From First Principles - The Physics of the World Cup: VAR, Smart Balls, and Soccer Aerodynamics (EP 45)

Episode Date: June 29, 2026

Hosted by Lester Nare and Krishna Choudhary, this episode is our World Cup special — a deep dive into the science, physics, engineering, and data behind the beautiful game.We start with the offside rule and the controversy around semi-automated VAR. How can a system decide whether a player is onside or offside by only a few inches? Krishna breaks the problem down like an experimental physicist: player speed, ball-contact time, camera frame rate, significant digits, and the error budget behind the line on screen. From there, we get into the actual technology: player tracking, digital twins, high-resolution cameras, and the connected match ball sensor that helps determine when the pass was played.Then we move from refereeing technology to the ball itself. Why does the 2026 World Cup ball look the way it does? How do Platonic solids, panel geometry, and surface seams affect the way a soccer ball flies? And why was the 2010 Jabulani ball so controversial? We go through drag, drag coefficients, wind tunnels, the drag crisis, golf ball dimples, and why the roughness of a ball can completely change its trajectory.Finally, we look at the hidden engineering of the World Cup pitch — real grass in NFL stadiums, LED grow lights, drainage systems, turfgrass science, and even 3D-printed cleat-foot testing devices — before ending with match momentum, possession value, hydration breaks, and the data science behind modern football analytics.Support the showDonate: FFPod.com/donateFollow: @FFPod on X / Instagram / TikTok / FacebookShow NotesSemi-automated offside technology and connected-ball systemsAdidas Trionda — official 2026 World Cup match ballAerodynamics of World Cup balls and the Jabulani drag-crisis controversyWorld Cup 2026 pitch engineering and turfgrass researchPossession value and match momentum in football analytics

If we take a look at that image, the ruling is extremely precise. That means that the VAR is able to discern down to just a few inches. How are you getting that precision? What they do is Hawkeye creates digital twins. The players get scanned, head to toe, and you create a digital twin of their body scanned by a computer. The ball actually has an internal sensor. It's a 14 gram sensor, an inertial measurement unit. That thing takes data at 500 hertz, 500 data points per second.

And it's measuring acceleration and things like that. So when you hit it, you'll know within 500th of a second when the ball was hit. Hello, Internet. This is your captain speaking. Lester Nare, joined as always by my co-host and our resident PhD Krishna Chowdery. This week, we are going to get into our World Cup special as we are all enjoying the world's beautiful game of football. and we're going to talk about some of the technology, physics, and science behind the beautiful game as we see it today.

As always, we were going to talk about the science from the ground up today because this is from first principles. So the World Cup means a lot to the both of us. We were just at the Iran versus Belgium game at Los Angeles Stadium in Englewood. The game ended in a zero-zero-zero draw. was still pretty sick. Nonetheless, the Iran golly did an amazing job. The stadium was created.

The energy, there's a huge, I think the largest Iranian population outside of Iran is in Los Angeles. There was a lot of, a lot of energy in the stadium. Yeah, yeah. And I mean, the World Cup means a lot because I grew up in India and in India, like, or in any really developing nation, World Cup means you stop what you're doing and you watch all the games. We used to root for either Argentino or.

Brazil. A lot of Brazil fans in India against whoever was playing. Argentina, because I think a lot of my parents' generation grew up with watching Maradona win in like 86 against England, and everyone's like, yeah. So it's, you know, I grew up watching it and then to actually see a game live, it was also unbelievable. I mean, for me, my family is a soccer family. I've played soccer my whole life. Right. You know, I mean, the 94 World Cup, I was, I was four. You know, I have those faint memories of like, you know, my dad's, you know, in his postdoc program, there was a bunch of Brazilians. And, you know, I played when I was young. My little brother plays professionally in the U.S. currently. And so as someone who has, you know, been in the national team pool, I was in the Olympic development program when I was younger. I wanted to play for the men's national team. I didn't make it. I wasn't good enough. But the idea that, you know, especially in this world, Cup hosted at home to see the progression of the U.S. men's national team. Quick shout out to the U.S. women's national teams, which is four-time World Cup winner. And so we do have great football heritage in this country. We've just not seen that translate into the men's game yet. I mean,

it's just a such an emotional thing to see it finally get its just desserts and not being called a foot fairy anymore. Yeah. And we're doing quite well. So far, so good. So far, I think we are our group. Yes. And, you know, we're going to, I think we're going to win it all, but, you know, we'll see what happens. We'll see. We'll see. So I've been watching a lot of the games. And I'm going to start with some, the first thing that actually got me going down this rabbit hole of technology behind the World Cup. I was watching the game with England versus Croatia in the group stage. And that, like, right before halftime, Croatia got an equalizer right before the half to make it 2-2.

Ivan Parisich delivered a perfectly weighted pass to Peter Musa. And from this perspective, it looks offside to me. Peter Musa is the blue shirt right outside the bigger box, whatever that's called. And he seems to be on this side of all the English defense. So then we can go into the next photo, which shows the actual judgment, right? looks offside to me. So this is, the offside rule is, is, is, is been something that has been changed and complained about for a long time.

And I think what's interesting about the off sides rule that is, is not as well understood is that the specific verbiage, because the idea is you have the, usually the goalkeeper is the last defender before the goal. And then, you know, if you're in between, basically if you're in between the, the, the, second to last defender as a forward like your off sides right and the idea is you want to stop camping and all this stuff yeah fine hanging around by the goal in this case people are asking well his arm is offside yeah so why is he not offside and technically the the definition for the offside rule is that it has to be a playable body part and the way that's defined is

that means the head the torso the legs and feet so hands Hands and arms do not count as off-size because you can't really play with those. So this is where you're seeing players now lean, but the issue is the shoulder. You don't want your shoulder to get over there, but if the arm is over technically based on the current rules, it's not off-side. And so like, again, there's sort of small details there. Right. But the off-size is very controversial. Some people have argued that we should, you know, the games would be more excited.

in more goals if it's your full body. Yeah. Not a part of your body. If I were to choose, I'm kind of inclined to say, yeah, I think it should be full body. Yeah, more goals, maybe. Like, I don't, like, if I'm leaning just over the line, like. So here's the deal. Go back to go back to that image. Yeah, yeah, yeah.

