Europa v Liga: Part 3,452,497

As we all celebrate the awesomeness that was traveling to Germany, beating a very tough team, and progressing to the next round of Europa, let me cool you all off with some cold water.  Don’t read below if you dislike math or probabilities.  I just did this because I’m avoiding working on my dissertation.  So thank you for indulging me.

Let’s be optimistic.  Let’s say that we are better than every team we will face for the remainder of the Europa league and are 3:2 favorite (a 60% chance of winning each tie).  Where does that leave us?

There still remain the round of 16, 8, 4, and the final.  So that’s a probability of .6 x .6 x .6 x .6 = .1296 or equivalently: a 13% chance of winning Europa.  If we want to be even more generous and say that we are 2:1 favorites (2/3 chance of winning) for each match this likelihood of winning europa jumps up to… .1975 or just under 20%.

Now, of course winning Europa league has two additional benefits: 1) direct passage to the group stages and 2) WE WIN A CUP!!!!!

For the former, this is really important and I’ll factor it in in a moment.

The latter is non-quantifiable.  We play to win trophies and to some degree its the only thing that should matter.  But if we’re being honest, Europa is a tournament we’ve won, and it is Europe’s second tier tournament…  So it’s hard to know how much to weight that against other factors.

So the question is, if we put all our energy on La Liga, what would our chances be of regaining the 5 point gap between us and Valencia and taking 4th (I consider 3rd unlikely/impossible).  Whatever that likelihood is, call it X, we’d still need to qualify for group stages.  To be consistent, lets say we have a 60% chance of winning that match.

If our only goal is to qualify for CL group stages next year, the question is, which is greater: a 13% likelihood of winning Europa or our chance of catching Valencia and then winning the playoff: X x 60%.

Solving for X, we should focus on La Liga if we believe that we have a chance of catching Valencia higher than 13/60 = 21%.  Using the more optimistic guesses about how we’ll perform in La Liga we’d get 20/67 = 30%.

For me, the bottom line is that La Liga is still our better chance at making it to CL group stages.  Valencia’s form has been shaky.  There are a lot of games left.

Now two caveates, one small and one big:

Edit: This article suggests that the first point below was incorrect.  If Villareal win CL it will not affect whether or not 4th place in La Liga qualifies for the CL playoff matchup.

1) It was pointed out that if a Spanish team wins Europa, the CL group spot comes at the expense of La Liga’s fourth place team.  So if Villareal won Europa we’d have almost no shot at CL.  If we granted Villareal the same generous chances of winning Europa (between 13 and 20%).  This would actually have a big impact.  Instead of needing a 21-30% chance of catching Valencia for full effort on La Liga to be warranted, we’d instead need that chance to be over 27-37.5%.

2) It could be that instead of going all in for one competition and abandoning the other, the best choice is actually a hybrid strategy where we try and go all out for both, or make partial sacrifices for each.  We refuse to choose and try our best to compete on all fronts.  This was almost impossible over the last month with so many absences and injuries, but as the team gets back to full health, this may actually be possible.  Ultimately, this is probably what I’m most hoping for.  I don’t want to choose.  Because I want us to win every game we play….

Of course these numbers will change quickly as each game is played.  So the strategy that is optimal today may change if one or another result happens this weekend.

OK.  I’m done.  Thanks for indulging me.