redfiona99

Following my Euro 2020 2021 posts (link), L raised an interesting point. While my theory that "closer to the centre = more likely to win, and less tightly connected = more likely to go out" has held up over several Euros, one Rugby World Cup, one Women's Football World Cup and one Men's Football World Cup (after the group stages), in those situations I knew enough about the relative strengths of the teams that my opinion might have been biased. The Copa America 2021 gave me an opportunity to demonstrate whether my theory worked in a competition where I wouldn't know as much about the relative strength of the teams taking part.

There were some complicating factors, starting with the COVID pandemic. Due to the pandemic CONMEBOL stated that nations could nominate squads of 28. The squad lists had to be with CONMEBOL by the 10th of June. Not all nations nominated 28, which does leave the diagrams looking lopsided.

( Plotting the first round teams gives me the following diagram: )

The national team closest to the centre is Chile, with Racing the club team closest to the centre.

River Plate and Bolivar are the club teams with the most players (7) followed by Atlético Madrid with 6. The lower numbers of players per club team are reflected in how much more spread out this diagram is compared to the equivalent Euro 2020 diagram.

Bolivia are the only unconnected team. Eight of the ten teams go through to the second round, and from this diagram, I would expect Bolivia to be one of the first to go out. The most likely other team to be be eliminated is unclear from the diagram, but I would guess one of Peru, Venezuela or Paraguay, but Brazil are actually one of the outer teams, which even I know suggests a problem with the system.

Even if you include all the players including injury (COMEBOL rules allowing outfield replacements as well as goalkeeper replacements) and COVID-related player replacements, you still get a very similar image.

( All players that played for the teams at any point )

Chile are still the central national team with Universidad de Catholica (Chilean team of that name) as the central club team. The clubs with the most players remain River Plate and Bolivar with 7 players and Atletico Madrid with 6.

Bolivia, Venezuela and Paraguay are the most outlying teams, followed by Peru, Ecuador and Brazil.

I suspect that the shape of this diagram is influenced by two factors:
1 - a lot of teams have players who play for club teams that only have representatives for that national team so the diagram is spaced out.
2 - a lot Brazil and Argentina players play for European clubs and those two teams have disproportionately few players playing South America, but have many players playing for the same teams so they're pulling each other away from the centre.

( Once two teams (Bolivia and Venezuela) were eliminated to give the quarter final teams, the diagrams looked like this: )

Chile remain the national team closest to the centre, with Universidad de Chile the club team closet to the centre.

The most outlying teams are Peru, Brazil, Ecuador, Paraguay - looking at the quarterfinal teams, my theory still doesn't work for the Copa America. (Again, I think because a lot of Brazilians play in Europe).

It took until the semifinal diagram for Brazil to no longer be one of the outlying teams, with Peru now being the outliers with the remaining 3 teams (Argentina, Brazil and Colombia) forming a solid triangle.

( Semifinal diagrams )

Argentina or Peru are the national team closet to the centre, with Everton (?!!) the club team closest to the centre.

Peru stick out.

Following the semifinals, ( the final diagram looks like this: )

It was a Brazil vs Argentina final, which I suspect everyone with a financial interest in South American football was hoping for. The final diagram is much more interlinked than Euro or World Cup finals. None of the linking teams are South American, very clear *all* the money is in the European game. This undoubtedly does have a distorting effect on other Federations' Federation Cups (e.g. player release for the African Cup of Nations).

One of the semi-finals is a match I'd been hoping to avoid. Because on the one side, there is England, and the lovely Marcus Rashford and Harry Maguire who I am also quite fond of, and on the other, there is Denmark, and everything and the lovely Kasper Schmeichel who I have, to an extent, grown up with.

I am not exaggerating about that, I come from a family of Manchester United fans (Mum remembers paying 20p to watch Denis Law and Sir Bobby Charlton play), so when boy cousin got a Manchester United annual, and I, inevitably got bored and ended up reading it, I became accustomed to seeing a young boy in goalie gear following after his giant father. And obviously, as time passed, the boy grew and is now the Danish national goalkeeper himself (rather beautifully summed up by the Danish coach here - https://twitter.com/EURO2020/status/1408785253481816069?s=03). It's very hard not to want Kasper Schmeichel to do well, especially after he helped Leicester win a title.

I am going to hate every minute of the game, although I fear I will be on match-monitoring duty because L thinks I'm less of a jinx than he is.

The semifinal diagrams look like this.

( Two network vis diagrams under the cut )

I've increased the repulsion strength slightly to make it clearer.

