Pack Habits of European Wolves

On Thursday last I saw a Tweet (unfortunately I’ve lost sight of it now) that was bemoaning a very specific flaw with the draw for the UEFA Europa league. The writer was unhappy that Wolfsburg of Germany, Wolves of England and Wolfsberg of Austria were all in different groups. What are the chances, eh?  Well, we can work it out.

The task is made a lot easier in that the group stage draw is seeded with four pots of twelve teams.  The ultimate Wolverine combination was technically possible because the three teams were in pots 1, 3 and 4 respectively. Sadly, Woolongong Wolves of New South Wales, Australia were not present in pot 2. Maybe the Europa League will eventually go the way of the Eurovision Song Contest and open that door one day. We can but hope.

We don’t need to concern ourselves with the actual draw order, we can just think about the possible outcomes. Wolfsburg are bound to be in a different group from all of the other pot 1 teams. It doesn’t matter to us whether it turned out to be group A, B or whatever. Likewise, the outcomes from pot 2 make no difference. There is no Wolfie interest in that pot. We care less about pot 2 than Boris Johnson cares about Remainers, and that’s saying something.

WOLFSBURG And a pot 2 team	Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team
Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team
Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team
Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team	Any other Pot 1 Team Any Pot 2 Team

So, Wolfsburg have to be somewhere, and we don’t care who they are with or what any of the others are doing. We are therefore looking ONLY at one twelfth of all the possible outcomes at this point, shown here in yellow. The white zones have another team from Pot 1.

For the outcomes of the third pot, we are only interested in where Wolves end up. As a WBA fan, even I’m only interested for blogging purposes. Assuming the draw is fair, they have an equal chance of ending up in any of the twelve groups.

So the yellow area … is divided into 12 equal pieces. Only one of these would have Wolves from Pot 3, shown here as Orange. They’d want Old Gold but they are pretentious like that.

WOLFSBURG And a pot 2 team

On the right, the Orange area would represent Wolfsburg plus any pot 2 team plus Wolves. The Yellow areas are Wolfsburg plus any pot 2 team plus any one of the other 11 pot 3 teams, all of equal probability.  So we are down to one-twelfth of one-twelfth of all the possible outcomes.

Hopefully it is now straightforward to see that the desired presence of Wolfsburg to join the other two in effect divides the orange area into twelve once more.  Only that twelfth of the twelfth of the original twelfth is now of interest, shown here as red but magnified to a different scale at the risk of confusing you.

The rest of the orange is Wolfsberg/anyone/Wolves/anyone.  All the combinations where Wolfsberg and Wolfsburg are together, but with no Wolves, would be somewhere over in the yellow zone. Likewise there would be some permutations in the white areas there which had thrown Wolves and Wolfsburg together, but without Wolfsberg. Try working out the chances using the same method.

Anyhow, it’s clear that the perfect packing of European Wolves would only happen in a twelfth of a twelfth of a twelfth of all possible draw outcomes. This is 1 in (12 x 12 x 12) or 1 in 1728, or as a percentage, around 0.058%. In round figures about one in 2000. Howl low is that? (sorry) This is low, but still higher than the chances of being killed by a wolf while the UK is winning the Eurovision Song Contest and much less than winning the lottery.

Thanks (or should that be fangs) for your interest!