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Dublin: 5°C Thursday 13 May 2021

How are football and mathematics linked?

David Sumpter chats to The 42 about misguided football pundits, Leicester’s improbable success and Barcelona’s symmetrical beauty.

Leicester's success this season seemed to defy logic.
Leicester's success this season seemed to defy logic.

A NEW BOOK assessing the links between football and mathematics has recently been published.

Soccermatics: Mathematical Adventures in the Beautiful Game by David Sumpter is a detailed look at mathematical side of the beautiful game, illustrating how it impacts on everything from shot statistics and league tables to the geometry of passing and managerial strategy.

The42 recently caught up with Sumpter, who is Professor of Applied Mathematics at the University of Uppsala in Sweden, to chat about his new book…

Tell us about how you came up with the idea for the book.

I’ve been working in applied mathematics a long time, so I’ve been studying mainly applied maths and looking at animal groups and looking at biology. How you can model bird flocks and fish schools and things like that.

Football’s been my hobby. I train my son’s team. Basically, I wanted to write a popular science book about how you apply mathematics and the connection with football seems very natural. There’s just so much mathematics in football. So there were so many different things to choose from and write about. So that’s how the idea came about.

Was there much that surprised you over the course of your research for this book?

I started off just thinking how I could illustrate different bits of mathematics using football, but then, when I got into it, I saw that there were lots of ways in which you could have good tactical understanding using mathematics.

One of the examples I’ve used quite a lot is passing networks. So you could look at how teams pass to each other and you can get an understanding of how they’re using space — are they using space as optimally as they can? Are they balancing attacks down the left and right wings? And you start to get lots of insight.

So after I finished the book, I’ve been working quite a lot on analysing real matches. I just did an analysis of Leicester, looking at their passing strategy and how they have longer passes than any other team. There are lots of different insights that you can get out of that.

So what’s your theory on the Leicester City phenomenon?

One of the really interesting things about it is that there were a lot of models around in football saying that the optimal thing to do was get passes into the box and score that way. There was a lot of work saying that you should play possession football basically. And that’s what all those (top) teams were playing — Arsenal in particular were playing that. I think it became too easy to read.

Leicester basically came with this counter-attacking football — very fast, direct passes. It defies some of the previous models, but it doesn’t defy logic. You can also look at what they do mathematically and there’s actually a very clear pattern. They’re passing the ball much more directly forward to goal than the other teams. And that’s why they manage to succeed.

I wouldn’t put (their success) down to just team spirit and random luck. There’s a strategic thinking behind that, which has led to their success.

Do you think we’re at the beginning of a seismic shift in terms of tactics and the way football is played?

I think of it as like an evolution. Long-ball football was played a lot in 1980s and 1990s Britain, and then it was really taken over from the continent that you should have this possession football. People just get too confident and blasé about that style of football, and then there’s a new stage in the evolution.

So in the book, I spend quite a bit of time thinking about how you apply principles from evolution to modelling the football game. One tactic evolves, everyone adopts it, and then someone will come along with a new tactic, and then that takes over. But then someone else will come along with a new tactic.

But (Leicester) winning is a big shift, but it’s all part of an evolutionary pattern of tactics, and that’s something you can study mathematically.

By writing this book, was your goal to make mathematics more accessible to the general population?

When I started writing the book, I really wanted to communicate what we do in mathematics. Because I think people think of it as this kind of abstract thing that’s not for them. The first thing I always hear is: ‘I was never any good at mathematics in school.’ A lot of mathematics is actually very applied and very (relatable) to things we see every day. So my first motivation was actually to get that across. There’s nothing better than football to get that across, because it’s something we see every day.

When I got into the book, I realised that there’s actually a lot that mathematics can give to football. So the more the book went on, the more detailed I got in the analysis of the game. The first aim was to communicate what I liked about mathematics.


Was it an easy book to write?

As a scientist, I had to take some time learning how to write as a popular science writer. It’s a really big challenge — you have to communicate clearly but you can’t cut corners, you have to be truthful and give a clear picture of how it works.

So that style took me about a year to learn how to write, and there was loads of stuff I ended up just throwing away. Once I’d learnt it, it was so much fun to write. What could be better? Watching old football matches, learning about different aspects of football and trying to think about different mathematical models.

I got up quite early each morning before my real job started and did some research, made some models and that was so much fun to do.

Did you uncover many different trends in football over the course of your research?

If you take a football match — two-thirds of the result of a football match is randomness and luck and one third is skill. The first thing you should think about when watching an individual football match is that two-thirds of the result is down to randomness. In a match, there’s about three goals on average, and one of those goals will go to the best team and the two others will be spread between the teams. So you can see straight away that there’s that randomness aspect.

But then, the difficulty and interesting bit comes in unravelling that last goal — that advantage you have in a match. And there, you have to look in detail at the passing networks they create, the triangles the players create, how the defence synchronises together, how players read off different opportunities — each of those has an interesting mathematical aspect to it. You can use tracking data — this data that Opta provide of passing networks. You really have to dissect and get into the details. So it’s two-thirds luck, one-third extremely important details which you need to analyse.

Footballers are often unfairly stereotyped as being a bit stupid, but you seem to suggest the top ones tend to be quite intelligent?