This is, this is, you know, I was watching this in the commentary. England was pissed. The British lady on Fox One was pissed. I was confused. And here's why I'm confused, okay? If we take a look at that image, the ruling is extremely precise. Okay, they're saying, oh, the arm is over the line, but the body is not, as you're saying, right? But that means that the VAR, this video referee thing is a review, yeah.

Yeah, is able to discern down to just a few inches. Yes. Okay? Yes. That's where the judgment is happening. It's like if his body was a few inches this way or that way, it would have been offside or on side. Okay. That is where I started calling BS. Okay. Because as any good experimental physicist, you are worried about those margins. Okay. And what you're telling me is that the plus or minus,

like in that judgment is within a few inches. Yeah. Okay. How are you getting that precision? I think a lot of people would like to know. Right. Because this is also something that's relatively newish, the semi-automated technology. Yeah, yeah. And it, like, from just a mental perspective, it didn't really make sense to me. So I'm going to lay out the argument here, okay? Yeah, yeah, yeah. So, offside depends on two things. Where the player is compared to the other players, so where the players are.

And also, when the ball was kicked, right? Because it's the placement of the players when somebody made the pass. Okay. Yep. So let's go into what the errors are in each of those measurements. Okay. The impact or the contact time when I'm like kicking a ball, the passer's foot in the ball, that's going to be approximately a hundredth of a second. Okay, so 10 milliseconds.

Now a player that's making a run, let's say, that's sprinting at his peak velocity. In that case, it wasn't peak velocity, but let's just imagine, right? At its peak velocity, he's going to be going like 10 meters per second, rough ballpark, right? Rough. And so while the passer is making, contact with the ball over that 10 milliseconds, the player will have moved 10 centimeters. That should be like, do you understand? So you're not, it's when the when part is ill-defined by 10 milliseconds, which means the where part should be, if you knew exactly where the player was,

it would already be ill-defined by 10 centimeters, okay? But I don't even think that that's, that's, And this is, this is, this is, um, hedging on the fact that I know exactly where the players are. Right. That again, I don't understand because you've got like, from my camera perspective, right? Um, the, the error in the cameras should be another few inches. So that's only going to add to that error budget. Um, but then I start thinking, okay, the passers foot and the ball make contact in 10 milliseconds, right? But like the camera that's doing this judgment is at like 30 frames per second. Yeah. Which means that like from one frame to the next is 30 milliseconds, right?

30 times. That's your time resolution. Right. So again, now you're going to a third of a meter. That's a foot. That's this big. And it's the difference. Is the error.

Yeah. And that, the offside judgment there was like, they were like, oh, this is here and the line is like cutting through his body. Didn't make sense to me. I think a lot of people who are anti-VAR are going to love this conversation. But so from a fundamental physics perspective, right, when you're, and this is something that you learn in undergraduate physics very, very early. There's an importance in significant digits. When you don't like, you know, when you're even like measuring the most simple experiment that you do, like the first week or two of undergraduate physics lab is you measure gravity.

Okay. And in order to do that, you're not really measuring gravity. Like that's not the important part. The important part is to measure the distance between. two timing like photo gates and then drop a ball so that you measure the time difference between this and this and then this and the impact to the ground and then you measure these two distances and the real exercise there is to say how precise do I know this distance and this distance how precise do I know when the ball hit the ground right and how many significant did like is it

point one seconds point zero one seconds so on and so forth Is it within a centimeter? Like, is it nine centimeters? It could be 10 centimeters? No, we couldn't. But it could be 9.5 or 9.7, right? There's a plus or minus there in the deviation. And so from that, you can then calculate gravity,

and you're not going to report it as 9.847265, right? Because you need a much more precise experiment to actually determine that level of precision of gravity. As we talk about, you know, a variety of fundamental research papers, the instrumentation is a key thing we talk about and the level of precision of that instrumentation matters quite a bit. It's why we have electron, you know,

it's why we have very, very, very precise detection machines in order to reduce that error. That error budget. Okay. And so that's why, like, I was just doing these calculations while watching this going like,

this is nonsense. There's no way that this could possibly be happening because you need to bring down both the time of contact, of the ball. Yeah. Right. To within a very small time step of like when did the player hit the ball. And then to where the players are.

Okay. They need to bring both of those errors down. Well, I looked into it and they have. Okay. This is, they have. This is so interesting because a lot of people, I'm so excited. I'm so excited.

Yeah. And so it turns out they hired this company called Hawkeye. That's what they do is Hawkeye creates digital twins. So in photo four, you'll see the players get scanned, head to toe, and you create a digital twin of their body scanned by a computer. And then that digital twin of the athlete can be dropped into a virtual simulation of the game to determine their exact position based on 16 different high resolution cameras. So in photo five, we've got the photos of the high resolution cameras. And one of the things that you learn in experimental science is like the error goes down by one over the square of n. So in this case, whatever, if you had just one camera and you were trying to track the position, with 16, your error goes down by a fourth.

Yeah. Okay, four times smaller. Yeah. Okay. That's quite good. But that's still not enough. The real magic here is the digital twins because it's something that we do a lot in science, which is we've got a model of our system. and then we've got data, we fit the model to the data to get really high precision.

We do this a lot with atmospheric transits of like exoplanets, right? Like the exoplanet goes through. We get some spectra. The spectra is noisy, but we try to fit models to that spectra to really understand what is going on. In this case, our model is the player's 3D digital twin, and we're fitting that model to the data from the 16 different sensors. I think most people didn't even know that they got scanned into 3D for reasons other than to be put into the FIFA, oh, excuse me, FC26, the game, because now FIFA no longer

gives EA sports the rights. So it's no longer FIFA insert year. It's now FC. But like, for most people, when they think about like, they think about motion capture and 3D scanning, that's the context. Yeah. I think it's a very important detail that that's why when you see those little die, like the little example photo we just show. Yeah. Yeah. That's, that's the 3D model of the player itself. Of the player itself. They're using like computer vision to actually like fit the 3D model to the player. And this is something that like we do all the time. Like even in neuroscience and

behavior experiments like when you have like a rat running around in a maze, you've got a camera that tracks the rat, right? And then there's, you can create a 3D model of like the rats' joints to figure out his body position, correlate that to the neurons that are firing and so on and so forth. It's used a lot in behavior experiments. I'm sure like similar technology is being used to recreate the player positioning at every given

moment. Because Ivan Parasich and Erling Holland are very different players. Yes, exactly. You know. It matters. Yeah. And it is kind of cool that like they have that kind of granularity. Yeah.

