It's obvious that Liverpool are in a very good position with 3 games remaining (4 for Man City), but just how good a position are they in? If you ignore the quality of the remaining opposition for these teams (admittedly a very important consideration), just how likely is Liverpool to win when you factor in all the possible scenarios that can occur in the remaining matches?It turns out, there's 19683 different results that can occur in the remaining matches that the top 3 teams can play. For example, the below is a possible scenario:
Man City W W W W
Chelsea L W W
Liverpool W W W
In this situation, Liverpool would obvious win the league. But what about the other 19682 possible scenarios?
Liverpool will outright win in 16084 (~82%) of them
Chelsea wins outright in 1026 (5.2%)
Man City wins outright in 992 scenarios (5%)
In 1491 (7.6%) scenarios, two teams will end up on equal points (725 for Liverpool/Man City, 676 for Liverpool/Chelsea and 90 for Chelsea/Man City)
And finally, there's 90 (0.5%) possible scenarios where all 3 teams can end up on the same amount of points.
I was just bored and worked this out, I guess the end result is Liverpool is in a pretty **** good position.