Manchester City are the team with most player left in, with 11, followed by Chelsea with 10 and Borussia Dortmund with 9 (here I must apologise to Dynamo Kyiv who had 10 players left in the last round, but I didn't mention them because I have to get the numbers by skim reading through a column.)

Spurs are just about the club team closest to the centre, Denmark are the national team closest to the centre.

The community view looks like this:
( Another one under the cut )

Leeds, Chelsea, AC Milan, Atalanta and Spurs are their own communities, while Manchester City aren't (no, I don't know why). This split is clearer on the unlabelled diagram.

( The last diagram )

First, a round up of my predictions for who would be eliminated in the group stages, as *someone* doubted the utility of the diagrams. My prediction was that "Finland, Russia, Ukraine and North Macedonia to be amongst the 8, with some of the remaining 4 coming from Wales, Turkey, Hungary, Portugal and the Czech Republic", so that's 5/8 correct, including Turkey, who more respected pundits had as alleged dark horses.

Yes, I make the diagrams because they look pretty and making them brings me great joy but the "outlying teams are eliminated first" theory has now held up over several tournaments.

With the removal of 8 teams, what does the diagram look like now?

( Two large images under the cut )

The club teams with the most players represented are Chelsea and Manchester City with 14 followed by Bayern Munich with 13. After the first round both Chelsea and Bayern have lost 1 player. No Manchester City players were eliminated.

Juventus are the club closest to the centre, with Spain, just about, being the national team closest to the centre.

The communities view is interesting.

( Two more network diagrams underneath the cut )

Although there are 16 teams left in, there are only 13 communities, with Germany + France, Spain + England, Austria + Switzerland forming multi-team communities.

As for predictions, from the layout of the network diagram, things do not look good for Wales, Austria, Czech Republic, Croatia and Ukraine. England vs Germany, France vs Switzerland and, to a lesser extent, Belgium vs Portugal are too close to call, working only from the network diagram.

As a football fan, I am looking forward to those last two matches a lot.

I'll begin with the unlabelled figure, because the labelled figure is very busy.

( Large image under the cut )

The colours are my attempt at replicated the official UEFA Euro 2020 colours, as best I can with the limited Gephi colour palette.

It is not the prettiest of this type of figure I've produced. I particularly don't like the cluster right in the middle of the diagram (between Germany and Bayern Munich in the labelled figure).

( Another large image under the cut )

I did warn you it was busy. That busyness, the tightness of the clustering, was what really jumped out at me. I've been making these diagrams since Euro 2012, and this is by far the most tightly inter-connected.

Looking back at the most recent international tournament before this (World Cup 2018), although that too was very busy, it wasn't as busy. There was at least some space between most teams and some clearly outlying teams.

This time, the nearest there are to outlying teams are Finland, Russia, Ukraine and North Macedonia. Wales and Turkey are not as outlying, but would be in the next layer in, followed by Portugal, Hungary and the Czech Republic.

Germany are the national team closest to the centre, while Atalanta are the club team closest to the centre. Chelsea are represented by the most players, 15, followed by Manchester City and Bayern Munich on 14.

A couple of notes: no, you're not imagining it, Spain, Poland and the Netherlands have slightly smaller squads that the other teams. Spain chose to only take 24 players, while Poland decided not to replace Arkadiusz Milik when he had to withdraw injured. The Netherlands made the same choice when Donny van de Beek withdrew injured.

Every team except Wales have at least 1 player playing in the home league. All the teams have at least one player playing in a foreign league. That is a first, normally it's England who don't have any, but even they have 3 non-England-based players this time. This may be the cause of the increased inter-connectedness of the diagram, although the number of non-English players in the Premier League has always been high.

Looking at the community view, there are 20 communities but 24 teams.

( Two large images under the cut )

France, Germany and Switzerland form one community, as do England and Spain, and Sweden and Denmark. This again demonstrates how tightly interconnected parts of the diagrams are.

This is probably due to the number of club teams their national team players share.

Historically, teams that are outlying do less well. With the way the tournament is organised, 8 teams are sent home after the first round. From this diagram, I would expect Finland, Russia, Ukraine and North Macedonia to be amongst the 8, with some of the remaining 4 coming from Wales, Turkey, Hungary, Portugal and the Czech Republic (I didn't expect the last two). Two caveats, firstly, this prediction was made from the diagram only, and has ignored what has gone in the first 5 matches. Secondly, it doesn't take the groups into account, so I know no one from group E is included but more than 2 groups have 2 teams named. I am reasonably confident in the prediction about Finland, Russia, Ukraine and North Macedonia, a lot less confident about the others. The lack of separation, due to the tight clustering, makes it hard to spot outliers.