World Cup 2026 - Final Network Visualisation

The unlabelled network graph looks like this: Even without the labels, you can probably guess the big circles are Spain and Argentina ;) 

The labelled graph looks like this:  

It's the battle of the Atlético Madrid players! 

Atlético Madrid have 9 players left, 3 playing for Spain, 6 for Argentina. 

Barcelona have 8, but they all play for Spain. 

Arsenal and Athletic Bilbao are next, with 3 players each. All 6 of those players play for Spain. 

Atlético Madrid, Chelsea, Tottenham Hotspur and Bayer Leverkusen have players on both teams. 

Chelsea, somehow, are the club team closest to the centre of the diagram. 

No prediction at this stage, the two teams are understandably equidistant.

Are the scrutineers picking on my driver? - Update after the Austrian Grand Prix

Some interesting points from the underlying data: The Austrian GP featured the first test where the check said "all classified cars" rather than all cars, or giving the number of the car tested. It was the steering wheel test. I have been assuming that "all cars" meant all cars entered. I think the wording of this check supports that but I want to give that caveat on all this data. 

The Austrian GP race scrutineering itself:  

No, I don't know what Liam Lawson did to the scrutineers. 

Obviously, it's not that extreme, because his standard residual of 1.06 doesn't hit the value of 2 that suggests significance but that's a lot of tests on one car. 

The difference from expected is not statistically significant with an χ² of 2.88. 

Season to date:  

The difference from expected is not statistically significant with an χ² of 3.06. 

The top 3 most over-scrutinized (Russell, Hamilton and Norris) make some sort of fits with their performance, because they are 3 of the top 5 at this point of the season. 

Similarly, two of the bottom 3 make sense, because the Aston Martins of Stroll and Alonso have not been going long distances so might miss some of the post-race tests, ditto for Bottas and Albon who have retired from half the races and a quarter of the races respectively. Hadjar being so low down still makes no sense, he's only not completed 2 races but all but one of the rest of the races he's been in the top 10. It's getting to the point where I want to triple check all my numbers, he's that low. 

For the British Grand Prix results, I'm going to be looking for that random top 10 finisher check, providing there are at least 15 finishers (which *spoiler* there were). If it doesn't happen, I may have to conclude there is no pattern.

World Cup 2026 - Semifinal Network Visualisation

I have listened to L's editorial guidance and am posting the post with a deadline. Austrian and British Grand Prix scrutineering posts are in the works, as is the first of the weekly Tour de France posts. I am making no promises on timelines because a work project is stealing my time. 

We're down to four teams and the network graph looks like this.  

The teams are close together, but one sticks out.  

Sort of understandably, being as Argentina is on a different continent to the other finalists, they are the team slightly further away from the others. 

The thing I find intriguing is that each national team has one club team close to it, because that club team provides a lot of national team representatives. For Argentina, it is Atlético Madrid (my heart belongs to Diego Simeone), England have Manchester City, France have Paris Saint Germain and Spain have Barcelona. 

It shows the financial strength of European football that the club team with the most players playing for Argentina is Atlético Madrid, not a team closer to home. 

The club teams with the most representatives left are Barcelona with 10, Atlético Madrid with 9 and Arsenal with 8. 

England are just about the team closest to the centre, with Chelsea the club team closest. 

There's something interesting going on in the community view. Although there are only 4 teams left, there are 8 communities. Labelled, it's clear that four of the communities are the nations, and the others are those teams that link more than one country (with some exceptions).  

The thing that intrigues me is that some teams aren't separate communities even though they link multiple teams. 

I think that happens when most of the players play for one national team, for instance of the five Aston Villa players left, three play for England. 

Chelsea will have a player in the final no matter what combination of teams wins the semifinal matches. 

Making predictions at this point is almost impossible, but the diagram says England and unclear because of how equidistant Spain and France are from the centre.

Formula 1 2026 - British Grand Prix

 Ferrari only win when I can't pay attention. Barcelona - I was being driven back from a fencing competition. Silverstone - being driven back from a fencing competition. Clearly, the solution to get Ferrari winning more is for me to do more competitions. [Editorial note, the joke is L's]

Ferrari mustn't have been expecting Leclerc to start so well given it meant they had to switch to strategy B by lap 8.

It was a race with several "things I hadn't seen before". An umbrella causing a (virtual) safety car and a brake aero duct failure causing a car to stop being able to steer.

