Unlikely World Series Title Pattern: 1917, 1918, 2004, 2005

[eldrick]

someone posted an interesting problem from another board.
now, the upcoming world series have chicago playing & they haven't won it since 1918.
last year's winner, boston, hadn't won since 1917 !
the problem posed was:
"what are the odds of two teams (not specifically having to be boston/chicago ) winning titles in 1917 & 1918, then not winning another title between them until they go back-to-back again in 2004 & 2005."
apparently 16 teams present in 1917 - 1918 & with franchise expansion there are ~ 30.
he gave the answer ( which i am having trouble working out ), which i'll post as soon as we get a coupla ( or even 1 ! ) reply.
many thanks

 

[EnumaElish]

When did franchising start?

 

[eldrick]

When did franchising start?

i'm not overly sure, but a gradual increase in team nos. from 1918 to 2004 can be assumed.

try the calculation with the assumption of following no. of teams thruout
1) 16 teams
2) 24 teams
3) 30 teams.

a general formula is of interest, for any N teams you wish to use.

my rough methodology was:

- assume that 2 teams winning in 1917 /1918 is a given occurence with probability of 1

- probability of the 2 teams not winning from 1918 - 2004 ( which is 86y ) is probabilty of only N - 2 teams winning for 86y = [(N - 2) / N]^86

- probability of 2 teams winning back-to-back = (1/N) * (1/N) which you multiply by 2, as it can happen in 2 ways = 2* (1/N)^2

then multiply all the aspects mentioned in bold to get a formula for the overall probability.

i'm just wondering if there is a flaw in my workings ?

 

[eldrick]

one thing that perplexed me was if you work out the odds for N = 3 to 10 ( each of 3, 4, 5,... 10 ) & say just 5y instead of 86y, you get an odd pattern.
someone try it & please explain it to me.

 

[eldrick]

the answer i was given to the original question was:

18,000,000 to 1

i hope this may help