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**Numbers**View PostThere is a proof that the iterative matrix technique always converges so long as the games played matrix is rich enough; the reason that you have to use the maximum likelihood technique where theta and h have to be estimated as well is that there is no such promise of convergence.... the iterative technique can blow up without ever solving. As Hunter has confirmed to me in correspondence, it might be possible to find a so-called majorizing minimizing expression that allows a matrix-like calculation on the the theta-h problem, but it would require someone to put in the work of finding that MM relationship -- it's a little like integration; there may be a trick that allows you to solve the problem, but it's not clear what trick you need. But the maximum likelhood technique I outlined above always works -- as long as there are no undefeated teams or winless teams.

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