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.

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

Amazingly, despite the craziness of the Monaco Grand Prix, where teams are now appealing other teams' appeals two weeks after the end of the race, the scrutineering results were pretty much as standard. 

The Monaco Grand Prix itself: Even without the dashed lines showing where 2 standardised residuals are (the point where the results probably become significant), you can see that with an χ² of 1.12, the number of times the cars have been tested is really close to expected. 

This is highlighted by 4 out 22 cars (or around 18%) having been tested exactly as much as expected. Those cars are cars 14 (Alonso), 27 (Hulkenberg), 30 (Lawson) and 55 (Sainz jnr). 

Even the largest deviations are tiny. Cars 3 (Verstappen) and 81 (Piastri) are the most over-scrutinized compared to expected with a value of 0.37. Cars 1 (Norris), 16 (Leclerc), 18 (Stroll) and 87 (Bearman) are the most under-scrutinized compared to expected with a value of -0.37. 

The season to date:  

Car 44 (Hamilton) is the most over-scrutinized compared to expected, with a value of 0.64. He is followed by car 3 (Verstappen), who has a value of 0.36, then cars 5 (Bortoleto) and 63 (Russell) with a value of 0.29. 

Car 6 (Hadjar) is the most under-scrutinized compared to expected with a value of -0.5, followed by cars 14 (Alonso) and 18 (Stroll) on -0.43. 

The rest make sense because they are either doing well (Hamilton, Verstappen and Russell) or have disaster cars (Alonso and Stroll) but Hadjar makes no sense because he's done well, and I'm not sure why Bortoleto has been tested so much because he's only had one top 10 finish. 

Somehow, Bearman has been tested the exact number of expected times with 195 tests. 

However, with an χ² of 1.62 it's clear that none of these differences are significant. 

It's clearer to see if you look at the version of the figure with dashed lines placed at 2 and -2 standardised residuals (or the point where the differences start to probably be significant). They really have reduced over the course of the season. That scale shows differences from expected are not significant.

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.)

Tutankhamun: Treasures of the Golden Pharaoh

The third event of the my 2020 birthday weekend was Tutankhamun: Treasures of the Golden Pharaoh. (The first two were Leonardo - Experience a Masterpiece (The Virgin on the Rocks) and The Duchess of Malfi) 

Like most people of my generation, I was fascinated by Egyptology from being a small child. I have vivid memories of attending an Egyptology exhibition with Mum at an age of less than 5, and the bug bit me. 

Mum actually attended the Tutankhamun exhibition first, and raved about it so much that when I had the opportunity to go, I had to take it. The exhibition website is here - TUTANKHAMUN: TREASURES OF THE GOLDEN PHARAOH » Saatchi Gallery 

The exhibition focussed on both the dig that uncovered the tomb and the contents of the tomb. Unless I ever get my act together and actually visit Egypt, this was the last chance I was ever going to have to see several of these items. 

Everything was exactly as beautiful as you’d imagine. I think having the objects in front of you makes it easier to imagine the artisans all those years ago making these things, and the talent and skill they had. I understand why lots of people are squeamish about mummies nowadays, and I understand “leave my bones alone”, but if immortality is having thousands of people pay homage and leave offerings of money at your tomb more than three thousand years after your death, I think Tutankhamun has achieved a kind of immortality very few ever will, and his immortality has pulled those artisans along with him.

(Note, it's very hard to write a blog post about "ancient beautiful objects are expectedly beautiful")

Did the sprint points and fastest lap points make a difference in Formula 1 in 2024?

I'm now two years late with this update on whether fastest lap points made a difference and since then they've removed the fastest lap points. Which I find hilarious because 2025 is one of the rare years where it might have made a difference to an important outcome. But that's for a later post. Let's look at 2024. 

2024 Fastest Laps  

8 different drivers and 4 different constructors won fastest lap points which is higher than the average for drivers (7) and equal to the average for constructors (4).

Constructors’s standings with and without fastest lap points Removing the fastest lap points makes no change in the Constructors’s Title. 

How about in the Drivers's championship? 

Drivers’s Championship standings with and without the fastest lap points Removing the fastest lap points makes no changes to the standings in the drivers’s championship at the end of the season. 

That means if we put together 2024’s results with the calculated total points if there had been fastest laps from 2009-2018, and the actual results in 2019, 2020, 2021, 2022 and 2023, 0 constructors results out of 169 have been affected by fastest lap points. 

In the drivers’ championship, the number of results affected is 13/373 (3.49% of all results), and none of those are in the top 3 of any given year. 

Let’s look at the sprint races, which I expect to have a greater effect due to the quite frankly ridiculous number of them and the points available for them. 

