Equilibrium in the Champions League III

This is just a very short post as a follow up to the two previous posts in this trilogy, which can be found here and here. Basically, those posts looked at how you could get complete equilibrium in the Champions League group stages, based on the teams' UEFA club rankings and then based on their coefficients.

This post is basically just a correction. I hadn't realised that Real Sociedad, although they had not been in European competition in the five years used as the basis for coefficient calculation, nevertheless have their coefficient calculated for the purposes of the draw. Whilst they don't get any points for their own achievements, they do get the 20% of Spain's national coefficient, which isn't too shabby at all and is actually enough to put them in 31st, above Vienna.

This therefore messes up the calculations I made in those posts for balanced groups and you can't even just make a simple swap of Real Sociedad and Vienna because I had Vienna in Barca's group. The word fiddlesticks comes to mind.

Another point is that, as Sociedad also don't have 0 coefficient points, but 17.605, the calculations for balanced groups would also be different. And it means that they wouldn't be 451st in Europe overall, but would be somewhere around 87th, meaning that balanced groups based on the overall UEFA club rankings are much more possible than I made out.

Whilst this is all quite disappointing, as it voids my results, it doesn't, I don't think, void the methodology, which I am convinced will stand the test of time.

Whilst I'm not going to redo all of the calculations, I can tell you that Sociedad's being ranked 31st of the Champions League qualifiers means that Man United aren't actually as lucky (l) as I'd made them out to be, as they get a luck score of just 1.33 and not 1.67. This doesn't however, affect the bigger picture of English luck, as they remain the only English side with positive (i.e. good) luck, based on the UEFA rankings.

Sorry about the error.