Math Of The Day

Football analysis, it seems, is increasingly dominated by numbers, as the mass of data available to fans continues to grow season-on-season.

Making sense of these figures can be an overwhelming business at times, and at least a basic grasp of mathematics is very handy when dissecting the average possession percentages, shots to goals ratios, pass completion rates and so on that accompany most match reports nowadays. That’s not to mention the geometry involved when watching Arsenal’s passing triangles in motion.

For one Gunners fan, though, this is all second nature. Marcus du Sautoy is one of Britain’s foremost mathematicians. A Professor of Mathematics at the University of Oxford, you may have seen Marcus (OBE) in the TV series school of Hard Sums, alongside fellow Gooner Dara o’Briain. Or you may have seen him at the Home of Football on a Saturday afternoon, where Marcus - author of works such as The Music of The Primes - holds a season ticket.

The Arsenal Magazine caught up with Marcus recently to discuss how his love of numbers and his love of Arsenal continually overlap.

First of all Marcus, why Arsenal?
I grew up in Oxfordshire but part of my family was based in Stoke Newington and when we visited them that’s how I first knew about the Arsenal, through my cousins, who were supporters. Eventually I ended up moving to London and that’s when I actually started coming to the games, but I was a fan before that. We moved to London when my son was born, 17 years ago - so it was a nice time to start coming to the games!

Did you being a mathematician have anything to do with making the choice to support Arsenal? 
Well, they were a very different team back then to the one they are today, of course. As a mathematician I think the team now plays a game that is full of geometry in motion. It’s a beautiful, strategic game that Arsenal play. One talks about triangles, and that’s true. The amount of room they give themselves because of the geometry off the ball means that I’m glad it’s the team I ended up with. Basically I think it’s the most mathematically-minded team, even if they aren’t aware of that themselves! They call Arsène Wenger the professor, and with good reason. I’m sure he is aware of that, and how similar football can be to a game of chess, for example.

Give us an example of what you might see, that others perhaps don’t?
Well, I play for a football team, Recreativo Hackney, out on the Hackney Marshes, and I also played for the England Writers’ football team, and we had a training weekend with Aidy Boothroyd. He really made us understand that although you look at the guy with the ball, the most interesting thing is the 10 who are off the ball. It’s those 10 who are creating a mini network around the man with the ball. It’s like the internet - the more connections you have with the player in possession, and the other players around you, the better it is. I can see that with Arsenal. Mesut Ozil, for example, seems to spend the first five minutes working out what the space looks like, where the other players are - then he can start to make things happen. So the triangles are all about the imaginary lines joining players, and the opposition are trying to put players in the way. It’s about how you most efficiently lay out your team, and keep it moving, so that there are maximum outlets. That’s the basis of a really good passing team - a good mathematical network.

How about other areas of mathematics, such as mechanics and physics, at play during football that we probably take for granted?
There’s a lot of maths behind things like the trajectory of the football, for example. When I speak to kids in school I often give the example of Robert Carlos’s swerving free-kick against Fabian Barthez [from 1997]. There are some fantastic mathematics at play there. We know that when the ball spins, it bends, but Roberto Carlos did something different. The ball was travelling so fast after he hit it, that the turbulence was what we call ‘chaotic’. Chaotic turbulence doesn’t break the ball very much, so it flies through the air more like a golf ball. Then it passes a threshold moment when the chaos goes and it becomes what we call ‘laminar flow’, then the spin takes over. You see the ball turn at a late moment. I don’t believe Roberto Carlos solved the Navier-Stokes equations to do that! But at least the maths explains what happened there. So if you know why things like that happen, then you can exploit it during a game to your advantage.

You mentioned Ozil. Do you think it’s true that some players are more mathematically minded than others?
Well a lot of people say to me "I hate maths because I haven’t got a mathematical brain" but I think all of us, because of evolution, have been programmed to have a good mathematical brain. If somebody kicks a ball, we have a good sense of where it is going to land. Our brains are subconsciously solving a quadratic equation. Mathematics is very much about predicting what’s going to happen next. If you can do that in a game of football, you will have an edge. So maybe those players who intuitively have a good sense of geometry and calculus, they’re the ones who will have the edge. I think you saw that in someone like Fabregas or Bergkamp, for example. There’s a quote from Dennis Bergkamp, 'Every touch of the ball requires a thought',and that’s how he played. He wasn’t seeing how the game is now, he was seeing where it will be in five or 10 seconds time. That is mathematics in action.