The sprint race points were as follows:  

Constructors points from the sprint races:  

Drivers’ points from the sprint races:  

Do the sprint race points have an effect on either championship? 

Constructors' championship with and without the sprint and fastest lap points  

No effect 

After 3 years, sprint points have had an effect on 6/30 constructors positions. 

Drivers' championship with and without the sprint and fastest lap points Bearman moves ahead of Ricciardo on countback (one 7th position versus a best of 8th) 

Giving points to almost half the field 6 times a year changes the position of 1 of the 24 drivers. 

Over 3 years with sprint races, 7/68 drivers results have been changed. 

What have we learned? 

• The pattern that the 1 point for fastest lap is too small to affect anything continued. 

• The sprint races don’t do anything to disturb the existing order, and only strengthen the points totals of the good teams, creating further separation between them and the weaker teams. The top 3 teams got ~ 50 sprint points each, the bottom 3 got 6. 

• Deeply amused that McLaren and Ferrari had the same number of sprint points. 

• The order of the drivers is unusually muddled up. Normally it’s very two by two by two. In 2024, not so much. 

For an awful lot more effort, expense and wear and tear, the sprint races do very little to the overall standings. Which strengthens my feeling that they’re pointless.

Formula 1 2026 - Japanese Grand Prix

Qualifying: 

In things that are not important yet, but will be important by the end of the season - Norris already on 3rd and final battery. Even if they can resurrect his second battery, that's too close to maxing out the allowed number of batteries for comfort. 

How much of Max Verstappen's sour grapes about this set of regulations, "I am retiring if we don't change" and so on is due to being beaten by the RB Juniors? 

Pre-race: Radio got slightly more hijinks than usual because of the delay due to repairs following one of the support races. 

Jack Black has noticeably better PR training than Chris Pratt, and sounded like he might have head of F1 before Jennie Gow spoke to him. 

Damon Hill talking about Murray Walker commentating over his victory is adorable. 

However, I disapprove of them whitewashing why the Japanese Grand Prix had to move out of monsoon season. "So we are in sakura season" indeed. 

The race itself: 

See McLaren, if you give him a car that works, Piastri goes fast. 

I did have a full-blown mini-conniption about Bearman's leg; his limping looked like mine when I broke my leg. So glad that it turned out only to be severe bruising. 

I don't think the accident is evidence that the new regulations are too dangerous, just that there is room for improvement. It's not like there aren't crashes with every set of regulations. 

Also, how much of that crash was due to tyres that weren't warm? 

Alice Powell gave a really good explanation around kneepads, and their painful necessity and why some drivers still don't wear them. 

The incident really changed the shape of the rest of the race. I acknowledge the race became duller after the safety car but there was racing up and down the grid and through most of the race, unlike last year's race, which, as someone described it, "could have been an email". Therefore I am still on team "I like the new regulations".

Film Review - Spies in Disguise

I can tell if you will like this film with one simple question - does the phrase "pigeon James Bond girl" thrill some part of your soul? 

If the answer is no, this is not the film for you. 

If it stirs or intrigues you, you will enjoy this film. 

Ignoring the pigeons (we will not be ignoring the pigeons), it's a sci-fi spy film aimed at kids with a remarkably peaceful message. The message doesn't quite work in context, but I figured out the bad guy was going to be more than just a plain bad guy when I twigged that the reason he sounded familiar was because that was Ben Mendelsohn. 

When a film has stock children's film message number 3 (violence is bad), it's the detail that matters. And there was lots of glorious, silly detail. 

Most particularly involving pigeons. 

Someone involved with this film has the same love of pigeons I have and it made me so happy. There was such detail in the pigeons, like the scene where they're flying off through St. Mark's Square. 

There's also some child-friendly body horror in the transformation sequence and exactly how difficult it would to get used to thing like monocular vision if you were used to the binocular vision humans have. (And Sterling as a pigeon gets feathers that look like a bow-tie and I'm sorry, I am the target audience for the film). 

It probably doesn't quite hold up as a good film, there isn't quite enough to it, and as I said, I don't think the message quite works but ... pigeon Bond girl goes a long way with me. (Yes, I am annoyed I couldn't find the end credits bit with her which is really done James Bond credit style. Someone involved also knew their spy references.)

Formula 1 2026 - Chinese Grand Prix

Sprint races: 

I'm listening to sprint qualifying and the sprint race on replay because I have the time. I still don't get what they're meant to add to the season. I understand people like seeing more racing, but if it's the same sort of racing as the longer race, what's the sporting aim? I understand the financial gain, more people attending on Saturday but for its sporting aim, I don't understand. 

It also adds financial risks for the smaller teams. I know Audi aren't a smaller team but I dread to think how much putting Perez's car back together cost. Now imagine if that was Haas or Williams. 