(Technical details sort of here - https://www.formula1.com/en/latest/article/a-car-should-not-break-wolff-laments-antonelli-mechanical-issue-with-italian-denied-epic-battle-for-silverstone-win.5juL2jTds26Hl4foTZIWnk)

That penalty for Antonelli was kicking a man when he was down. This time he wasn't deliberately going beyond track limits.

So happy that Ferrari got a 250th F1 Victory. Harry Benjamin on the BBC commentary was not helping by describing Leclerc as "the man who bleeds scarlet". We Ferrari fans are already unreasonable on the subject of Leclerc.

World Cup 2026 - Quarterfinal Network Visualisation

(The Austrian Grand Prix scrutineering post, and the British Grand Prix summary and scrutineering post are coming, I just thought this was a bit more urgent) 

Okay, last's round's predictions were not as good as they could have been. I got Brazil vs Norway right, and was right to suspect England vs Mexico would be close, got France, Argentina and Morocco's results correct, but was way out on Belgium vs United States and got Switzerland vs Colombia wrong (although I said it would be close). I was right that Spain being pulled out of the centre of the diagram by all their Barcelona players made it hard to predict their result from the diagram. 

Also, I didn't predict how close Egypt got to beating Argentina. 

What do the quarterfinal diagrams look like? 

The unlabelled diagram looks like this: Labelled it looks like this: France are the national team closest to the centre, with Paris Saint-Germain the club team closest. 

The club teams with the most representatives left in are Atlético Madrid, Barcelona and Arsenal with 10. 

The average number of degrees of contact each circle has is 1.364. 

The number of communities is still one per team, so 8. 

The unlabelled community view looks like this: Labelled, it looks like this:  

What about my predictions? 

It's much harder at this point, with the teams other than France pretty much equidistant from the centre, and no "gravitational" clump. 

France vs Morocco - Diagram says France 

Spain vs Belgium - Diagram says Belgium, although I think that's because Spain are still pulled out of the centre by all those Barcelona players. On the other hand, anything can happen in knock out football. 

Norway vs England - Norway just (that sound you can hear is L cursing me) 

Argentina vs Switzerland - Diagram says Switzerland. I think that's the Atlético Madrid players pulling Argentina out. Also [Legal team have redacted a paragraph-long rant about exactly how many World Cups the referees are going to give this Argentina team.] Switzerland could do it ... (I feel I need to add a conflict of interest statement, I drew Switzerland in a sweepstake at work.)

World Cup 2026 - Last 16 Round Network Visualisation

Delayed by fencing, which I enjoyed immensely despite the sprained ankle. 

Second round results: I said Senegal vs Belgium would be a cracker. 

The whole centre of diagram gravity vs centre of diagram really did come into play in the second round - if you were a team on the left hand side of the diagram you went out. Except Egypt, and they were playing another team from the left hand side. 

Of the matches where there was a clear prediction, gravitational centre ended up being more important, which is useful learning. 

The diagram for the last 16 teams isn't as tightly packed any more, which means that should be less of a thing going forward.  

The labelled version of the graph looks like this:  

The list of club teams with the most representatives has changed - especially Bayern Munich given Germany are out. What we've got instead are a small clump of teams with 12 players left in (and yes, these are the teams that were causing the cluster in blue in the first round and in the top right of the diagram in the second). They are Paris Saint-Germain, Arsenal, Barcelona and Manchester City. Atlético Madrid is the next on 11. 

Norway are the national team closest to the centre, while Inter Milan are the club team closest. 

The average number of degrees each circle is linked to has gone down to 1.377. 

The number of communities in the communities view is now 16, so one per team. Labelled it looks like this:  

As to my predictions (which I don't mind making late because you can see the diagrams I'm basing them on): 

France vs Paraguay - France 

Canada vs Morocco - Morocco 

Portugal vs Spain - Diagram says Portugal, reason says Spain; all those Barcelona players pull Spain out of the centre, the same thing that happens to their women's team and always skews the women's diagrams. 

United States vs Belgium - Diagram is not clear, this may be closer than people expect. 

Brazil vs Norway - Diagram says Norway, I don't think that's impossible. 

Mexico vs England - Diagram is also not clear 

Argentina vs Egypt - Argentina 

Switzerland vs Colombia - Diagram says Colombia but could be close!

Formula 1 2026 - Austrian Grand Prix

 This year I've often said how much the new regulations have improved the action, or at least made it more interesting for spectators. I have to acknowledge that that didn't happen at the Austrian Grand Prix, and the only points of interest were due to the differing tyre strategies of the front runners.

