Chelsea winning the quadruple is as likely as Liverpool relegating to Championship

After a comfortable win over Derby County in the League Cup quarterfinal, Jose Mourihno and Cesc Fabregas had a little disagreement over their team’s chances to win nothing less than quadruple this season. The Spaniard, probably encouraged by lack of resistance from Championship opposition, said that Chelsea “have all what it takes”, while the manager insisted that “it is impossible”.

What is the true probability of Chelsea winning a quadruple or any other combination of trophies, as of December 17^th, 2014? To derive probabilities, I used bookies’ coefficients (if someone has better estimations, which is confirmed by a long record of beating bookies, please let me know: not only will I use it for this and similar post, but I also will invest money in your strategy).

1. Premier League – 62,6%

The Premier League seems to be the most likely trophy for Chelsea this season. Arsenal and Liverpool are clearly not contenders, Manchester United are not there yet, too, so it leaves Manchester City as the only serious competitor for the Premier League title. With a 3-point cushion and looking really solid, Chelsea are believed to be heavy favourites to win the league. Paddy Power gives 1/2 odds to Chelsea winning the league, which, assuming 5,4% bookie’s margin (they must take your money, right?), is translatable into 0.626 (62,6%) probability of winning.

2. League Cup – 56,9%

Unsurprisingly, Chelsea have a good chance to win the League Cup mostly because they are already in last 4. The fact that Sheffield United are one of their contenders also helps Chelsea’s chances. However, with Liverpool and Tottenham still in the competition, it is just above the coin flip for Chelsea to win this trophy: Paddy Power’s odds are 4/6, translatable into 0.569 (56,9%) probability of winning.

3. FA Cup – 15,8%

To estimate the probability of a cup tournament that has not even started (okay, has not started for its true contenders) is not an easy thing, especially given random approach to the draw. Paired against Watford at home, Chelsea are at 5/1 at the moment (translatable into 0.158 (15,8%) probability of winning). However, it may change drastically after the 4^th round draw.

4. Champions League – 11,2%

This will be the hardest one for Chelsea to win. With the likes of Bayern, Real Madrid and Barcelona still in contention, and PSG to begin with, one will not be harsh on Chelsea saying that their chances to win the Champions League are slim. Chelsea’s chances are ranked fourth among all participants with odds of winning 15/2, translatable into probability of merely 0.112 (11,2%).

Quadruple – 0,63%

Now, to calculate the probability of winning the quadruple, we simply need to multiply the probabilities of Chelsea winning each of the four tournaments, which is:

0.626x0.569x0.158x0.112=0.0063 (0,63%)

In fact, Chelsea have 1-in-158 chance to win the quadruple this season. Just for comparison, it is much less likely than Bayer Leverkusen winning the Champions League (100/1) and in the same region as Liverpool relegating to Championship (175/1). Honestly speaking, Mourihno’s point of view is closer to me than Fabregas’.

What about other combination of trophies? 

The table below presents all the possible outcomes:

As you can see, it is most likely that Chelsea will end up with one or two trophies this season, while them winning the Premier League and the League Cup is the most likely outcome.