Is it better that this remains subconscious for the players, or do you think the players would benefit from understanding the maths behind their play? Some players would benefit from having extra knowledge they could tap into, and over time it would become subconscious anyway. My mathematics is so subconscious that I do it without thinking, and in a sense the footballers are doing that as well. So if Arsenal needs a mathematician to work with them or sit on the bench, I’m happy to volunteer!

What about the statistics that have become more prevalent in football lately? Do you find it useful to analyse football in this way?
Yes, but it’s still not on the same level as you will find for sports in America like baseball or American Football where the stats are massive. Look at Moneyball for example - if you have more information, you are certainly going to have an edge on things. What’s interesting is deciding on what stats to measure. We don’t have many goals in football, so what else do you look at? A friend of mine has a betting company and he measures all sorts during the games. One thing he measures is how often a crowd go “Oooooh!” during a game, and that’s quite a good measure of how often goals were nearly scored. He’s a millionaire now, basically from using maths and stats to analyse a game, so there must be something in it!

What do you say to people who argue football is too organic to reduce it to numbers and formulae?
Of course what makes football such an exciting game is the element of randomness in it as well. Even if the stats say someone should have won the game, sometimes they don’t. The joy is anything can happen. But when you are betting for example, it’s about long-term numbers and trends that help you to predict things, and maths can definitely help with that.

Do you think football is missing a trick by not looking more into the mathematics of the game?
I think so. There’s a lot of conventional play, and not much thinking outside the box, which is what maths is very good at. Free kicks are generally conventionally taken so why not try some different strategies? Mathematics is good at game theory, and many Nobel prizes have been won by mathematicians who looked at game theory – people like John Nash. So why not apply that to free kicks? Do you ever see people try something really different? Maybe putting a wall up is not the best solution, for example. At least it’s worth looking at. I think football is quite conservative in many ways.

Have you ever done any research on football yourself?
I wrote a book called The Number Mysteries, and there’s quite a lot of football in there. Things like how I used prime numbers to get my team promoted. My team, Recreativo Hackney, came rock bottom of the league, so I thought, “Can I use my maths in any way to help us?” It was about the time David Beckham went to Real Madrid and took the 23 shirt. Everyone had their theories as to the significance of that – it was Michael Jordan’s number and so on. My theory was it was a prime number – an indivisible number – and I had just written a book on prime numbers. I put Sol Campbell’s 23 Arsenal shirt on the cover by the way, to wind up my Spurs supporting friends! So I had written this book, and then I looked at Real Madrid’s squad and all the Galacticos were wearing prime numbers:

Roberto Carlos in 3, Zinedine Zidane in 5, Raul 7, Ronaldo 11 and Beckham 23. Maybe they were the first team to have a mathematician on the bench! So I said to my team, it’s a crazy theory, but let’s try having all our shirt numbers as prime numbers. We did it for a season and got promoted! So maybe that’s something Arsène could think about!

You do some work with Arsenal in the Community’s maths programmes in local schools too. Tell us about that.
The work the education team is doing here is absolutely fantastic – the range of material being produced is amazing. For most people maths seems a bit dry, but if you get them engaging with something they love, like football, then you’re onto a winner. The Arsenal education team have put together a great range, from primary to A Level, and my plan is to help them promote it, and maybe put on a day of maths and football. I have seen the kids at work and you can see that as soon as they see maths in a football context, it starts to make more sense for them. It’s not an obvious connection maybe, football and maths, but it works.

Finally Marcus, what are your thoughts on this season? What will be the magic number at the end of the season – Arsenal’s finishing position?
Well, every season I start off saying, “This is the season,” but this year we really have had a great start. We didn’t lose any players, and have obviously bought a particularly fantastic player in Ozil - wearing a prime number! But I think it’s a really open season, with plenty of other teams having been destabilised. Ozil is playing like Bergkamp or Fabregas, but we don’t depend on a single player. There are lots of options, which is the good thing at the moment. So I’m expecting us to be number one at the end of the season!