So that's the where the players are. Now what about the when? Right? Because I said the 30 frames per second is not going to do you any good. Even the 50 frames per second if you have a high speed camera is not going to do you any good. And by the by the judging by the size of that camera. Yeah. Like that's not like one of these like 100 frame for second.

second cameras, right? So to get the timing down of when the ball was hit, the ball actually has an internal sensor. It's a 14 gram sensor, an inertial measurement unit, an IMU that's used in like gyroscopes and things like that for aerospace. In this case, they stuck it. It's inside the FIFA ball, like just beneath the surface. That thing takes data at 500 hertz, 500 data points per second. And it's measuring acceleration and things like that. So when you hit it, you'll know within 500th of a second when the ball was hit. So now you can finally get the, the, like a level of resolution.

A resolution down to that size. So now when they show that line, that line has a thickness of about a centimeter or less. Otherwise, it should be a blurred out line. Right, right. Because I don't know where the ball was, when the ball was hit. Yes.

Right. So that kind of made sense. And combined, this gives the comprehensive VAR system. You've got the 500 hertz from the ball. You've got these 3D positions from the players, and that's where you get that line. And so when people hear VAR, they think,

and it did used to be this way where it was just some people in a room and they would draw lines manually on the video. Yeah, based on a video. At an angle that was not the correct angle, all these things. Yeah, all these things. And it's like, but now it kind of makes sense. Now it's actually. With the amount of data that's going in,

can understand if the air budget is for like that thickness of the line is like way smaller. It's reasonable. Yeah. Now, again, in the World Cup, not in all leagues in the world, not a club level, everyone's a little different, but specifically for the World Cup and their VAR system. Yeah. Yeah. And so I wasn't done there because this got me thinking about other stuff.

Okay. Like, for example, you've got the sensor that's in the ball. Yeah. How come the sensor is off like to the side just. underneath the ball surface. And if you look at the 2022 World Cup, that also had a sensor, but it's at the center.

It's suspended at the center. That kind of naively made sense to me. But off to the, just under the ball, doesn't make sense to me because it's kind of lopsided now. And so just for folks who may be listening, you know,

the, the 2026 ball basically has like an AirPods size case, an AirPods case or like a wireless headphone case size, just nodule just below the surface. on one particular spot in the ball versus in 2020, it was sort of looks like the structure of, we talk about, there's a center point in the center of the ball

where the sensor is. And again, naively, it's like, yeah, the center point. Because you want to tell where the balls are on all sides? If it's on one side, how would it know on the other side? Yeah, yeah. And if it's on one side, wouldn't it be like lopsided? It would like affect the rotation, right? So there's a reason why the sensor should be right underneath the surface.

And this kind of also makes sense. I just thought it was a bit weird that they didn't do it even in the beginning then if this is the reason. And the reason is that you want higher linear speed. Like if you've got the sensor right at the center, right, and the ball is not moving and just spinning, the sensor is not going to register a lot of movement. And these things are accelerometers at the end of the day. And an accelerometer measures linear acceleration. It discerns spin based on linear acceleration.

how like, oh, at one point there's an acceleration in the X direction, then it's in the Y direction, then it's in the X direction, then it's in the Y direction, and the cycling is going to get you the spin rate. Well, if you're closer to the edge of the ball, then as the ball spins, you have higher linear acceleration, and so your signal noise effectively is like larger. Right. Right. Right. It makes sense. And so that makes sense, why it would be over there. But that means that you have to balance it. And actually, I thought back to my classical mechanics days. And it's very easy to balance something and make it look like a sphere because all you have to do is if you have one thing over here and you know you want the center axis to be like that origin point, then you just

make a similar weight on the other side. But that can't be enough because now you have a preferred axis. So you need two other on this end and on this end. And then what ends up happening is for those who are in undergraduate physics and have taken an advanced course in classical mechanics, what you're doing is making the inertia tensor diagonal in that like there's a matrix and everything else is a zero except the stuff in the diagonal and all of the diagonal elements are the same

because you have the same mass here, here and here. And so you can just factor out everything and it becomes the identity matrix where you have zeros everywhere and just one-one-one and it looks exactly like a sphere. And this is one of the coolest problems I remember homework problems in my classical mechanics was like proving that like a sphere

spins the same way as a cube in for all intents and purposes which is kind of crazy to think about like a sphere literally looks the same from every side right in the sense that like for example I can take a sphere like let's say a uniform sphere and I can attach a string to it to the to the ceiling and then when I when I like twist it

it's gonna oscillate like this and the frequency of oscillation like this doesn't matter where I attach on the sphere because if I rotate the sphere this way and then try to do it, the torsion pendulum is going to be exactly the same, okay, the frequency of oscillation. For a cube, naively you would think,

if I attach the string on the flat part or if I attached it to the corner, the frequency of oscillation should be different. But no, because the inertia tensor is identical in the sphere and the cube or even one orientation, no matter how you rotate it, those things like don't change the inertia tensor.

It's what's called a unitary transformation. I just remember this from like, it was like an undergrad problem at Princeton. The class was called DeathMex. And this was one of the problems to like prove that like this is the case. But yeah, it turns out it's like super easy to do now. So now you've got a sphere, you just make the balancing and everything works out. And so part of that point there is it's not just that there's one sensor on one point of the ball and that one hole like in the image.

