The Nottinghamshire graduate researching the maths behind football penalties

Billy Watson has now graduated Kings College London with a first-class degree in Philosophy, Politics and Economics
-Credit: (Image: Billy Watson)

A 21-year-old graduate from Nottinghamshire has conducted ground-breaking research on the maths behind penalties in football. Billy Watson, who grew up and went to school in Kimberley, has produced the thesis for his university dissertation which has now been published in Cambridge University Maths Magazine.

Having studied Philosophy, Politics and Economics, Billy has now graduated with a first-class degree from Kings College London and is the first person in his family to attend university. "My parents didn't go and I don't have any siblings so I didn't really have anyone to ask for advice," he said.

"I was always a good student at secondary school but I'd never really thought about university until I went to college. I didn't initially know many universities and I'd never lived anywhere but Nottingham so when I got there it was obviously a big change."

While he has always been a massive football fan, Billy says it wasn't until the second year of his studies that he became interested in the theory behind the sport. After receiving good grades for a module on game theory, he decided to continue down that route and returned to the subject for his final dissertation project.

The 21-year-old also found inspiration in an unlikely place - an old episode of the BBC game show QI. "I remembered they were saying the best place to shoot a penalty is down the middle because the goalkeeper always goes left or right, but the players never do it because it makes them look silly if the ball gets caught.

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"I thought 'there must be something more to it,' so I made an accurate model and explored why this is so common. It had been studied a bit before but not to this extent.

"I used this old data and looked at over 500 matches which helped me understand where penalties are usually taken and where the goalkeeper dives."

Despite the technicalities and statistics behind Billy's research, the 21-year-old came to find that the answer to his thesis was much more about human emotions. "You have to consider the players' guilt and embarrassment.

"Football is a spectator sport. The goalkeeper only stays in the middle of the goal 3% of the time, but scoring in one of the corners feels more impressive and is more of a spectacle.

"If a player shoots down the middle and it’s saved, it looks like they haven't really tried, whereas if you shoot left or right at least you look like you've tried."

Billy acknowledges his research is particularly topical given the timing of the 2024 Euros where England's performance so far has been generally viewed as lacklustre. The former Kimberley School student says that based on his research, the team should be taking a different approach.

"If they care about spectacle and impressing fans then there are different strategies they can use. As an England fan however, the only thing I care about is getting the ball in the back of the net and not about scoring a good penalty.

"Players should shoot in the middle, however obviously if all players do that then the goalkeeper is going to clock on. But when England are in a situation where it's one penalty and one player at one match, they should shoot in the middle."

Despite the success of his research, Billy says sports theory is not his usual area of interest as he favours ethics and philosophy. In fact, academia in general is something that does not interest the graduate who is instead joining the family local estate agency.

"I flirted with the idea of working in the academic sector for a while and friends have suggested I should. The thing is I didn’t ever think I’d ever go to university to study game theory.

"It's always been maths that I've been obsessed with from a young age and I think in one way or another that will stay. I will probably teach chess, which should keep my analytic brain working.

"But whatever I do, it will keep my passion alive." England made it to the quarter-final of the Euros after a dramatic 2-1 extra time win over Slovakia on Sunday, June 30. Gareth Southgate's men will now take on Switzerland, kick-off 5pm.