Probability of winning a soccer/football game

[tbeat]

I was wondering if there is a way to calculate a probability distribution in the next example:
Let's suppose we have Team A and Team B.
We know that Team A has the next probability distribution regarding the AVERAGE goals the team scores against ANY other team in a match:
Team A scores 0 goals: 60%
Team A scores 1 goal: 30%
Team A scores 2 goals: 10%
We know also the probability distribution regarding the average goals Team A receives against any other team in a match:
Team A receives 0 goals: 45%
Team A receives 1 goal: 50%
Team A receives 2 goals: 5%

In the same way, we have for team B:
Team B scores 0 goals: 15%
Team B scores 1 goal: 35%
Team B scores 2 goals: 50%

Team B receives 0 goals: 20%
Team B receives 1 goal: 75%
Team B receives 2 goals: 5%

Is there a way to calculate the probabilities for all the possible results if there's a match between Teams A and B, taking into account all the data available?

I tried to somehow mix the probability of Team A scoring goals, and Team B receiving goals, but couldn't find a way to succeed in it.

Thank you for your help!

 

[JeffM]

Anything you do is likely to be arbitrary. The problem can be summed up in a single example by noting that the probability of team A scoring two goals against team B fully determines the probability of team B losing two goals against team A. But based on the averages, team A has a 10% probability of scoring two goals, whereas team B has only a 5% probability of having two goals scored against it. When the two teams play against each other, at least one of those probabilities is wrong (and you do not which is wrong) or both are wrong. In short, the data you have tell you nothing about the probabilities when team A plays against team B.