I completed my write-up of my revised derivations of the soccer Pythagorean formula. It fixes the problems that I had with overpredicting points and calculating win and draw probabilities that exceeded unity. Maybe I should come up with a better name, because it no longer looks like the Pythagorean equation.
Here's the document link:
I hope these equations will be useful to the soccer community. Just remember to acknowledge me and this site -- it is the culmination of four months of work.