They really are. I don’t know many footballers personally, but I’d be surprised if footballers are stupid, because they’ve got to do so much. If you take a baseball player, all he’s got to do is hit the ball as hard as possible out of the ground, or throw the ball as hard as possible with spin on it. But footballers have to be so aware of what goes on around them, such complicated tactics that they have to know about, they have to have a very good idea of what people around them are going to do.

If you take (Danny) Drinkwater and (Jamie) Vardy this season, people might not think Vardy looks like the most intelligent sort of person, but he has a very good understanding of what the players around him are going to do. He makes his runs at exactly the right time.

So I imagine that they are clever and there are studies that show they have above average spatial intelligence, so I think it’s definitely wrong to say players are ‘stupid’. Sometimes, you have a mathematician like me doing quite abstract analysis — some ideas that are coming out in analytics now, they can be communicated directly to the players — you can show them their shot statistics, where they’re shooting from successfully and not shooting from successfully, and they can understand and process that information, and improve it again.

Do you think football is being embraced more by intellectuals in recent years, and if so, why?

I think it is changing. I don’t think there is a more mathematical game than football. There is no game that has the same level of interaction between the players. What makes football interesting is that you do have this interaction, you do have these tactics, and you have the evolution of the tactics. I think it is a very intellectual sport that you can talk about on many different levels.

In the book, I list off the working class origins of football and I kind of use that as inspirational material in the book. I do think it’s something which is becoming more and more interesting for academic discussions and so on.

On a somewhat similar topic, what do you make of the current state of football punditry?

Liverpool v Sevilla - UEFA Europa League Final - St. Jakob-Park James Milner is sometimes under-appreciated by fans and pundits. Source: PA Wire/Press Association Images

I don’t want to be too critical about particular commentators, but it’s just amazing how much time we spend talking about the refereeing decisions. It’s a small part of the tactical build-up of the match — there’s too much concentration on that and the individual characteristics of the players.

I really have difficulty understanding the criticism of Mesut Ozil, for example. He’s done more successful passes into the box than any other player. Statistically he outstrips everyone. And then there’s criticism of him because he’s ‘not a leader character’.  That’s not correct. There are other problems with Arsenal, but saying you have to have a certain type of personality to be a successful footballer is not really the key. You have to look at the underlying statistics in many cases, and that is missing.

One of the statistics they use is ‘distance run during a match’. Distance run during a match is a useless statistic of how well you’ve been playing. If you’re running around after the ball all the time, you’re not doing a good job. If you’ve got the ball at your feet, controlling the game, then you’re going to run less distance. So the statistics should reflect what actually happens in the match. There should be more attempts to explain how the statistics work properly.

What’s the biggest misconception in football analysis currently?

One of them is this obsession with refereeing decisions. Also the one about the ‘personality’ and the facial expressions of the players and how important that is. Before I started studying this properly, that was a thing I was interested in — the players’ personalities and what they were like and of course, it’s natural that we’re interested in that.

But when you’re actually analysing a game, those are not the interesting things to look at. The body language of a player is not the key thing — it’s what he does with the ball at his feet.

It’s going to be a small factor if you’ve got a bad attitude and you’re not getting on with players in the team. But my favourite example, because I’m a Liverpool fan, is James Milner. People don’t like James Milner very much — he’s sort of boring. But he delivered more passes into the box than any other Liverpool player this season and he’s all over the pitch, delivering passes, building up the play. That might be a bit boring for certain people, but he’s the one who’s creating in the team, so that’s the sort of thing that I find difficult to take — when you look at the statistics and they’re slightly different from the story that’s told about the player.

Do football clubs fully appreciate the links between maths and football, and is it something they could further exploit in future?

I think they can exploit it. All the clubs are looking at this stuff, but what isn’t happening yet is it isn’t integrated into what they’re doing on a weekly basis. Right about now, the season’s over, they’ll be saying to the mathematician guys they have working for them — ‘okay, we need to scout some players for next season’.  Then they’ll be crunching the numbers for that. But it’s not integrated into how they’re preparing for matches. They’re not looking at the statistics and the tactics adopted by the other teams during the season.

It’s mainly used now for buying and selling players. So that’s a big challenge for us mathematicians — to integrate what we do on the tactical analysis on that side of the game. I wouldn’t blame the clubs, especially the managers who are under incredible pressure and have to get results in a short period of time. But there is a lot more they could use as part of the data they’re collecting.

You cover Barcelona in the book. How does maths influence how they play?

Spain Soccer La Liga Sumpter says there is symmetrical beauty in watching Barcelona play. Source: Daniel Tejedor

They really start (players) at an early age. There’s good and bad aspects to this, but they’ve got them playing in triangles and diamond shapes day after day on the training pitch from when they’re about 10 years old. Of all the touches and movements they make, they develop a very natural understanding with one another.

I do a lot of analysis of how they use space and triangles when they play — especially the team from 2010-11. Messi was a striker then with Xavi and (Andres) Iniesta (in midfield). The understanding they had, which was built up for many years, with these triangles to create space… It’s not that they were sitting there doing the maths to calculate these things, but they just learnt what works on the training field over and over again, and through that learning process, they become very good at creating these shapes.

As a mathematician afterwards, you can appreciate the symmetrical beauty of Barcelona. But it’s not something they deliberately planned out — it’s more of a learning process.

Soccermatics: Mathematical Adventures in the Beautiful Game by David Sumpter is published by Bloomsbury. More info here.

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About the author:

Paul Fennessy

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