Updating the odds

Football-wise, two very eventful weeks have passed. Chelsea's lead has been cut down further in size to 7 points. However, there are but 5 matches left for each club. So has Man Utd's odds of winning the EPL title increased or decreased (according to my model, of course)? Which factor has the bigger impact on the probability, the reduced lead or the decreased number of matches?

Just to recap, Man Utd's and Chelsea's remaining matches are:

For Man Utd,
Sunderland, Tottenham (a), Middlesbrough, Chelsea (a) and Charlton

For Chelsea,
Bolten (a), Everton, Blackburn (a), Man Utd and Newcastle (a)

I continue to use the same assumptions and model. This means that if Man Utd beat Chelsea at Stamford Bridge, they will then need two more victories. If not, they'll need four more (near impossible!).

My estimates of both clubs' chances of winning each of their remaining matches (excluding the match where they play each other) remains unchanged after a *ahem* review (given in square brackets after the team's name):

For Man Utd,
Sunderland [0.95], Tottenham (a) [0.65], Middlesbrough [0.9] and Charlton [0.85]

For Chelsea,
Bolten (a) [0.7], Everton [0.8], Blackburn (a) [0.7] and Newcastle (a) [0.75]

Following the same steps as before, for Man Utd, we will therefore be modelling it with the Binomial(4, 0.8375) distribution. For Chelsea, it will be the Binomial(4, 0.7375) distribution.

So we're after the following probability:

Probability(Man Utd wins the league) = Probability(Man Utd beats Chelsea) x Probability(Man Utd wins two more matches than Chelsea for their respective remaining matches) + Probability(Man Utd loses to Chelsea) x Probability(Man Utd wins four more matches than Chelsea for their respective remaining matches)

I leave the rest of the working as an exercise for my readers...





Just kidding!

Again, you'll have to trust my binomial calculations. We will then obtain

Probability(Man Utd wins the league) = 0.3 x 0.162 + 0.7 x 0.002 = 0.050


Rejoice, for that's an increase of 1.3%! And I hope I have managed to bring some smiles to the Man Utd fans reading this post.

Still 4 days to go.