World Cup 2026 - Group Stage Network Visualisation

This behemoth is why everything else, including the Monaco Grand Prix post for my F1 race scrutineering series is late. 

(Please don't feel sorry for me, another part of the reason is I spent the weekend fencing and then watching Women's T20 World Cup Cricket live.) 

This post being delayed means I can at least feel confident that complaints that 48 teams are too much because too many less good teams will get in have been overshadowed by the performances of Qatar, Haiti and Cape Verde (Curacao, don't feel bad, Germany do that to teams). 

48 teams is too many for my system and I really need to find a way to automate this into R. Yes, I know I say this every time. 

Some interesting points from putting the graphs together: 

All national teams except Curaçao have at least one player in their home league and at least one in a non-home league. 

There are no Real Madrid players in the Spanish squad. I'm sure there was a time when that was unthinkable. Interestingly, and possibly showing the strength in depth of the Spanish league, one of Barcelona B is in the Egyptian national side. Luckily, I know how to handle this from the 2025 Women's European Championships 

Teams have taken a lot longer to name replacements for injured players. Historically, they've been really short turn arounds, but Canada and Austria have taken 8-9 days to name their replacements. I'm not sure if that's a side effect of the larger squads or longer turn around times between matches. 

What does this World Cup's interconnectivity diagram for the group stages look like? 

Each national team and club forms a node, with links representing player connections. Larger circles indicate more interactions.  

I've gone with a red to white colour scheme for small to large sizes because red and white are the colours present in the flags of Canada, Mexico and the United States of America. 

I had to turn on the attraction distribution toggle because otherwise several of teams, particularly Ivory Coast and Türkiye, overlap significantly. 

Because of the sheer number of players, and club teams they play for, labelling doesn't really help with clarification. Even with attraction distribution toggled to on, there still a lot of overlap (Senegal and the Netherlands) and near overlap (Belgium and Morocco, Scotland and the United States). 

You can see that some club teams do have a lot of players represented, because their circles are large even compared to the national team circles (which have 26 links, the maximum value of any circle). 

The club teams with the most representatives are: 

Manchester City with 19 

Bayern Munich with 17 

and Paris Saint-Germain with 16 

Belgium are the national team closest to the centre, with Sunderland, Crystal Palace or Inter Milan the club teams closest to the centre. 

The community view does some fun things. You would expect 48 colours if each team is a separate community. There are only 32 colours. 

There are some interesting patterns - the two rightermost teams are the same colour, as are the three teams that cover the top of the diagram. The bubblegum light blue cluster that seems to have eaten the orange cluster have intrigued me. 

If you add the labels to the community view you get some fun groups.  

What are the 32 groups? (These are not in order on the picture) 

Groups 1-14 are individual teams separate because they have lots of players who play for clubs which feature relatively few players from other national teams 

1) South Africa - grass green colour - kept separate because most of their players play for Mamelodi Sundowns or Orlando Pirates who have no non-South African players representing them. 

2) Panama - dark forest green 

3) New Zealand - pinky red 

4) Curacao - electric light blue 

5) Australia - lilac 

6) South Korea - Jaguar green 

7) Canada - dark red 

8) Haiti - mid blue 

9) Cape Verde - pale mint green 

10) Colombia - mid purple 

11) Czechia - pale sky blue - in their case it's all the Slavia Prague players 

12) DR Congo - sort of peach 

13) Bosnia and Herzegovina - pale brown 

14) Qatar - bright pink 

Group 15, Saudi Arabia (pale green) is where that pattern starts to break down. Saudi Arabia's players are clustered in a few teams (Al-Nassr, Al-Hilal, Al-Ahli) but other countries have players that play for them. 

The next group (groups 16-20) are teams that are linked to lots of clubs with players from other countries, but they're still individual communities:

16) Norway - brown 

17) Scotland - pale orange 

18) United States - olive yellow 

19) Sweden - dark blue 

20) Ghana - pale navy blue 

Then we reach the multi-country groups, which I've ranked from least obvious reason for grouping to clearest. 

21) Switzerland and Tunisia - pale blue - slightly inexplicable, because there are few direct links, possibly they are linked by Burnley 

22) Ecuador and Mexico - mid brown - possibly linked by the UNAM and Tijuana players 

23) Senegal and Argentina - pink - another vague one, the link seems to be Marseilles. 

