I'm working on predicting outcomes of games given statistics from the two teams involved. Two of the statistics I have are below:
AGA (average goals against): The arithmetic mean of number of goals a team's opponent scored in each game.
AOP (average offensive production): The geometric mean of (the ratio between the number of goals a team scored and their opponent's AGA in each game).
Now I have two teams, A and B, that have not played each other, but may have played zero or more of the same teams. A simple way to predict the number of goals scored by A against B is to multiply A's AOP by B's AGA. Is there a way to get a standard deviation of this predicted outcome from the numbers given? What if I had the values averaged to give the AGA and AOP in question?
Could the same be done for division between two statistics instead of multiplication?