They've now internally offset it. Yeah, like they just offset the mass right on on all the three axes. Yeah. And as long as they're perfectly perpendicular, you're good to go. Which is why the manufacturing process also does matter quite a bit here. Because, you know, making it perfectly perpendicular is not. Yeah. And you do have to make it perfectly because otherwise I think these players at the top level are going to know.

They're going to know the difference. Yeah. And the other thing that brings me to like Adidas is like making new balls. every World Cup. I didn't know that. I thought it was the same ball. But no. It's like different balls.

So if you go to the FIFA store or if you go to a game, what you'll see in one of the stores is they have the mini soccer ball collection, these like size one balls. They'll have every World Cup ball, right? Oh, wow. Box set, right?

Because that's their whole stick. That's their whole thing. Yeah. And we're going to talk more about the history of those balls coming up. But before we do that, some housekeeping, as you can see. And for me,

I'm loving this, talking about my favorite game in the world on the pod is incredible, but from a science-based perspective. And if you love this show and want to continue to support us, sharing it with family member, a friend, a colleague, throwing it in the group chat, shooting the DM. You can always watch all of our episodes on YouTube and Spotify. That's where we have all our full episodes, as well as directly on the website at fFP.com. FFPpod, excuse me, dot com. We also include our research papers when they are there, and we have some special, new, interesting, interactive explorers

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we always put clips out for each episode and makes it super easy to share. If you want to support the pod directly, you can donate at ffpod.com backslash donate. Any amount helps the two of us continue to talk about the amazing science that not only FIFA apparently is doing, but particularly fundamental science research, which is really what we talk about very often. And again, we will continue to take book suggestions for the new bookshelf that will go somewhere in between the two of us back here in the studio. We are about to receive our new neon signs, which I'm super excited about.

as long as they are not too big. But I'm so excited about this episode. I want to get back talking about the new ball. Yes. And also one more thing about housekeeping in the comments. Please comment on our YouTube or on Spotify. Who do you support winning this World Cup? And it better be America.

But anyways. That's a good one. It's coming home. It's coming home. I love how they play West Virginia after the... Oh, take me home country roads. Take me home. It's talking about the World Cup.

Yeah. We're taking the World Cup. home home here yeah to the u.s yeah the tour of the 50 states maybe exactly it's going to be basically tour of the world in our own country yeah all right so let's talk about this new ball yeah all right so this year it's called the trionda it was officially unveiled on october 2025 by adidas the official match ball who is that guy yeah jude bellingham the uh sometimes the darling of english football sometimes the villain of English football. The number 10, really his celebration when he scores a goal,

he puts his hands out like he's the Jesus statue in Brazil. Oh, hilarious. Great player, used to play Dortmund, made the jump to Real Madrid. You know, I think he... Is he playing now for England? He is playing now. He is playing now. Yeah, and at first, you know, he has a little bit of beef with...

Part of it was media-driven, part of it was real. So the English manager... The English media is crazy. They're crazy about... They're crazy on this. And they're talking, sorry, but they're talking a lot of shit about America. I hate it. I'm not a fan of that.

I'm not a fan of that. I'm not a fan of that. Look, some of us, we watch the Premier League. We have nothing negative to say, just relax, okay? You don't have to point it at us. The small Jude thing that's funny is, so the current English manager is Thomas Tuchel. He's a German. The English, we're not happy about that because they thought it was sabotage.

Oh, kind of like how their royal family is German. Yeah. But they don't have a problem with that. So what's going on there, guys? Anyways. So Thomas Tuchel, former Chelsea manager, by the way, is now the English manager. And him and Jude have had some personal beef. Thomas Tuchel runs a really tight shop.

He doesn't like ego. It's a team. And at first, the media was like, is Jude going to play? Is he not going to play? But he started and he's played. He scored a goal. He's done well. He's a key part of their team.

However, he's also an individual. Adidas athlete. And so he's always in a lot of the Adidas commercials. Oh, okay. Because he's obviously a big player in the world. I will also love to hear people's thoughts about each World Cup, Nike and Adidas, both put out these like huge commercials with all of their stars. Adidas had one version.

Nike had another very different creative directions. I have my thoughts. But I'm curious to see how people, how, what people thought about the World Cup commercials, The full ones, not the clips, the full thing from both. Have you seen either of them? So the Adidas one is the Timothy Chalameh one? Yes. Right?

Yes. And the Nike one is the one where Cristiano Ronaldo comes out of the fire, right? And it reminds me of like V for Vendetta. Yes. Yes. Very, very different. There's a huge legacy to these. Like they've each, like, you know, there's the Jogobonito era with Nike.

But I was more just like impressed at how many big names were in each of them. Yeah. Right? It was like crazy. A lot of money. Yeah. A lot of money. I'm not a huge fan of the non-football players being in these commercials.

Oh, yeah, yeah. I don't know if I'm into that. If they're celebrities, if they're just like normal background actors who played play football. Like, that's fine. Oh, yeah. But like LeBron, LeBron was in the Adidas one. You know. The Nike one.

Oh, yeah, that was the Nike one. The Nike ones. Don't sue us. I get it. I get it. You have, you know, cross-sport. branding, but LeBron has his own commercials. He doesn't need to be there.

Travis Scott, I don't know that you need to be in. I don't know that you need to be there. I don't know. I mean, just like, I don't know if you need to be in the Odyssey. But, okay. Moving on, moving on. All right, okay, this episode, as you get, it's casual. It's a World Cup.

It's World Cup, it's World Cup, baby. All right, so the Trionda, right? It consists of three countries that are hosting. Yes. So you've got the Mexican, like, I guess the talon thingy, then the maple leaf, and then America has the stars in the blue. Okay. Now, the challenge is the following. You want to make an artsy ball, but you got to play with the number three, right?

And three is kind of a weird number because it's odd. It's like not symmetric about a sphere type stuff. You got to, like, fit three somehow. Okay? Now, to understand this challenge, let's begin with the inaugural cup in 1930. Okay? In the 1930 finals, they had this volleyball-looking thing. Both Argentina and Uruguay had actually different preferred balls.

