the birthday paradox at the world cup

8/12/2019 The Birthday Paradox at the World Cup

1/7


2/7


3/7


4/7

News - The birthday paradox at the World Cup

www bbc com/news/magazine-27835311[17-Jun-14 11:32:54 AM]

arm handshake between Benedikt Howedes of Germany and Saphir

aider of Algeria - they share the pain of celebrating their real birthday

st once every four years, because both were born on 29 February.

this point the statistically inclined might be asking a few questions.aybe the sample size is too small to demonstrate the point

onvincingly?

e can respond to that by adding in the squads from the 2010 World

up, too. That yields another 15 shared birthdays, making 31 out of 64

quads over the two world cups - still pretty close to 50%.

hese results give us pretty much what you'd expect if birthdays were

ndomly distributed, but there's a healthy argument in sporting circles

bout whether that's true in a group like this.

he explanation

ere's a simple explanation of maths behind the birthday paradox. More

egant and sophisticated versions can be found on the internet.

Imagine you walk into a room of 22 people, none of whom have a

birthday in common. The chances you'll have a unique birthday feel

pretty high - there are only 22 days taken by the others, and 343 days

free, so you'd fancy your chances that no-one shares your birthday.

This may be one reason the birthday paradox feels counter-intuitive.

We tend to view problems like this from our own individual perspective,

and for any individual the chances of sharing a birthday are low.

ut let's work out the probability that everyone in that group of 23 has a

nique birthday.

For person 1, the chances are 100% because every date is clear. For

person two, there's one day they would share with person 1, but the

other 364 are clear, so their chance of a unique birthday is 364/365.

For person 3 it's 363/365, and so on through to person 23, whose

probability of having a unique birthday is 343/365.

To find the probability of everyone in the group having unique

birthdays, we multiply all those 23 probabilities together, and if we do

we end up with a probability of 0.491.

The probability that a birthday is shared is therefore 1 - 0.491, which

comes to 0.509, or 50.9%.

ened kt Howedes of Germany (left) and Saphir Taider of Algeria were both born on 29 February


5/7

News - The birthday paradox at the World Cup

www bbc com/news/magazine-27835311[17-Jun-14 11:32:54 AM]

ut if that is the probability that any two people in a group will share a

rthday, what about the probability that you will share a birthday with at

ast one other person in a group? For that to be greater than 50%, you'd

eed to have a group of 253 people. Perhaps your friends in social media

ight be the best place to look.

he theory is that in sports, there are advantages to having a birthday

at's just after the cut-off date for school or team selection. When you're

oung, if your birthday is just after that date, you're going to be oldest

nd likely most physically developed of your year group.

his natural advantage makes is more likely you'll make it onto a sporting

am, that you'll perform well and get more attention from the coach. This

en feeds back into better performance, setting up an enduring

dvantage over peers with less fortunate birthdays.

s a complicated and controversial idea. In 2006, Steven Levitt and

ephen Dubner of Freakonomics fame proposed that people born in the

arly months of the year would be overrepresented at the World Cup that

ear. They based this on the decision by Fifa in 1997 to make 1 January

e age cut-off for international soccer competitions.

evitt ended up backtracking after someone analysed World Cups prior to

006 and found this wasn't the case. Levitt suggested that age cut-offs

r domestic competitions might vary between countries, conflicting with

e Fifa date and complicating the effect.

or the 2014 World Cup players, the four months with the most birthdays

e January (71), February (77), March (68) and May (72). These are all

bove the 61 birthdays a month you'd expect if they were evenly

stributed.

nd the months with the fewest birthdays all come in the second half of

e year: August (57), October (46), November (49) and December (51).

he 2010 data show the same thing - above average early in the year,

elow average towards the end.

his is just a quick look at the figures and not a definitive analysis, but it

osnia Herzegovina's Asmir Begovic and Sead Kolasinac's birthday falls the day before their team faces

geria


6/7


7/7

the birthday paradox at the world cup

Documents