And the many brakes on fire, which I'm presuming was due to the mixture of high temperature and high altitude. I'm not sure what explains Liam Lawson's assumption of fire, unless his cockpit just felt that damn hot!

I am also presuming Red Bull turned the wick up on their engine for their home race, the way Ferrari do for Monza.

The effect the timing of the safety car had on the outcomes of the strategy calls highlights the importance of luck - it's normally Leclerc hit by "safety car 1 lap after it would have been useful for him"; this time it was Antonelli.

The current Ferrari team don't seem to be able to have two good races in a row. As a Ferrari fan, hearing the commentators asking "is the Ferrari strategy clever or just really, really stupid?" is frustrating because the answer is always that it's really, really stupid.

I think Andrew Benson on the BBC radio commentary described it best, the Ferrari strategy is "... hoping for something instead of racing with what's in front of you right now". They are just hoping, not planning for the various possible outcomes or making something happen. It's so frustrating!!!

World Cup 2026 - Second Round Network Visualisation

This has been written in a hurry between me waking up after the last round of group stage games played overnight and the first of the second round matches this evening. 

Truly, this turn around time is too tight for data visualisations. I worry how this short turnaround time will affect the preparation of the teams. 

Group stage results: 

I am not surprised that two teams from Group A went out, all the teams in that group were on the outside of chart. I am surprised that South Korea were one of the two. (From distance on the diagram, I presumed it would be Czechia and South Africa to go out from that group) 

The diagram didn't have Scotland going out, but I was also not surprised that Haiti weren't the roll over some people thought they would be. 

The weakness of Türkiye and Tunisia was unexpected given how central they were. I don't think anything explains Uruguay's performance other than sometimes, everything goes wrong. 

In terms of my predictions, this is how I did (blue is right, red is wrong): Qatar, Jordan, Iraq, Egypt, Uzbekistan, Iran, Cape Verde (never have I been so happy to be wrong), South Africa, Panama, New Zealand, Curacao, Australia, Czechia, Bosnia and Herzegovina and Saudi Arabia 

15 guesses (because none of group C were obviously sticking out) - 10/15 correct. 

Following the removal of the teams that have gone out, the network diagram now looks like this: Labelled, it looks like this:  

Average degree (number of links between circles) has gone down slightly from 1.427 to 1.416. 

The team closest to the centre are Croatia - although exactly where the centre is has been thrown off by South Africa sticking out by that much. I would guess the centre is actually Cote D'Ivoire. 

The "weight" of the diagram is also thrown off by a lot of teams clustering at the top. 

Union Saint-Gilloise are the club team closest to the centre. 

The club teams with the most representatives still in are Manchester City with 18 players left in, Bayern Munich with 16 and Arsenal with 15. 

A couple of other teams have enough players left in to be seen as large(ish) orange circles. They are Paris Saint-Germain (14 players still in), Barcelona (13) and Crystal Palace (12). 

One of these teams is not like the others. 

What does the community view look like: Labelled it looks like this: There are 32 teams left, but only 22 communities. 

The communities are as follows: 

Group 1 - Teams that are individual communities: 

1) South Africa - Light pink 

2) Australia - dark green 

3) Cape Verde - olive green 

4) Canada - pale(ish) purple 

5) Switzerland - electric bubblegum blue 

6) United States - mid blue 

7) Mexico - pale sandy brown 

8) Ecuador - grass green 

9) Ghana - Pink 

10) DR Congo - red-brown 

11) Algeria - dark grey 

12) Egypt - mint green 

13) Netherlands - serendipitously orange 

14) Paraguay - red-pink 

15) Sweden - sort of pale RAF blue 

Group 2 - two team clusters: 

16) Japan and Croatia - also orange, because I can't figure out how to change colours 

17) Norway and Colombia - pale grey-blue 

18) Ivory Coast and Senegal - bright green 

19) Morocco and Belgium - bright blue, like I said, I don't know how to change colours. 

20) Spain and Argentina - mid green 

Group 3 - large multi-team clusters: 

21) Bosnia and Herzogovina and Austria and Germany - paler pink 

22) Portugal, Brazil, France, England - dark brown. These are being pulled together by club teams that have a lot of representatives (Paris Saint-Germain, Manchester City, Arsenal) 

What does the updated network graph suggest about the second round matches? 

A complication for this round is that South Africa protrudes so far from the main cluster that the geometric centre and the "gravitational" centre no longer match. Several predictions depend on which definition you prefer. 