And Argentina used theirs in the first half. Uruguay used theirs in the second half. So they had different balls for the two halves of the World Cup. And Argentina was leading at halftime with their ball. And then Uruguay won the match, which is just, kind of hilarious to think about, right? So that was in the 1930s. And then Buckminster Fuller.

Buckie. Yeah, he's an American architect. And he changed the ball in the 1970 World Cup. And it was the first time that Adidas actually manufactured the official ball. Adidas has made the official balls ever since. What he did was use geometric shapes. He was a big fan of using, like, you know, the Epcot like ball. that Epcot Center, that looks a lot like that.

So the Fuller's Ball, that Buck Minister Fullerine, it's the classic ball that we know from the Pele in 1970 World Cup. This pattern is now so iconic, right? It's got the black pentagons, and I think that's photo 13. Black pentagons, white hexagons, 20 white hexagons for 12 black pentagons. Now this is like the soccer ball. Yeah. If you grew up playing at any point in time prior to like the

modern era. This is everything you played with. Yeah. And because it's got so many panels, what you're trying to do is create a shape from fabric that is a sphere, right? That's the challenge. And now this ball is so spherical that now players can start curving their kicks intentionally. They can allow the shape to have a predictable path through the air. How does that soccer ball actually work, though? Okay. Well, it's actually derived. from a platonic solid, which is our emblem here, part of our logo. You start with an icosahedron, which is a bunch of triangles, and then you take the points and you just squish them.

Okay? So an icosahedron is a bunch of equilateral triangles put together, and you take all of the pointy edges and you start squishing them. So here's the hykosahedron. It starts out. You start squishing them until you get a regular hexagon, A regular hexagon meaning the pink part, all of the edges are the same size. That's when you get the soccer ball shape.

Okay? Very, very nice, very, very beautiful. This year's ball is also derived from a platonic solid, but actually from the simplest one, from the tetrahedron, not from the icosahedron. And this is where the genius of starting to use three, because you still want to use triangles because triangles have that three. So what you do is you take the triangle, the equilateral triangle in your tetrahedron, you start shifting the shape such that the points become these flaps.

Those flaps then have the patterns for the three countries. And then you put that together just as the tetrahedron was, but now in terms of a sphere. Okay? And so we're just basically sort of taking the core shape of the triangle and just taking that surface area and making it a blob. Yeah. That can then be patched together, right? Now the problem is, compared to the Bucky Ball, this has fewer. seams, right? Yes. And if it's got fewer seams, there are fewer grooves within the ball. Right. Right. The Bucky

ball has 20 hexagons, 12 pentagons, so a lot of these edges. Yes. And so there's a little roughness there. Yes. With this one, there's fewer seams. So there's fewer grooves. The ball is going to be a little bit smooth. So you have to counteract for that. And this was especially bad in South Africa with the Jubilani ball that apparently everyone hated. Yes. And this was 20. Yeah. The Jabalani ball. Jabalani was famous. We were sophomores. Yeah, I was, I was just graduating. I had just graduated.

Yes, yes, yes. I remember I just graduated high school and we were in India for the World Cup. Yeah. This is so, and you know, at the time, it's so funny because I remember, you know, you don't always, because you play in in both high school and college and club. You usually, you play with select or sometimes you'll play with some of these Adidas or Nike balls. Yeah. They became a little bit more popular later on.

But you wouldn't really play with the World Cup ball, you know, in practice or whatever. But when the Jabalani came out, one of the things people love, it had this weird knuckle. So like, this is when, like, you know, Cristiano Ronaldo is making these 40-yard free kicks in the Premier League. And the people, goalkeepers hated it especially. A lot of players hated it too. but people who are like goal scorers or people want to take free kids, they liked it because they would move around weird.

Okay. And so they were like, this is great for me because I'm going to score. Yeah. Keep it's nowhere it's going. And I don't really, like I think, I remember at the time, one of the things that would struck me about it was,

and I didn't necessarily think about it, is the surface was so smooth, in part because it didn't have all the seams that you just talked about. But it was extremely, extremely controversial, alongside the Vuvuzelas. Yeah, the Vuvuzela is also very controversial. Yeah.

And that's exactly right. You were saying that, you know, it moved weird. It moved so weird. Goalkeepers hated it. Hated it. Right? There is a nice fundamental physics reason for why it moves weird. And that's what we're going to cover here.

Okay. Okay. The physics of soccer ball flight and how the texture of the ball affects that. Because the shape of the ball is just, it's a sphere. Right? But the rough ball. is really where the magic lies. Okay?

So when you have a new ball, you got to make sure it's not the Jabalaniar. You got to make sure it's not that bad. And so Adidas actually did a bunch of tests, 300 lab tests. Those aren't published, but a group of scientists did independent tests. This is from the University of Puget Sound in Washington,

and then there's also some universities in Japan that landed their wind tunnel to, do some of this testing. And it's really cool because they published a paper in Applied Sciences out of the MDPI publishing hub. Trionda enhanced surface roughness relative to the previous World Cup soccer balls. And they compared the physics between this soccer ball and all the previous ones. And it's actually really, really cool. The main thing that they care about here is drag. And that's the thing that, you know, most anyone cares about when it comes to aerodynamics. So drag is, you know, the resistance of the air to your motion. Okay. And it's always proportional to the

velocity squared. That kind of makes sense because the faster you go, the harder you're hitting the particles and the more particles you're hitting. So there's a double factor of the velocity, right? There's like you're moving through this, so you're hitting the air molecules at a faster speed. So you're transferring momentum faster. And also there's more stuff that you're hitting the faster you go. So that's why you get a V squared. It's also proportional to the area because the larger the cross-sectional area, the more air particles you're going to be hitting. It's proportional to the density of the air, obviously, because like, you know, the denser the air, the more the drag is going to be.

The denser the fluid, right? And then there's something called the drag coefficient, which in this case is the CD. That's the coefficient of drag. And that's like the number that gives you the drag force. Okay? There's like all of those factors plus something having to do with the surface of the ball and the shape. the surface of the object and the shape, I should say. Okay?