24) Algeria, Belgium and Morocco - this is the orange group eaten up by the large blue group, except Algeria who are half the diagram away. Club Brugge, Strasbourg and Napoli seem to be the link between Belgium and Morocco, then Lille links Algeria to the other two. I'm not sure if those links are the reason they're a separate orange group rather than being part of the electric blue group. 

25) Japan and Croatia - pale green - makes slightly more sense, share Ajax and SC Freiburg players. 

26) Austria and Germany - mid green - yes, I know. Mostly it's the number of Austrian players playing in the German league. 

27) Spain and England - pale pink - linked by Arsenal, Manchester City and Barcelona. 

28) Uzbekistan and Iran - bright green - clearly linked by Persepolis, Tractor and Esteghlal 

29) Egypt - mid blue - Egypt seems to be separate because they link the clear Uzbekistan and Iran group and the clear Jordan and Iraq group, but are also linked to other teams as well, so don't fit into either of those groups. 

30) Jordan and Iraq - bright pink - linked by Al-Karma and Al-Zawraa. 

31) Paraguay, Uruguay, Brazil - dark brown - linked by Palmeiras and Flamengo. 

Then there is 32) Ivory Coast, Türkiye, Portugal, France, Netherlands - the electric blue group trying to eat other groups. Strongly linked by Paris Saint-Germain, AC Milan, Inter Milan, Galatasaray, Fenerbahçe, Chelsea, Real Madrid and Sunderland. What happens to that group as the World Cup progresses is going to be interesting. 

The size, shape and pattern of the network graph, and the fact that 8 of the 12 3rd place teams will go through to the second round makes predictions really hard but doing my best to interpret it (and ignoring results so far). 

If the interconnectedness does reflect competitiveness (which is a big if), then the teams that appear most isolated may struggle. 

From the graph, things do not look good for Qatar, Jordan, Iraq, Egypt, Uzbekistan, Iran, Cape Verde, South Africa, Panama, New Zealand, Curacao, Australia. 

(The first person to point out that there is no one from group C in there will be shouted at). 

It's after that that it gets intriguing (not just for group C):  Czechia, Bosnia and Herzegovina and Saudi Arabia look to be the next 3 out, with still no one from group C. 

Because the rings are quite concentric, it's really hard to tell who is the next outlier, which could be a good sign for how competitive the group stages might be. 

The strength of linkage also suggests football is now global enough to justify the expansion to 48 teams.

Formula 1 2026 - Monaco Grand Prix

Or would anyone who knows who the top 10 were please stand up 

I'm reasonably sure Kimi Antonelli won the race, and I'm reasonably sure Max Verstappen didn't get any points. It's everything in between I'm really not sure about. 

As a racing fan, even the new regulations cannot produce racing at Monaco. 

As a fan of sporting chaos, I was pretty much here:  

The same imp that causes me to want Atlético Madrid to beat free-flowing teams was having a field day. 

I mean, I don't think it's a brilliant look for the sport that positions are still being decided 5 days later (Gasly's Monaco third place reinstated after appeal), when the preliminary parts of the next Grand Prix have already started and it means that I can't congratulate Aston Martin on their first points of the season because I have no idea if they'll keep them. 

But you can't say nothing happened at Monaco.

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

The most important feature is that the random check of a top 10 finisher happened in this race, supporting the theory that that check is done every two races. This means the next time should be Barcelona, which gives a way of testing the theory further. 

What do you mean the race result is more important?! 

Let's look at the scrutineering at the Canadian Grand Prix itself:  

The two cars most over-tested compared to expected were Verstappen (car 3, with a value of 0.74) and Hamilton (car 44, with a value of 0.56), which makes some sort of sense since they were two of the top 3. 

Leclerc (car 16) was the most under-tested, with a value of -0.74 then comes Ocon (car 31 with a value of -0.37) which is unexpected since they both finished the race when other cars didn't. 

Five cars were tested exactly as much as expected, the cars of Gasly, Hulkenberg, Colapinto, Bottas and Piastri. 

None of the differences from expected are statistically significant (for the people who want the details, the results give χ² = 2.0109, df = 21, p-value = 1). 