By the way, do we think engine vibrations are why Perez's car fell apart? 

Discussing Williams, I love Sainz jnr so much. He understands that engineers respond better to gentle encouragement than shouting. 

Main race: 

Concerning McLaren - has there been a worse start to a constructor's title defence? There being two different problems leading to the cars being out might actually be worse than there just being a single problem hitting both because that's two problems they need to understand, fix and prevent from reoccurring. 

Audi have a better excuse for cars that don't start given they are new to this F1 engine making business, and at least they now have a 50% average start rate, rather than McLaren's 25%. 

For once, it's not Ferrari whose strategy is ruined by the timing of the safety car. It had to happen one day. I suspect Vasseur would prefer it if they didn't keep racing each other but it's definitely adding to the glory of Ferrari as a concept. And I love Leclerc's radio message saying how much he enjoyed the racing.  Fun still has a place in F1.

Not saying they have form but when I saw a Haas and an Alpine hitting each other, I presumed Ocon and Gasly.  I was wrong, but only partly ;)

That Red Bull is a problem that even Verstappen cannot overcome.  BBC Radio said that he only had 4 DNFs in 4 years before this, which underscores the importance of having a solid car if you want to win the driver's World title.

Truly, nothing says F1 like those moments where they have to use "normal" tech on advanced technology, like gaffer tape, or this time, clippers to tidy up Ocon's bodywork.

The Shanghai circuit really is hard on tyres.  My Mum, not an F1 fan and watching under sufferance, even she was going "look at that tire wear!"

I am very happy for Colapinto - my occasional snarky comments about his performance in last year's Alpine was never directed at him personally, just at how badly Alpine handled swapping him in for Jack Doohan, so I'm happy for him to finally get some points.

Kimi Antonelli, he's so cute!!

via GIPHY

(GIF is Clawhauser, a leopard from Zootropolis, going 'so cuuuuuute'. It is an accurate visual representation of my reaction to Kimi Antonelli.) 

I, and Toto and Bono, could all have done without the lock up towards the end. There's nothing like a little mistake to liven things up. 

(I am sharing the following links so that everyone can see them (and for cheering up purposes if I ever need them) 

https://www.tumblr.com/ef-1/811141285720326144/kimi-antonelli-i-am-about-to-cry-to-be-honest 

 

https://www.formula1.com/en/latest/article/they-helped-me-to-achieve-this-dream-emotional-antonelli-hails-mercedes-as.6uMgvW0qCCkUdPKQJzkuyh ) 

He's so adorable. 

New regulations - 2 and a bit races in: 

It is too soon to decide whether the new regs are good or bad. 

So why am I talking about it? Mostly because this is the first break the F1 season has had. 

The reason these regs were introduced was to improve racing. It was necessary. The last set of cars were too broad and the tracks were too narrow to allow over taking. The circuits can't be broadened, so the cars had to narrow. 

Similarly, there was no way to defend from DRS overtakes (the DRS button killed joy). The new system at least allows some way of defending. 

As a viewer/listener, the first two races this year have been more interesting than most races last year. 

When the drivers and team owners are interviewed, the ones whose cars were not so good with the last set of regulations but are good now like it, the ones whose cars were good and now they're not hate it. What a surprise! 

I'm more interested in the views of say Haas who were middling before and are middling now. Their views are less likely to be tainted by the effect of relative results.

Formula 1 2026 - Australian Grand Prix

Yes, I know this is late. 

The racing: I can sort of, in a theoretical way, understand the people whinging about all the new buttons. It is not pure car goes vroom racing. But, unlike the last set of regs, there was more overtaking and more ability to fight against overtakes. I am mostly in favour so far. 

This may be slightly biased by Ferrari not having produced a lemon this time. 

The race itself: Oscar Piastri got got by the hometown race curse. And how! 

(I am legitimately intrigued by whether there is actually a home race curse. I'm presuming the way to look at it would be % Did Not Finish in home races vs all other races. Note to self - put that on the to-do list.) 

Also cursed - Hulk and this year's Aston Martin. 

I am not sure if Leclerc and Hamilton having to contend with Ferrari's strategy team counts as a curse. 

Hadjar's race lasted long enough that his engine going doesn't count as a curse. I think the new warning flashing lights on broken cars are a good idea. 

I already had the greatest of respect for Cadillac's attempts to do it all from scratch, but I only just realised Audi have their own engine, they're not just using a Mercedes. Bonne chance both of them. 

The result supports my theory that Mercedes were sandbagging in testing. 

I am once again astounded by how credulous BBC radio commentary can be - two ticks after "never trust the drivers" they're believing both Piastri and Verstappen's not-mea-culpas about their respective crashes.