Germany vs Paraguay - Germany 

France vs Sweden - One of the problems with the tight "Manchester City, Arsenal, Paris Saint-Germain" group that includes France, Portugal, England and Brazil is that it pulls those teams out of the centre of the diagram. That means that going off absolute centre of the diagram, the prediction is Sweden wins but going off the "gravitational" centre of the diagram, it'd be France to win. 

South Africa vs Canada - Canada 

Netherlands vs Morocco - Diagram says Morocco 

Portugal vs Croatia - another split decision: diagram says Croatia, weighted centre says Portugal.  Experience says Croatian witchcraft. 

Spain vs Austria - The rewards for finishing second in a group are getting a match vs Spain rather than a match vs Switzerland for 3rd. Truly, Austria have been stuffed by the draw. 

United States vs Bosnia and Herzegovina - Diagram says US 

Belgium vs Senegal - Diagram says this should be close. Having watched both teams (yeah, not sure why the team whose matches I've seen the most of are Belgium), experience also says this could be a cracker. 

Brazil vs Japan - another one affected by absolute centre vs gravitational centre. 

Ivory Coast vs Norway - Diagram suggests Norway just, but another match that could be a cracker. 

Mexico vs Ecuador - Diagram unclear 

England vs DR Congo - another one affected by absolute centre vs gravitational centre. 

Argentina vs Cape Verde - Oddly, another one affected by the centre issue. 

Most "any given Sunday" of ifs. But if Cape Verde could do it ... 

Australia vs Egypt - Diagram says close 

Switzerland vs Algeria - Diagram says Switzerland 

Colombia vs Ghana - Diagram says Ghana. Another one with the potential to be a cracker. 

Because so many teams are still in, the diagram is still very busy. I am looking forward to several of those matches.

Are the scrutineers picking on my driver? - Update after the Barcelona Grand Prix

The scrutineering numbers at the Barcelona Grand Prix did some interesting things. 

The Barcelona Grand Prix:  

I have no idea what Norris has done to require that much scrutineering. 

I mean, with an χ² of 3.23 it's not significant, but, with a standardised residual of 1.30, that's the largest deviation from expected we’ve seen all season. (The full series can be found here) 

The other thing that interests me is that there was no random check on one of the top 10 finishers despite there being more than 15 cars officially classified as finishing, which throws off my theory that it's every second race if there are 15 or more finishers. However, finishers 15, 16 and 17 were only technically finishers, they stopped out on track but were classified as they completed more than 90% of the race distance. It's possible that race scrutineering treats those sort of finishers differently. The next time my theory can be tested will be the British Grand Prix. 

The Season as a Whole:  

The difference to expected is not statistically significant with an χ² of 2.39. 

Hadjar being that undertested still confounds me given how well he's been doing. Unlike Alonso, Stroll and Albon, his results don’t obviously fit the “cars that don’t finish get fewer checks” pattern. 

Hamilton, Russell, Norris and Verstappen being over-tested compared to expected makes sense, they've been doing well. 

Antonelli only having been tested exactly as often as expected shows the effect of small numbers (there only having been 7 races so far).

Formula 1 2026 - Barcelona Grand Prix

The Barcelona Grand Prix was the Barcelona Grand Prix. Even the new regs couldn't bring racing to Barcelona. 

What racing there was was mostly Mercedes on Mercedes, and intra-team racing is so much less stressful when it's not Ferrari. 

There is definitely a weakness somewhere in the Mercedes system, because that's now both Mercedes and both McLarens who have stopped on track with a total car failure. 

I think Hulkenberg wins for weirdest cause for a retirement - Hopefully a link to Hulkenberg's instagram If the link doesn't work, he was driving close behind Lawson, Lawson's caused some gravel to kick up. One of the stones pierced the bodywork on Hulkenberg's car, hit the in-car fire extinguisher and the ERS kill switch, shutting the car down. Definitely unlucky. 

Like everyone else, I've noticed the increased number of mechanical retirements this season. It's to be expected when there's such a large regulation change. I also think the regulations were so stable for so long that it lulled viewers as well as teams into a false sense of security about how often racing cars break. I remember the previous Hockenheim layout which used to kill a third of the field by over-taxing their engines. 

I am getting to the best part: 

Ferrari victory 

Ferrari getting lucky with a virtual safety car and not stuffing up strategy 

Lewis Hamilton winning in red. 

I'm not sure what made me happiest - how happy Hamilton looked, how happy his race engineer sounded or the cheers of "Lewis, Lewis, Lewis" from the pit crew.