Looking at the season to date: None of the differences from expected are statistically significant (for the people who want the details, the results give χ² = 1.6534, df = 21, p-value = 1). 

The most over-tested compared to expected are Hamilton and Russell, which makes some sense given their performances. I'd expect Antonelli to be higher than he is, but that's probably the effect of small numbers (the average car, tested exactly as often as expected, would only have been tested 165 times). 

The most under-tested are Hadjar and Alonso, followed by Piastri. Piastri and Alonso make some sort of sense with 2 DNFs which were DNSs for Piastri, and Alonso having 3 DNFs in 5 races. Hadjar is unexpected, because, although he's had 2 DNFs, so have Stroll, Hulkenberg and Albon who have been tested more closely to expected than Hadjar. 

None of the cars have been tested exactly as many times as expected. 

The most interesting result isn't who is highest or lowest. It's how much the residuals have shrunk as the season has progressed. You can't really see it on the individual post-race image. You can see it a bit if you look at the season to date residuals vs. where the numbers move towards significance at a standardised residual of +/- 2. One way to show it would be an animation of the season-to-date charts at the end of the year.

Formula 1 2026 - Canadian Grand Prix

Sprint Qualifying 

Are Williams actually cursed? (We know Lawson is cursed, there seems to be a transferrable Antipodean curse, whose original victim was Mark Webber.) 

The info about tyres being colder because the race is earlier in the year does explain some of the extra knocks and crashes. 

The sprint race: 

You know that point in recent seasons that makes Red Bull go "see, there's a reason we write number 1 and number 2 driver into contracts"? I think we've reached it. 

I don't blame either Mercedes driver for getting elbows out but it is going to make the rest of the season interesting. (I am reminded of what Barrichello said about Button the year Button won the driver's title - "love the man, hate the driver".) 

The full race: 

Ooooh! Damp, changeable Montreal. We are being spoilt! (Sorry, after what they did to Hockenheim, the Canadian Grand Prix is my favourite.) 

Poor Lindblad, the start is a terrible moment for total car failure. 

Ferrari were not the team that screwed up their tyre strategy. I have no idea how to handle this information! 

It was a strange day all round for McLaren, given the mechanical issue Norris had and everything that went wrong for Piastri. I think it was that anti-Antipodean curse. I just wish it hadn't pulled poor Alex Albon into its orbit. 

There was racing! I do love how excitable Harry Benjamin gets. 

Inter-team racing is so much less stressful when it's not Ferrari. 

Poor Russell! Given Norris also retired with some sort of mechanical issue, is this a sign that there is a weakness in the Mercedes engine? 

Perez's car falling apart might be worse than either of the engine failures. 

I dread to think what Alonso's seat issues is code for, given various past seat issues for various drivers - I'm thinking of the time Hadjar's car tried to castrate him in particular. 

While there was less racing after Russell retired, there was racing up until the end, which again supports the argument that the new regulations are working.

Benford's Law - Refresh and month 1

While writing the F1 scrutineering posts, I realised that was the exact testing I needed to be doing for my Benford's Law project (https://fulltimesportsfan.wordpress.com/2021/03/17/obey-benfords-its-the-law-an-introduction-to-my-benfords-law-project/). 

This makes it an excellent opportunity to redo that project, but better, and to finalise it. 

The Benford's law project focussed on the leading digit of all numbers in the lead articles for one year of BBC.com front pages. 

It began in February 2021. 

The 28 daily news articles contained 436 numbers written as numbers (~ 15 per day). 

The data looks like this: Calculated, it's X² = 37.434 

df = 8 

p-value = 9.576 × 10⁻⁶ 

The difference between the expected and the observed is statistically significant. 

Therefore, the leading digits do not obey Benford's law. 

Obviously, this is just one month's worth of data. Most of the deviation comes from the digits 1 and 2. 

1 is massively over-represented (with a standardised residual of 4.7) and 2 is underrepresented (standardised residual of -2.4). 3, 4, 7 and 8 are present as often as they are expected, while 5, 6 and 9 are slightly under-represented, with 6 being significantly under-represented (-2.07).

Further reports to follow (I make no promise on time line, the World Cup and the Tour de France will keep me busy).

