Brazil midfielder Paulinho (left) and striker Hulk share a birthday on July 25. Reuters

Mathematicians are running the rule over the World Cup - less for the quality of the soccer than for the chance to prove an intriguing statistical quirk called the "Birthday Paradox".

Strange as it may sound, 16 of the 32 teams with 23-man squads at the tournament in Brazil have players who share a birthday, although mathematicians are far less surprised than the rest of us.

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

While it appears to defy logic, the "Birthday Paradox" stacks up and the World Cup proves it exactly.

"It might look far-fetched," said mathematician Peter Frankl, who is based in Japan. "Mathematics deals with the counterintuitive on a daily basis," he added.

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

Frankl said this is no coincidence. "It is hard to convince people, but it's almost always exact," the Hungarian said. "Actually, with 32 teams and 23-man squads, 50 percent is less than the expected result, mathematically speaking."

He said people need only to think back to school days when many students would have shared a birthday with a classmate - the probability of two schoolchildren in a class of 30 sharing a birthday being 70 percent.

The mathematical principle holds true at the World Cup where half the sides, including Brazil and Spain, have at least one pair of birthday boys. Argentina, France, South Korea, Switzerland and Iran have two.

Some teammates will celebrate joint birthdays at the tournament, although champagne and cake are likely to be banned.

On Friday, Bosnian pair Asmir Begovic and Sead Kolasinac will have to toast their joint birthdays in secret, if so inclined, with a must-win game against Nigeria kicking off the following day.

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

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

Agence France-Presse

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