Now, with real objects like balls, there is something called the drag crisis. And that's what happens when you calculate the drag coefficient, the drag force, for different speeds. Naively, you would think that the drag coefficient is a constant. It shouldn't depend on how fast I'm going. The effect of velocity is already in that equation. Right. Right. But there is a non-linear effect on the coefficient itself that doesn't have to do with this physics argument.

Okay? That's interesting. There's something else that's going on. And actually, it turns out, the drag coefficient drops suddenly when there's higher speed. That's weird. That's weird. At higher speed, it's easier to go through. So you can see in the wind tunnel tests why this is happening.

So this is at NASA Ames Research Center. NASA loves aerodynamically testing these balls. So here you've got a soccer ball in a wind tunnel. The air is coming in from the left. And as you're spinning, what's happening is your laminar flow of the really nice air is getting broken up at the surface of the ball. And it's creating turbulent flow behind it. Right?

That has a very weird effect on the drag. Okay? Here's what's going to happen. The wake behind that ball is going to create a region of low pressure. You can imagine, like here the ball is stationary and the wind is going through, right? But in real soccer play, the ball is going to be moving through, like, in towards the right. Yes. In this direction.

Yes. Right. Now, on the right hand side, the ball is hitting the air particles. So there's high pressure, right? Because it's like a piston that's like sort of compressing air. And on the behind it, there's going to be low pressure. So there's going to be a force backwards that is not just the particles hitting, but there's like a pressure difference. Yeah.

And that's going to cause some weird stuff. Okay. Okay. Yep. And it turns out that the faster you move, that that low pressure effect becomes less and less. Interesting. Which is a little bit non-trivial. So let's go to the next photo, which is photo number 20.

Yeah, here's what we're doing. The ball is moving to the right-hand side. Yeah. Okay? On the left panel, the ball is not moving that fast. When the ball is not moving that fast, the wake is actually a lot bigger. So the region of low pressure is a lot more, which means that pressure difference is, is bigger. And if the pressure difference is bigger, the drag force is going to be bigger.

There's going to be a bigger contribution due to that pressure difference. On the right-hand side, now you've got the ball moving faster. When you go faster, the laminar flow disconnects from the ball faster. And when that happens, you can actually like flow through the ball. Like you can follow the curve of the ball more, which is a little bit non-intuitive. Like the faster you move, the more the laminar flow hugs the ball. And so your low pressure region is actually smaller, meaning that the pressure difference is not that much, which means your drag has actually gone down.

The faster you move, the drag actually goes down. This makes me think of all the signs to F1 cars, which deal with a variety of these concepts very heavily. This is a big part of it. You want to make that low pressure region behind you not that big so that you have like a lot. Which is why the cars are designed the way that they are. Yeah.

And so the weight can be different at different speeds, right? And if you go to the photo number 21, this is the curve that you're going to be looking at. On the x-axis is the speed of the ball. On the y-axis is the drag coefficient. At low speeds, you've got a laminar boundary. And so the ball is going to hug, I mean, sorry, the laminar flow is going to hug the ball, but then it's going to disconnect very quickly. And you're going to get a massive low-pressure region.

that's going to cause a lot of drag. Oh, actually, that makes sense. As I increase the speed of the ball, the laminar flow is going to hug the ball, and there's not going to be that much low pressure, which means that the ball is just going to be fine. At least that effect is gone. And so your drag coefficient,

there's a period where the drag crisis happens. That's the drag crisis regime, right? It should be flat, but it's not. There's a part that goes down. It's almost like if you give the flow more time, it will dissipate outwards. But basically the faster to move it, you don't give it enough time

almost to get out of that sort of contour of moving around the object that's coming through it. Exactly. And so that's where you get the lower pressure behind. And this is why golf balls are not perfectly spherical. They have those divvets.

Actually, if you go to the next one, photo number 22, this is a golf ball in an aerodynamic simulation. The left is a ping pong ball. There you can see the laminar flow leaves basically at the equator here. From pole to pull. And you have a massive low pressure region.

And so the ping pong ball is going to experience a lot of drag and it's going to do like weird stuff. And that's by design because you want the ping pong ball to be light and to be able to sort of stop within the distance of a ping pong table. The golf ball on the other hand has these divots and that creates turbulence. The turbulence is by design to make that low pressure less of an effect so that it goes farther. There are there away.

Right? Yeah. And that's the whole point of roughness on a soccer ball. Yeah. That makes, and this now gets to the idea of why the Jabalani was so different. Because again, we'd had this sort of classic style for such a long time.

Yeah, we had the Bucky ball with all of those seams and all of that roughness. That's kind of like the golf ball's divvets. Right? And we tried to get all fancy. Yeah. You know. And why specifically, right?

So if the ball is too smooth, what that's going to do is, there's going to be a transition, as you saw in those curves, right? There's a transition from low speed to high turbulent speed. And what I want is to tune that transition, where that transition is happening. Now, if the transition happens too far up, right? Yeah, yeah, yeah, yeah. Let's stay on this one.

So if the transition happens too far up, what's that, what is that going to do? That means that it's in the typical range of free kicks, corner kicks, and all of those things, right? The long passes. and when this occurs, the ball is kicked at high speed, but as it slows down, it's going to be in that transition point, and it's going to go into a spot from low drag coefficient to high drag coefficient,

and it's going to start doing weird things. What you want is most of the ball's trajectory to be in that low drag coefficient spot. This is why with the Jabalaniar, it would start going really fast, and then the last minute. Yeah, because it slowed down into the high regime. This is exactly what the scientists saw,

in the wind tunnel measurements. That's so interesting. On the x-axis is the drag coefficient. On the y-axis is your velocity. All of the other balls, the aurela. On the x-axis. On the x-axis is the velocity. On the y-axis is the drag coefficient.

The main thing to see is that all of the other balls, the trionda is in red. All of the other balls are in the other colors from all the different other FIFA World Cups. The Jabulani is in the yellow. It's the only one where the drag crisis is happening at a higher speed. Yeah.

Yeah, yeah, yeah. Which, and that, I mean, this correlates to exactly what people saw. Exactly. Yeah. That's fascinating. So, but this is like now quantitatively, you can see that Jabalani is the outlier. Yeah. Yeah.

