The Geometrical Wonder of Lionel Messi

I never imagined, when I first started writing about maths and football in 2015, that the result would be this. But here I was, flying down to Barcelona to study Lionel Messi up close and personal. To help the documentary makers understand his geometry.

They sat me close to him in the stand and asked me to provide my own analysis. A geometrical proof of why Messi was the best player to have to ever walk on a football pitch.

It wasn’t a difficult task. I had already shown in Soccermatics that Messi’s goal scoring made him a once in a lifetime event. Large deviation theory predicts that we shouldn’t expect another Messi to come along for another 70 or so years. I had created Voronoi diagrams of how he and his team mates broke down space. Messi and his team (especially to 2010–11 one) was already mathematical perfection.

But being in the city of Barcelona inspired me to think one step further.

An idea has fascinated me for a long time as to how the best football players understand space in a way us mere mortals cannot grasp. And now, as I strolled through the city, past each new curving work of Guadi, I couldn’t help but see why this city, shaped by arcs and dynamic structures, is so captivated by a game that provides both of these to unlimited degree.

Even the curves of architecture reflect the curves of goal scoring probabilities.

Barcelona is a city of shape, form and passion. And the living genius, providing the wonder to its inhabitants, is no longer Gaudi. It is Messi.

The film crew put me in a basement somewhere in the cultural centre of the city and asked me to find the beauty of Messi’s movements in mathematics.

I tried. I don’t know if I succeeded. To see how close I (and they) got you will have to watch the Wonder documentary yourself. But here are some images I showed to the film crew in that basement.

The beauty of Messi lies not only with his skill on the ball, but also in the way he creates space. Here is one of the ways he does it which they illustrate in the documentary. He sees the movement…

He changes his own direction and displaces those around him…

And this is where the space comes from. Equally distant from all three opposition players, he finds a new way through.

This manipulation of space comes not only from the way he dribbles, but also from the way he moves off the ball. Here in El Classico. Real Madrid has structure one second. Then Messi moves, just one shoulder…

and the structure is replaced by a space, with our genius in the middle…

Each time we see Messi, he warps both space and time. It is as Paco Seirulo says “Einstein”, it is the theory of relativity. He puts the best defenders in the world in a quantum state oftwo minds.

He opens up new possibilities where no-one else could ever do the same.

There are a large number of statistics that support the hypothesis that Messi is the World’s best player and even that he is the best player to have ever lived.

But the wonder does not come from these numbers. It comes from the patterns, the movements, the space, the rapidity of the feet, the tango dance and the precision.

Watch Wonder. Watch myself, Pep Guardiola, Juan Mata, Paco Seirulo and many others try to understand Messi. I think we all fail, but it is worth watching us try.

Professor of Applied Mathematics. Books: The Ten Equations (2020); Outnumbered (2018); Soccermatics (2016) and Collective Animal Behavior (2010).