Reverse Poisson, how to work backwards?

[Shinigami]

Hi, just wondering if someone mathematically inclined could help me with this... i understand how you can use average goals scored for the home & away team to derive the probabilities of Home win, Draw, and Away win.. and i have the excel spreadsheet to compute this.. My question now is, if i have a set of probabilities, say 43%/27%/30% and i want to reverse the process to compute the average goals scored.. how do i go about this using the excel spreadsheet?

[Shinigami]

Re: Reverse Poisson, how to work backwards? i believe there should be a certain formula to decompose the Poisson result back & find the two X,Y variables (average goals scored)... so does anyone know how? thanks...