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Dublin: 23 °C Wednesday 23 July, 2014

The World Cup helps prove the Birthday Paradox

Thirty-two 23-man squads. Sixteen of them have players who share a birthday. Read this explainer…

Bosnia's Sea Kolasinac and goalie Asmir Begovic share a birthday.
Bosnia's Sea Kolasinac and goalie Asmir Begovic share a birthday.
Image: Thanassis Stavrakis/AP/Press Association Images

MATHEMATICIANS ARE ENJOYING the World Cup – not just for the quality of the football – but also for the chance to prove an intriguing statistical quirk called the Birthday Paradox.

Strange as it may sound, 16 of the 32 teams at the World Cup have players who share a birthday – though mathematicians are far less surprised than the rest of us.

Statisticians have known for some time there is a slightly more than 50% chance that in any group of 23 people, two of them will have the same birthday.

While it appears to defy logic, the Birthday Paradox stacks up. And delightfully, the World Cup – with its 32 teams of 23-man squads – proves it exactly.

“It might look far-fetched,” Japan-based mathematician Peter Frankl told AFP.

“Mathematics deals in the counter-intuitive on a daily basis.

When people make millions on the stock exchange or try to predict the future, you are talking about the theory of probability.

However improbable it sounds, precisely half the competing teams have at least one shared special day, and five have two pairs of birthdays.

No coincidence, explained Frankl.

“It is hard to convince people but it’s almost always exact,” said the Hungarian. “Actually with 32 teams and 23 people, 50% is less than the expected result, mathematically speaking.”

Frankl says one need only think back to school when many people would have shared a birthday with a classmate – the probability of two schoolchildren in a class of 30 sharing a birthday being 70%.

“With 41 people in the classroom, the chances are 90%,” he said.

The mathematical principle holds true at the World Cup where half the sides, including Brazil and holders Spain, have at least one pair of birthday boys.

Argentina, France, South Korea, Switzerland and Iran have two.

Some team-mates will celebrate joint birthdays at the World Cup, although champagne and cake are likely to be banned.

On Friday Bosnian pairing Asmir Begovic and Sead Kolasinac will have to toast their joint birthday in secret if so inclined – with a must-win game against Nigeria the following day.

South Korean players Kwak Tae-hwi and Son Heung-min might be able to enjoy a birthday tipple on 8 July, unless the team repeats its astonishing run to the World Cup semi-finals of 2002.

Though something of a long shot, if the teams face each other in the last 16 on 30 June, Germany’s Benedikt Howedes and Algeria’s Saphir Taider will come face to face – both players only getting to celebrate an official birthday every four years because they were born on 29 February.

Sceptics trying to shoot down the theory by claiming the data field is too narrow will be disappointed to learn that by including the 2010 World Cup squads, 31 out of the 64 squads had shared birthdays, still hovering near 50%.

“Sometimes in mathematics it’s no use trying to explain things to your wife, children or neighbours,” said Frankl. “But I’ve tried the Birthday Paradox about 20 times in lectures and it’s only failed once.”

- © AFP 2014

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