Right. And every other one effectively trends across the similar profile. And what you want is whenever you make a new ball, you want it to basically do the same thing that the others did. Right. You don't want it to do new things. You can make it look pretty, but make it work the same. Yeah, make it work the same. So they're like, whatever the players trained with, that's what they're playing with.

Right. Yeah. And I think just as someone who's played like the. way the ball worked, like it is, it is good, like from a playing perspective. Like, I would not want, I can't really think of how I would want it to operate differently. Like there's, there's, you know, Futsal is an indoor soccer game where the ball is weighted totally differently because it's not supposed to go in the air. Yeah.

And it's very, very, very different. And I don't like it. I don't, but I get it. Like, I get, it's a different game. It's a different game. Yeah. And they also calculated the trajectory. So they took all of their drag coefficient data and they said,

said, okay, let's simulate a trajectory. The y-axis isn't important. It's a kind of like, what percent of deviation was the trajectory different based on like something that was purely a flat drag coefficient? And the X-axis shows velocity. But again, the main thing to see is the Jabalani and the yellow is the outlier.

It's doing this weird. Everything else is following the similar trajectory. Yeah. Right? Of like how the data looks. But in all of their graphs, Then they have multiple sort of plots showing the behavior of all the different balls. And in every single one, Jabalani is just showing something completely different.

I can't believe they got away with this. Yeah. This is actually, it's also, you know, I think the fact that the science is backing up the visual observations. Yeah, it's kind of cool. And the player observations are the player experiences that folks had is this kind of nice. Yeah, I think that's pretty cool. So this particular Trionda ball, this is the most tested ball in history. It also went up in the NASA ISS.

they were doing center of mass and balance in microgravity experiments, which I'm going to be honest, I really don't understand. Like what? Like we're going to be playing Enders game football in like zero G or something. Like what is the need? But I also, I mean, it reminds me of that one show with Steve Corell about Space Force where he's asked like, why are you sending an orange to space for $10,000? And he's like, you know what?

Sometimes these astronauts that are up there for a year, need to remember because they're like eating airline food they need to remember what an orange tastes like and so sometimes maybe they're just playing football yeah but then just say that don't be like oh microgravity why no i don't know i don't care how the how the fiefa ball does in microgravity that's i that's so you know hey shout out to adidas shout out to nassah first football's face yeah great photo yeah okay so that's not everything right because the ball, so the ball is moving in the air, but it's also got to interact with the turf. The turf is actually pretty cool. It's non-trivial to make the turf because we've got

a lot of different stadiums across an entire continent, which means different climates. Some of them are in a coverage stadium. Some of them are in the scorching heat. Some of them are in like Seattle and Vancouver. And this is a living, breathing entity, right? FIFA says that you have to have like living grass. Yeah, the pitch is great. I want to be careful because people associate turf with artificial. Oh, yeah, that's what I mean by, yeah. But the pitch, the field.

The pitch, the field has to be grass, living grass. Not the NFL's turf. No. They're very upset about that we've taken over all these NFL stadiums. We've put in real grass. Oh. And they're like, why can't we get? Because especially for football and like, I can't believe they don't do real grass.

But it can be done. Yeah, I mean, like real grass is also a big thing in the Wimbledon, right? It's like their courts have to be like really precise grass. And so, and once the grass is installed, you got to keep it alive for several weeks. And that's a difficult task. So FIFA has assembled a crack team of turfologists.

Yeah, led by John Sorachan of the University of Tennessee and John Rogers of Michigan State University. They're kind of managing this whole thing. The two Johns, we got the two Johns. We got the two Johns. And they do research on turf grass conditions.

Like this next photo, this is from the University of Tennessee. They've got an indoor turf research building that is showing how like LED lights can be used to grow grass. Like the purple light is something that is the chlorophyll centers of the grass are sensitive to. That's going to cause the grass to grow more. It's kind of crazy that like so much is going into it. Sorachan's team actually invented something called Flex, which is a portable device that's outfitted with a 3D printed foot. with soccer cleats. And this thing is, this thing is like, it's, it puts down how a normal foot would go on the grass to measure the responsiveness of the grass and to sort of calibrate all of the grass to be the same

across all of the stadiums. Like the amount of, the amount of stuff that people are inventing to, to keep this beautiful game going. I think that's kind of cool. This is, this is really sick.

And I'm going to make a brief plug. I'm pretty sure it's the the Bernadillo, the new Real Madrid Stadium. They have like multiple, so where the pitches, it's literally they will lower it down several stories and there's multiple, there's like multiple pitches stacked vertically on top of each other. So it drops down and then it slides. And so they can literally replace the pitch.

So it's like imagine, imagine you have like an oven, a pizza, oven with multiple racks. Wow. Right? And so they literally will swap out pitches, bring them into the underground facility to mess up with it, but they can just basically, it's like this multi-level, multi-pitch. It is an unbelievable system. That's crazy.

We may want to do a follow-up on that because it is one of the coolest things I have ever seen, and they spent a lot of money for it. But it's also the cathedral of football because they're the biggest, most winningest team ever, although, you know, I won't comment as a as a Chelsea boy. Up to Chels. But, you know, there is, I think the point just being like there is a lot of work. Yeah. That gets put into this.

When this World Cup started, the pre-World Cup matches were not done in FIFA World Cup stadiums. Everyone's like, the Americans don't know what they're doing with the pitches. That are da-da. Relax. I mean, look at this next video that we're going to show of the 2026 World Cup and how SoFi Stadium, Sorry, Los Angeles Stadium prepped for it. Yes. Okay?

Here, they're showing they put the sand. They're putting like black tarp down. Then they're putting sand on top because the sand is sort of where the water is going to go and then get drained out. And on top of that, they're putting the turf. Then they've got these LED lights that go in every single night to make the grass grow. It's an incredible engineering feat. And all of this turf, sorry, all of this grass is coming from like Colorado or something. You know?

