Friday 29 October 2010

Controversy in The Morning Fourballs

The Scottish League Cup draw was made today and attracted comment as the two leading teams in the country avoided each other.  What were the chances, assuming a fair random draw, that Rangers and Celtic would avoid each other at this semi-final stage?  With only four teams, it is easy to list all the possibilities.

There is a 25% chance (1 in 4) that any particular ball will come out first.
Then there are three possibilities for the second ball, two for the third and only one for the fourth.

There are only 24 different possibilities, as listed systematically below:

First Team drawn out
Second Team drawn out

Third Team drawn out
Fourth Team drawn out
An Old Firm Semi-Final?
Aberdeen
Celtic

Motherwell
Rangers
No
Aberdeen
Celtic

Rangers
Motherwell
No
Aberdeen
Motherwell

Celtic
Rangers
Yes
Aberdeen
Motherwell

Rangers
Celtic
Yes
Aberdeen
Rangers

Celtic
Motherwell
No
Aberdeen
Rangers

Motherwell
Celtic
No
Celtic
Aberdeen

Motherwell
Rangers
No
Celtic
Aberdeen

Rangers
Motherwell
No
Celtic
Motherwell

Aberdeen
Rangers
No
Celtic
Motherwell

Rangers
Aberdeen
No
Celtic
Rangers

Aberdeen
Motherwell
Yes
Celtic
Rangers

Motherwell
Aberdeen
Yes
Motherwell
Aberdeen

Celtic
Rangers
Yes
Motherwell
Aberdeen

Rangers
Celtic
Yes
Motherwell
Celtic

Aberdeen
Rangers
No
Motherwell
Celtic

Rangers
Aberdeen
No
Motherwell
Rangers

Aberdeen
Celtic
No
Motherwell
Rangers

Celtic
Aberdeen
No
Rangers
Aberdeen

Celtic
Motherwell
No
Rangers
Aberdeen

Motherwell
Celtic
No
Rangers
Celtic

Aberdeen
Motherwell
Yes
Rangers
Celtic

Motherwell
Aberdeen
Yes
Rangers
Motherwell

Aberdeen
Celtic
No
Rangers
Motherwell

Celtic
Aberdeen
No

So you can see that there is an 8 out of 24 (or 1 in 3, or 33.33%) chance of an old-firm semi-final.  It is twice as likely (16 cases out of 24, or 66.67%) that the Old Firm teams avoid each other.

This would be true, if both Celtic & Rangers reached the semi-finals, no matter what the identity of the other two teams involved.

Let’s see if the evidence from the 21st Century provides any ammunition for hot-ball conspiracy theorists.  Scotland has two cup competitions, the League Cup and the FA Cup.  Here is a summary of Old Firm clashes.

Season
Both C&R in LC SF?
Notes
Both C&R in FAC SF?
Notes
2010-11
Yes
Drawn apart
Not yet known

2009-10
No

No

2008-09
Yes
Drawn apart*
No

2007-08
No

No

2006-07
No

No

2005-06
No
Played each other in an earlier round
No

2004-05
No
Played each other in an earlier round
No
Played each other in an earlier round
2003-04
No

No
Played each other in an earlier round
2002-03
Yes
Drawn apart*
No

2001-02
Yes
Old Firm SF
Yes
Drawn apart*
2000-01
Yes
Old Firm SF
No


So, there have been six cases of both teams reaching a semi-final draw since 2000-1, five of which have been in the League Cup.  These have led to two Old Firm semi-finals, and four occasions where they stayed apart, three of which (*asterisked) led to an Old Firm cup final.  There are four other occasions where the teams had been drawn together at an earlier stage of the competition.  There have been nine Old Firm cup ties over these eleven seasons, with perhaps one or two more still possible this season.

Any evidence for conspiracy theories?  Well, conspiracy theorists, what I say to you is, “Will ya wheest? Ma heid’s loupin!”  Or something like that.  That’s the only bit of my souvenir tea towel (and I love Scotland by the way) that is applicable.  These numbers are entirely within the natural random variations that can be expected, and don't let anyone tell you otherwise.

This weekend's hopperatic areas will be the NW of England for Mossley v Nantwich Town in the FA Trophy and the Welsh borders for TNS v Neath in the Welsh Premier League.  Watch this space!