My 18-year-old daughter, Elise, has never been that interested in football. I sent her off to summer camps as a kid to try to get her interested. She played for a half season with a local team. And I took her to a few matches (most notably when she was four she saw Arsenal beat Umeå in the first leg of the Champions League final). But football wasn’t really for her. I share a lot of things with Elise, not least our temperament, but a love for the beautiful game isn’t one of them.

But now I have found the…


What does Timnit Gebru’s firing and the recent papers coming out of Google tell us about the state of research at the world’s biggest AI research department.

The high point for Google’s research in to Artifical Intelligence may well turn out to be the 19th of October 2017. This was the date that David Silver and his co-workers at DeepMind published a report, in the journal Nature, showing how their deep-learning algorithm AlphaGo Zero was a better Go player than not only the best human in the world, but all other Go-playing computers.

What was most remarkable about AlphaGo Zero…


Anyone working in tech will know the type: the mini-Elon Musk. The young man who thinks that his brilliant idea is going to be the next Uber, Spotify or Tesla. He presents himself with confidence and assurance, but you suspect that, deep down, he has no idea what he is talking about.

There are, of course, women of this type as well. And we certainly shouldn’t (based on a few anecdotes) draw conclusions about men and women as a whole.

That’s where researchers can contribute: to find out whether men are, in general, overly-confident in their own abilities and how…


hen Boris Johnson addressed the nation to announce new coronavirus restrictions last month, he talked about how the virus would “spread again in an exponential way” and warned us that the “iron laws of geometric progression [shout] at us from the graphs”.

My first reaction, as an applied mathematician, was to smile to myself at his careless use of mathematical ideas. Disease spread is nearly always exponential, it is just another way of saying that the virus multiplies over time. So, it is not the exponential nature of the growth itself that has changed, but the multiplication constant (the R…


It is very likely that at least some of the people who suggested using an algorithm to predict A-level results thought that they were being scientific and rational. They imagined that their algorithm would be neutral, remove bias and do an overall better job than the teachers, who are too close to the students to remain clear-headed.

The irony is that it is exactly this thinking that is unscientific, irrational and biased. Let me explain why, starting with a metric from football called ‘expected goals’. Expected goals are calculated by feeding a lot of data (shot location, whether it was…


Maths is often seen as hard.

Not ‘hard’ as in ‘difficult’ (it can be that too, of course) but ‘hard’ as in delivering hard truths, undeniable facts and fool-proof reasoning.

For me, maths isn’t like that. My 20 years of experience as an applied mathematician — modelling everything from gambling and football to racial segregation and epidemics — has taught me that maths has a softer side.

Maths can be used to think about whether you should give up (or stick with) a romantic relationship. It helps you deal with feelings of insecurity that arise when you compare yourself to…


I was totally amazed how many entries their were for the ‘Friends oF Tracking’ Liverpool analytics challenge. The brief was:

1, Use one or more of the tools we have learnt so far (pitch control, speed and acceleration, passing networks, pass maps etc.) to analyse the data.

2, Feel free to combine with other data available from other sources on Liverpool.

3, Produce an output (short report/video) that can be communicated either to a coach, a video analyst or players.

4, Write technical details in a separate appendix.

5, Post a link in comments below and/or to Twitter using #FoT.


Dan Katz, licensed psychologist and psychotherapist, explains why Thomas Erikson’s success with his book Surrounded by Idiots is one of the biggest pseudoscience scandals in recent history. This version was translated in to English and edited by David Sumpter, professor of mathematics at Uppsala University.

Over the last few years, hundreds of thousands of Swedes have spent an estimated total of more than ten million euros on a book which many of them believed contained a scientific account of human psychology, written by an expert in the area. The book’s success has led many companies and other organizations to order…


One of the biggest challenges, as machine learning and AI is increasingly used to make decisions about everything from credit risk to employee recruitment, is how to evaluate its fairness. Do algorithms make judgements that are sexist, racist or otherwise discriminatory? And how do those using them mitigate against bias?

When asked what they think, many AI practitioners will say the right thing. But what drives their decisions when they actually start building a system?

This was the question that motivated Johanna Fyrvald, who wrote her Masters thesis with me as supervisor last term. Through three interviews with academics and…


‘Zlatan Ibrahimović! I want to go and give you a man hug!’

These were the words of commentator Stan Collymore after he witnessed the gigantic Swede rotate his body vertically through 180 degrees, meet the ball in a bicycle kick and lob it over Joe Hart’s head from over 25 metres. Seconds before, Collymore was calmly describing the game as a “worthwhile exercise” as England and Sweden looked forward to the World Cup qualifiers. Suddenly he exclaimed, “O my God, an insane goal! I’ve just seen the most insane goal I’ve ever seen on a football pitch!” …

David Sumpter

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

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store