The Birthday Paradox at the World Cup

The Birthday Paradox states that in a group of just 23 people, the odds that two of those people will have the same birthday is 50%. If the size of the group goes up to 70 people, there is more than a 99% chance that two or more of them will share a birthday -and it is likely that more than one pair will have shared birthdays.   

But perhaps the best data-set of all to test this on is the football World Cup. There are 32 teams, and each team has a squad of 23 players. If the birthday paradox is true, 50% of the squads should have shared birthdays.

Using the birthdays from Fifa's official squad lists as of Tuesday 10 June, it turns out there are indeed 16 teams with at least one shared birthday - 50% of the total. Five of those teams, in fact, have two pairs of birthdays.

The list is: Spain, Colombia, Switzerland (x2), USA, Iran (x2), France (x2), Argentina (x2), South Korea (x2), Cameroon, Australia, Bosnia Herzegovina, Russia, Netherlands, Brazil, Honduras and Nigeria.

One of Argentina's pairs, Fernando Gago and Augusto Fernandez, share the same actual birth date - 10 April 1986.

The fact that soccer players were born in the same year is not at all surprising, considering the narrow age range for world-class athletes, but finding the exact results predicted by the Birthday Paradox is rather neat. BBC magazine has more details. -via the Presurfer

(Image credit: Twice25 - Ghearing family)

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While the chances of getting two of the same birthdays in a group of 23 is about 50.7%, the chances of getting exactly 16 of 32 groups to have such a pair is only about 14%. It is about like asking how often would you get exactly 16 heads our of 32 flips, there will be quite a few times with 15 or 17 (26 % of the time), 14 or 18 (22% of the time), 13 or 19 (16% of the time), 12 or 20 (11% of the time), etc. It seems odd, at the least, to use examples of statistics where the result is exactly the average, or examples of probability where the result is exactly the expected value, as it might convey the wrong thing about how such math works.

It would also help if they don't call it a math axiom in bold right at the start, as it most certainly is not an axiom, which in math (and a few other fields) is quite specifically something unprovable but assumed.
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