Just thought I'd make a comment on how my algorithm differs from Laxpower.com's. Basically, I am solving a least squares problem in linear algebra for those who know what that is. Essentially, I use a similar strategy to Laxpower, in that I am attempting to make
P(i) - P(j) = D(i,j)
where P(i) and P(j) are the power ratings for teams i and j, and D(i,j) is the goal differential for those two teams for when they played each other head to head. I have not implemented a home field advantage, but it would be reasonably easy to do.
I implement this by setting up and solving the equation
M*A*P=D
where P is the list of power rankings for all the teams (which is unknown), and D is the list of goal differentials for all the games. A is simply a matrix which maps the correct power ranking with the correct goal differential. M is a masking matrix which simply eliminates the entries of A that represent games that haven't happened or never will. Then I use a linear equation solver to find P in a least squares sense (I use MATLAB's \ operator).
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