Dear Uncle Colin

I gather UEFA is toying with the idea of using the Swiss System for future Champions Leagues. Without wanting to sound cheesy, that seems a bit cuckoo. What’s it alp… I mean all about?

Strange Wayto Implementa Soccer System

Hi, SWISS, and thanks for your message - this question is definitely yodelling my tune!

So. The first thing to say is, I don’t think UEFA are implementing a Swiss system at all - from the look of it, it’s more like the MatchVision system. There are some similarities between the two, but also significant differences.

### The MatchVision model

I’ve sort of pieced this together from various sources, so it’s likely to have some errors in it; if you know better, I’d love to hear about it (just drop me an email). Please read all of the sentences in the following with “as I understand it” as an implied caveat.

The idea of the MatchVision model is to do away with groups, but not to replace them with a (hugely expensive) round-robin tournament. (With 36 teams, that would entail 540 matches – 1080 if they played home and away.) Instead, they use a system of pots to try to make sure no team has a significantly harder or easier schedule than another.

For example, the 36 teams could be divided into four pots of nine teams each, sorted by UEFA ranking - the elite teams in pot A, good teams in pot B, medium teams in pot C, and what they diplomatically call ‘emerging’ teams in pot D.

Each team plays three matches against teams in their own pool, two against teams in each of the other pools and one other game ((I gather this is pot A v pot D and pot B v pot C)) - meaning that each team’s schedule is broadly of a similar strength.

So how do you rank teams in this format? Simple! You put them all in a giant league table. The top 8 qualify for the last 16 (yeah, you heard me); the next 16 go into a playoff round, and the winners join the top 8. The rounds are seeded like a tennis tournament so that (in general) the better your ranking in the first stage, the easier your route to the final.

It’s pretty neat. I’m not sure I buy all of the arguments for it (they claim it eliminates match-fixing and the need to play the final round simultaneously, both of which I’d need convincing about), but it seems like a format that means the better teams advance, there are fewer dead matches, and - the main benefit over the Swiss system - allows teams to plan in advance.

### The Swiss System

The Swiss System is widely used in chess and other sports, but not (so far as I know) in football. It’s a shame. I like the Swiss system.

Again, the idea is to avoid groups and round-robins; instead, matches are determined dynamically each round so that teams with similar records who haven’t played each other before face off. (The thinking is that you don’t, in principle, know before the tournament which players are better than others. Obviously you do in practice.)

In chess, there are all sorts of complicated rules for how the players are grouped precisely, about stepping up and down groups, about trying to alternate black-and-white - it feels a bit like epicycles have been added repeatedly.

My implementation for football would go something like:

• On odd match days:
• generate a league table (breaking ties at random)
• find the set of matches such that…
• no pair that’s played before plays again
• the sum of the squares of the differences in league position is as small as possible ((There may be more than one of these; pick at random))
• On even match days:
• generate a league table for teams who have played an extra home game and one for those who have played an extra away game
• find the set of matches pairing a team from one table with a team from the other under the same criteria as before

(This is how I’d run a league under the threat of coronavirus, incidentally. It can be stopped fairly at pretty much any point.)

I hope that helps!

- Uncle Colin

* By the way: designing tournaments is something you can hire me to do. Email commissions@colinbeveridge.co.uk if that’s something I can help you with.

* Edited 2021-03-10 to correct name of model