• Nov 11th 2008, 02:05 AM
McGraw
Hi.

I'm struggling to get my head round this issue I'm discussing with friends.

It regards the chances of any of the top 4 teams from last season in a league playing each other on the same day.

So, assuming 20 teams (they play twice, home and away) who each play on the same day once a week for 38 weeks, what is the chance that the teams who finished in positions 1-4 last season, will play each other on the same day at any point in the season given a random fixture draw.

I've been told 17% but that seems too low to me.

Can anyone explain how this would be calculated?

Thanks.
• Nov 11th 2008, 01:04 PM
awkward
Quote:

Originally Posted by McGraw
Hi.

I'm struggling to get my head round this issue I'm discussing with friends.

It regards the chances of any of the top 4 teams from last season in a league playing each other on the same day.

So, assuming 20 teams (they play twice, home and away) who each play on the same day once a week for 38 weeks, what is the chance that the teams who finished in positions 1-4 last season, will play each other on the same day at any point in the season given a random fixture draw.

I've been told 17% but that seems too low to me.

Can anyone explain how this would be calculated?

Thanks.

Hi McGraw,

Let's say the 4 teams are A, B, C, and D, and let's assume the matches are chosen by random draw each week. On any given week, then, the probability that A will play one of B, C, or D is 3/19, because there are 19 other teams and they are all equally likely to be chosen. Let's say, for example, that A plays B. Then the probability that C will play D is 1/17 by similar reasoning. So the probability that the 4 teams will play each other on any given week is (3/19) * (1/17) = 3/323.

Since there are 38 weeks, the probability that the 4 teams will NOT play each other at all is $(1 - 3/323)^{38}$, and the probability that they will play each other at least once in 38 weeks is
$1 - (1 - 3/323)^{38} = 0.2985$.
• Nov 12th 2008, 12:43 AM
McGraw
Thanks very much.