In reasonably good approximation, football goals are
- independent of each other
- scarce
Such independent and scarce events can be described by Poisson distributions
- To describe a Poisson distributed random variable, we only need its expectation value \(\lambda\), i.e. its average
- If we know \(\lambda\), we can calculate the whole distribution
This means for football teams: Once we know how many goals to expect for a team on average, we can calculate the probability for this team to score exactly 0, 1, 2... goals
We can then easily compute the probabilitiy of each final result
From the final results we can get the odds for a home win / draw / away win bet