing a regression a constraint needs to be implemented. I believe there is a flaw in the above analysis. I stumbled upon this possible error as I have been reconstructing "Analysis of sports data by using bivariate Poisson models" by D Karl's et al and applying regression to the data above.

If you were to do this

response = Riffle[hgoals, agoals]
GeneralizedLinearModelFit[{X, response}, ExponentialFamily -> "Poisson"]

You get an error, "The rank of the design matrix 40 is less than the number of terms 41 in the model. The model and results based upon it may contain significant numerical error."

There needs to be a constraint in the regression. Maybe I am incorrect??