Right. So they got to ship it in. Yeah, they got it like, this is an incredible endeavor. Yeah. For a stadium that as big as Los Angeles. Yeah, which is a massive. And the grounds, which we were there at are great. And again, obviously the actual event, the actual match stadiums, we're going to have the best. Yeah, yeah.

And like they've got a drainage system to get the water out because the grass has to be wet. They've got fans to blow air across to stave off fungi. like, it's dope. When it comes to entertainment in the U.S., we spare no expense. Yeah, exactly. The last thing that I wanted to touch on was as I was watching these games,

I noticed something called match momentum. Momentum. And I love data visualization and data analytics. So I got interested in this thing because I was like, how does that work? Like, how do you know? Because it tracked to me visually when I was like, oh, like this team is doing well.

The momentum for them was up. But as an analytics guy, you start asking like, okay, how do you actually calculate that? Because there's some, there's not some guy being like, oh, I judge the momentum to be this now. There's some automated algorithm that is doing it, right? And so what is that algorithm? I couldn't find much on it, but I found a few things. First thing what they do is they calculate something called possession value. Okay.

So possession value measures the impact of individual events, like individual passes and things like that that are going on on the pitch, on the probability of one team scoring within the next 10 seconds. and they have some like data way to train what that is. Like for example, we've got the example that they use is Kevin DeBrona. Oh, Kevin DeBrona. Yeah. And the example they use is. So for example, let's say Kevin DeBrona is at the center.

Yeah. And then he passes it to a dangerous area in the opposition. Yeah. Right? Like he passes it over. So now it's closer to the goal. Yes. Now the possession.

value of that move was something like point one or point two because he's increased the chance of getting to goal. Yeah. Now, in order to calculate momentum, what you're going to do is you're going to look at the maximum possession value for each team every single minute. This is kind of cool because what they're doing is they're comparing the two most threatening situations in that minute. They're not actually doing a average over all the passes.

They're looking at the extrema. Like what was the most dangerous thing that team A did versus what was the most dangerous thing that B did? In every minute interval. Yeah. That's kind of nice because now you're not washing out the stuff that actually matters. Because in football, like, things can happen very quickly, right? So you want to reward the maximum stuff more than like, oh, it just passes here and there. If you just average, you're going to like water down everything.

So that's one thing that I thought was really cool. And a lot of times in data analytics, you have to make these kinds of choices about what is the part of the data that you carry. about. So they measure the possession value of that maximum move over the past minute and they weighed it based on how long ago that happened. So they've got like some time kernel that they convolve with. That's actually a good way to do it because if you just did it on like raw possession stats like you know you could have even in the Belgium Iran game. Yeah. Belgium would be way overweighted and they were in large pockets where they were not particularly dangerous. Yeah. And Iran had these like you know moments that were much more.

impactful, even though they were mostly out of possession, at least in the first half. Yeah, exactly. That's why I think I like that they only keep these, like, the maximum part instead of averaging. And then the momentum is given by the difference between the two. Yeah, okay? That makes sense.

And one really cool sort of visualization that I saw was, I mean, there was a tweet by someone saying that, like, the match hydration breaks. Boo! Are like, boo! They're showing that the match hydration breaks change the momentum.

Yeah. Right. And this is from the, I think this is the Kurokau versus Germany game that's showing that like Kura Kau was just getting going and then the match hydration break happened. I don't know what the best way to sort of quantifiably measure this difference, right?

Because like you'd have to compare with all the games. You'd have to make the same kind of data analytics. But then also like at any games, moment match momentum shifts, right? So how do we make the judgment that it only shifted during the hydration breaks? And it could shift either way, right? It could shift to being more of Germany or more of Kurokow and things like that. So you can't really only look at like the match momentum switching as an effect because it could mean that like it made the momentum even bigger for one side or the other. I don't really know. And if people have ideas for how to do data analytics to like

do an A-B testing of this kind of thing. One idea I had was to look at the time constant of how quickly the match momentum is shifting in either direction. So now you're agnostic to which direction the match momentum is shifting, and you're looking for the timing of the squiggles. And if this is true, what you would see is that the time constant

of the shift should be shorter during the hydration breaks than it should be during normal gameplay. Right. Or during like the same 22 minutes for a match that didn't have match momentum. That's sort of like a first pass at how I would do the data analytics here if I was given this thing. I mean, the problem there is there is also already an inherent time constant in how they're measuring it, right? I can't go slower than a minute or like five minutes depending on how they smooth this thing. So it's a tough question. The eye test is telling me, at least in this game that it works, but that's end of one.

so I don't know. Hydration breaks are terrible and it's a stand on the game and it should not exist. The only circumstance is if it's above X temperature Fahrenheit or centigrade or whatever, but otherwise it should not exist in the game. It's it is a total catastrophe. It's very upsetting to me. But that's not a scientific opinion. Yeah, right.

You know, whether or not it interrupts the momentum, I think there are good arguments that it does. from the eye test. This is not the beautiful game that we were raised on. This World Cup has been incredible. Yeah, it's already been great. The groups expanded. The group stages is exciting. We're seeing the Dark Horse teams that are supposed to do well, not due well.

Cape Verde. Cape Verde is doing, like, it's just killing it. Unbelievable. We have a new top goal score of all time. Yes. And Lionel Messi. LaMedia Mall has made his first World Cup goal ever, Erling Hollanders arrived.

Killing Mbapai said, do not forget about me. I'm still here. I'm still fighting. It's been super fun. Our group chat's going so crazy over all the games. It's been a blessing to have it in the U.S. There is a lot of people who do a lot of work

to make things like the World Cup happen. And it's not just the coaching staff. It's not just the media ecosystem. And some of them are scientists. And some of them are scientists. And the science of the World Cup is indeed very very. very fascinating. We hit another hour on this one,

even though we were trying to keep it tight, keep it light, but what happens when you're doing this is just, it's fun. We like to talk a lot about it. I am your host, Lesterneri, joined us always by my co-host

and our resident PhD, Go Team USA, Christiana Chowdery. We will see you all next week and we will be winning the World Cup in about two to three weeks from now. And so when that happens, come back and comment and let me know.

When it doesn't happen, don't come back and don't comment.