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Two of my articles now gracing the walls of Faraday’s former quarters at the @London_Inst! Don’t worry though! If you’re not popping by @Ri_Science any time soon you can read them at the links below!

Surgery used to be a gory and risky affair. Today, they are routinely performed by robotic assistants. We saw first-hand the impact this is having at Southmead Hospital @NorthBristolNHS 🤖🏥

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Sources https://t.co/hPJLmjvQa9. https://t.co/GRZgOtpuBE https://t.co/D06j9BUWpU https://t.co/FTeihwbTP5

So, if you love mathematics as much as us and Lucy Bronze, tune in for tonight's game come on the #Lionesses! But please, don’t make us sit through another shoot out... it’s coming home!

Bronze demonstrated perfect pattern recognition - and how to break it - during the shoot out against Sweden. She noticed how Falk dove early for penalties, often resulting in a save. Bronze changed her strategy – shooting down the middle and definitely improving her outcome!

Pattern recognition is another essential for a successful shootout; you’ll have spotted the notes on the sides of the keeper's water bottles. They show previous penalty placement, and the probability of those placements being repeated – who said sports and statistics don’t mix!

If the shooter goes bottom right, and the keeper dives left, their outcome could be improved if they’d chosen to dive right instead. Penalties are a zero-sum game – as the success of the taker directly impacts the keeper's outcome, and vice versa.

In ‘nash equilibrium’, a solution in game theory, it's stated an opponent can’t improve their chances by changing their strategy, given the other player’s strategy stays the same. But this can’t directly apply to penalties, as a change in strategy could improve the outcome.

Game theory suggests a mixed strategy is optimal – if you take the same shot, regardless of where, the keeper will notice the pattern. So, an unpredictable strategy helps break the patterns posted on the sides of the keeper's water bottles.

In the nail-biting 14 penalties, 6 were saved, 3 missed, and 5 scored – a 35.7% conversion. Both keepers dived the correct way for 5/7 penalties. So how does England ensure another penalty win? The answer lies in mathematical theory, as well as Chloe Kelly's hop, skip and thump!

The countdown is on for England vs Italy in #euro2025 – let’s hope the #Lionesses get the job done in 90 mins but juuust in case, we’ve taken a quick look at the mathematics behind the penalties, just like #Lioness Lucy Bronze did to help secure the win against Sweden! 🧪⚽

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