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

The Miami Grand Prix itself: 

So yes, they are picking on my driver, that's the only reason Leclerc (car 16) could be the most over-tested driver compared to expected. 

More sensibly, none of those numbers are significantly away from expected. There was no "extra check of a random top 10 finisher", even though there were more than 15 finishers. So the reason for the check isn't there being 15 or more finishers - that's one theory ruled out. Maybe they only do the test every other race? At least that's a testable hypothesis. 

The season to date: Over the season so far, Russell's car (63), is the most over-tested compared to expected. Which makes sense given he's finished all 4 races, and quite highly in all of them. 

Car 6, Hadjar, is the least tested compared to expected. It makes some sense, he's not finished two of the races, but he's not alone in that. Possibly it's just a quirk of small numbers, because there have only been 136 expected tests. 

1, 55 and 87 (Norris, Sainz jnr and Bearman) have been tested exactly as much as expected. That's fewer cars than after the Japanese Grand Prix, but I think that's because there were a lot of people had incidents during the race so there was more variation in the number of tests. 

None of the differences are statistically significant. 

After 4 races in of potentially 22, no drivers have been significantly over-tested, but the pattern of how close to expectation the number of checks is over the season varies, possibly as a function of small numbers at this time.

Formula 1 2026 - Miami Grand Prix

Before the race: 

To have one car burst into flame is unfortunate, two smacks of carelessness, Audi. 

I have been caught in a US thunderstorm before (Gulf of Mexico in my case), I do not blame them for moving the race. Y'all have excessive weather. 

The race itself: 

It all kicked off at the start, didn't it. 

Hadjar Vs his car is one of *the* pictures of sports frustration.  

I sympathiese with Sainz jnr's complaints about Verstappen's aggressive overtaking style. Personal opinion, Verstappen's going to keep doing it until someone counter-bulldozes. Complaining to the stewards doesn't work. 

Sky and BBC both suggested that the way stewards investigations happened at the Miami Grand Prix made it feel like there is one rule for the top of the field and one rule for everyone else when it comes to the timing of penalty decisions. I have tremendous sympathy for the impossible position the stewards are in, and that there's too much going on for them to make decisions on everything at the time. A simple solution might be if they just make a decision that they're going to review everything after the end of the race or maybe incidents after half way through the race will be reviewed after the end of the race. If they stick to a rule like that, people wouldn't complain about inconsistency (or not about inconsistency around this). 

Even amidst the small changes around the rules, one thing doesn't change - Ferrari's strategy causing a driver to have a breakdown on radio. At some point, even a Magic Eightball would do better. Or, the way Andrew Benson phrased it on BBC Radio [slight paraphrase] - "Ferrari's strategy is a persistent mystery to most in the paddock". 

I think that Leclerc should get bonus points for not crashing at the end, not a time penalty, but this is why I am not allowed to be a steward. 

My opinion on the tweaks to the tech regs: 

These changes have been made in the middle of a season, so there is no way they could have been large changes. Verstappen wanted much larger changes and was always going to complain when he didn't get them. Part of Verstappen's problem isn't the regs, it's that Mercedes got the regulations right and designed a car that works under them and that McLaren have been able to catch up a lot more quickly than Red Bull have been able to. While there are reasonable complaints to be made about the new regs, they gave us an interesting Miami Grand Prix, which I thought was impossible.

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

The Japanese Grand Prix itself: Further to my theory that not finishing means less testing, once Piastri (car 81) finishes a race, he is the most tested car in that race. 

With 20 finishers, the bonus testing of one of the top 10 finishers happened. This time it was Lewis Hamilton, car 44. This is more than 15 so that fits in with my theory from the Chinese Grand Prix post. 

Bearman (car 87), one of the two non-finishers, was the least tested car. Stroll, car 18, the other non-finisher, is the second least tested. This supports the theory that non-finishers get tested less. 

As with the previous races, none of the differences are statistically significant. 

Season to date up until the end of the Japanese Grand Prix Russell (car 63) is the most tested compared to expected with a standard residual of 0.59. 

Alonso (car 14) is the least tested compared to expected, possibly because of how few laps that Aston Martin has finished this season. 

