Could maths help in taking the perfect penalty?

Penalties – the word has long struck fear in the hearts of England fans.

But on Saturday, Gareth Southgate’s men defied England’s less-than-ideal record in major tournaments, dispatching all five against Switzerland to make it through to tonight’s Euro 2024 semi-final versus the Netherlands.

Now a graduate from Nottinghamshire has told the BBC he believes he holds the secret to shootout success.

Billy Watson, 21, from Kimberley, has combined maths, statistics and psychology to calculate the best place to aim in penalties.

“The conventional wisdom is that you shoot down the middle, but if you keep shooting down the middle, your keeper is going to understand what your strategy is,” Mr Watson said.

Instead, he says his calculations show players should use a mixed system – aiming for the top left or top right, and down the middle only very occasionally.

“I used a branch of mathematics called game theory to try and understand why penalty takers don’t shoot down the middle, even though that is statistically supposedly the best place to put it,” said Mr Watson.

He was the first in his family to go to university, and has just graduated from King’s College London with a degree in PPE – politics, philosophy and economics.

Mr Watson decided to carry out the research for his dissertation after watching an episode of BBC panel show QI – which concluded that the middle is the best place for a penalty to go.

That did not feel quite right to him.

“Actually if you shoot down the middle every time, the keeper will understand what your strategy is and they’re going to stay in the middle,” Mr Watson said.

“So what you want is a mixed strategy, where you shoot in the top left a percentage of the time and the top right a percentage of the time.”

He said his dissertation impressed his tutor, who suggested he would look to publish it in Math Plus Magazine at University of Cambridge – and it achieved an impressive first-class mark of 85.

Following England’s quarter-final success against the Swiss, Mr Watson said Cole Palmer, Jude Bellingham, Bukayo Saka, Ivan Toney and Trent Alexander-Arnold “broadly” followed his model.

“They didn’t shoot down the middle and they shot left 60% of the time and right 40% of the time,” he said.

“Something else I found interesting was the difference between [Manuel] Akanji’s penalty and [Xherdan] Shaqiri’s. Akanji shot low, making it quite an easy save for [Jordan] Pickford, but Shaqiri shot high.

“Even though Pickford guessed the direction of both penalties correctly, the extra height in Shaqiri’s made all the difference. This is exactly why my model prefers shooting in the top corners over the bottom.”

England will be aiming to get the job done within 90 minutes later, from 20:00 BST, especially given their penalty defeat to Italy in the final of Euro 2020 – and the fact that prior to Saturday, the Three Lions had only won one of their last five shootouts at World Cup and Euros tournaments.

“There’s always an element of luck when it comes to penalties,” Mr Watson said.

“Whether they’ve been crunching the numbers or wearing their lucky charms, I’m happy as long as they’re putting the ball in the back of the net.”

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