rynner2 said:
Peripart said:
Statistics can be a very counter-intuitive branch of mathematics. It's slightly unlikely that 2 PL managers (out of 20) share the same birthday, but for any given group of people, you only need 24 or 25 (I forget which) for there to be a greater than 50% chance that at least one pair share a birthday.
I know that, but I was not considering random pairs, but one particular pair, involved in one specific, top-of-the-table, match. The match selects the managers, so there are only two to consider. Therefore it seems to me the chance must be about 1/365. Factor in the chance of the two top teams playing each other late in the season, and the chance must be even smaller!
The more general Birthday problem is discussed on Wiki:
https://en.wikipedia.org/wiki/Birthday_problem
(23 people are needed for a better than 50% chance.)
An article discussing this (and football, again!) is this:
The birthday paradox at the World Cup
By James Fletcher, More or less, BBC Radio 4
It's puzzling but true that in any group of 23 people there is a 50% chance that two share a birthday. At the World Cup in Brazil there are 32 squads, each of 23 people... so do they demonstrate the truth of this mathematical axiom?
...
"The birthday paradox is one of maths' greatest hits," says Alex Bellos, author of Alex Through the Looking Glass: How Life Reflects Numbers and Numbers Reflect Life.
"It's something you can say in one line which gives you this 'wow'!"
In its most famous formulation, the birthday paradox says that you only need a group of 23 people for there to be a greater than 50% chance that two of them share the same birthday.
(For lovers of detail, we should be clear that by birthday we mean day and month, not year.)
Bellos points out that the birthday paradox isn't a logical paradox - there's nothing self-contradictory about it, it's just unexpected.
...
At the 2010 World Cup, Algeria's squad actually had
three players whose birthday fell on the same day, 5 December. No squad achieves that this time round, but 2014 might have the rarest shared birthday of all.
Imagine this scenario: Germany come top pool of G, and Algeria come second in pool H. On 30 June the two teams would then face each other in the round of 16.
If it happens, watch out for a knowing glance from the bench or an extra warm handshake between Benedikt Howedes of Germany and Saphir Taider of Algeria - they share the pain of celebrating their real birthday just once every four years, because both were born on 29 February. 8)
...
And some interesting stats about the distribution of World Cup Birthdays (see article for discussion):
For the 2014 World Cup players, the four months with the most birthdays are January (71), February (77), March (68 ) and May (72). These are all above the 61 birthdays a month you'd expect if they were evenly distributed.
And the months with the fewest birthdays all come in the second half of the year: August (57), October (46), November (49) and December (51).
The 2010 data show the same thing - above average early in the year, below average towards the end.
This is just a quick look at the figures and not a definitive analysis, but it at least suggests that the theory that World Cup players tend to be born in the first half of the year isn't dead and buried.
(So no wonder I didn't get picked for England!)
http://www.bbc.co.uk/news/magazine-27835311