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 21^st 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!