One good race has catapulted Piastri from the most under-measured to the middle of the pack. This demonstrates why I think the numbers will tend towards the expected as the season progresses, except for possibly the drivers who are frequently in the top 10 and those whose cars do not finish. 

None of the differences are statistically significant, and now 7 drivers are exactly on expected, fitting in with the theory that the numbers will converge as the season progresses.

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

Results from the Chinese Grand Prix 

My first observation of the scrutineering at the Chinese Grand Prix is that different things are checked at different Grands Prix. 

That makes some sort of sense. 

F1 engineers are a bunch of overgrown schoolboys and girls looking for a way to get around the rules. If you always checked the same things, they'd make sure those things were legal and that everything else wasn't. But, at the same time, there is no way to check everything on every F1 car every race. So always checking most important things and varying which of the other things you check makes sense. 

On the other hand, some of the differences don't make sense. An example is that, after the Australian Grand Prix, one of the top 10 finishers (car 63 - George Russell) was chosen for "more extensive physical checks". 

After the Chinese Grand Prix, no car was similarly chosen. I don't think it was number of finishers, Australia had 16, China had 15. Possibly >15 is the cut off? 

It's something I'll keep an eye on as the season progresses. 

Below is a bar chart of the number of checks compared to expectation (measured using standard residuals).  

The most tested driver is Leclerc, while Piastri, Albon and Alonso are the least tested. 

None of the differences from expected are statistically significant. 

Most of the under-tested drivers are those that either did not start or had to retire from the race which supports the theory that under-testing is related to not completing the race. 

The season up to the end of the Chinese Grand Prix:  

Piastri (car 81) being the most under-tested supports my theory that the under-testing is due to not finishing and is exacerbated by him not even starting those races. 

George Russell (car 63) being one of the most over-tested I can explain because of how well he and Mercedes have done. Ocon (car 31) being equally over-tested, I can't explain, because Haas haven't performed as well as Mercedes and Ocon isn't the top-performing Haas driver. 

The number of drivers that have been tested exactly the number of expected time, now 4 rather than the 2 after the Australian Grand Prix, also makes sense if, as hypothesised, the number of tests will converge towards expected as the season continues.

Are the scrutineers picking on my driver? - an unexpectedly timely series

Background: 

As in many sports, after each Formula 1 race, the equipment is scrutinised. 

In the heart of every Formula 1 fan lies a conspiracy theorist, and yes, the universe is out to get your driver or team. 

So, do the scrutineers pick on any particular driver? 

Methodology: 

This entire project would not be possible without the FIA Docs Bot on Mastodon (@fiadocsbot@mastodon.social - https://mastodon.social/@fiadocsbot) run by @seppewyns@mastodon.social (https://mastodon.social/@seppewyns). 

Originally, I started this last year, but things got away from me. FIA produce a lot of documents per race (normally 75-80 of them) so I lost track of the documents and I am not going back to find them. 

Therefore, I am restarting the project for this year. 

Matters are not helped by the tests not being the same each time, which means that putting the results in is a very manual process, but there will be more about that in the post about the Chinese Grand Prix. 

Results from the Australian Grand Prix 

There were a total of 812 checks. If they were evenly spread, you would expect 36.9 checks per driver. I have rounded this to 37. (I am aware that this rounding will affect the numbers over the season but you can't have .9 of a check.) 

Driver 5 (Gabriel Bortoleto) was checked the most, 41 times. 

Driver 27 (Nico Hülkenberg) was checked the least, 32 times. 

This makes me suspect that drivers that do not start the race get fewer checks. 

With 21 degrees of freedom, the χ² = 2.92 value is not statistically significant. 

Let's look at the deviations in one chart (thanks to R stats). This chart compares the standardised residuals for each driver. A driver with the exact number of checks performed as expected would have a value of 0.  

For the 4 drivers with the largest difference to expected, 2 had slightly more checks than expected (Bortoleto and Hamilton) and 2 had slightly less (Hülkenberg and Piastri). 

For Hülkenberg and Piastri this might be because they didn't start the race therefore their cars were not available for some of the pre-race tests as well as the post-race tests. 

Conclusion: 

At this time, no, the scrutineers are not picking on any driver. (I feel I need to add that's what I expect the end results to show too.)