Tuesday, 20 May 2014

World Cup Group Permutations

I deviate momentarily from games to talk about the 2014 FIFA World Cup.

I'm sure this has been done before but I find it quite interesting to analyse the various combinations of points possible in the Group Stage. For those who are unfamiliar with the Group Stage, basically it's a round-robin format of 4 teams where each team plays each other only once. Only the top two teams qualify for the next round of 16.

I will attempt to artificially categorise and describe the situations that lead to each permutation. All credit goes to the lovely contributors at Wikipedia for their helpful tables and links.

Category 1: "Super" Powerhouse and "Lesser" Powerhouse

This is the most common group that one can think of - two dominant teams, A and B, with A being significantly more dominant than B. The other two residual teams in the group, C and D, are simply no match for the two dominant teams so their results against each other don't really matter.

There are two variants I observe here:

Variant 1.1 [Clearly distinguishable ascending hierarchy]:
A > B > C > D

Here, A is clearly the strongest. It is equally clear that B is second strongest. And C is third strongest, being stronger than weakest D. Typically you would expect 9, 6, 3, 0 points in that order from first to last.

Example 1: Group E 2010 FIFA World Cup
It is arguable of course whether Denmark was significantly stronger than Cameroon in 2010 (it is probably the better argument that Poland was significantly stronger than Costa Rica in 2006 below though?).

Example 2: Group A 2006 FIFA World Cup

 Costa Rica300339−60

Example 3: Group H 1998 FIFA World Cup


Variant 1.2 [Big Bully, Little Bully; Indistinguishable "Weaklings"]:

A > B > C = D

In this variant, A is clearly the strongest. It is equally clear that B is second strongest.
However, C is comparable in strength to D.

Example: Group H 2006 FIFA World Cup
 Saudi Arabia301227−51

Category 1b: Dominant but relatively equal duo

This is a major variation to Category 1.

The variation is simply that the powerhouses A and B are almost equal in strength.
Thus this means that, at least in theory, A and B should neutralise each other out and draw against each other. A and B are expected to (but don't necessarily) win their respective games against C and D.

Variant 1b).1 [Flawed Duo]: This occurs where one of the duo fails to meet expectations and doesn't win one of their games against weaker teams C and D.

Example: Group C 1994 FIFA World Cup
 South Korea302145−12
Whilst Germany and Spain drew with each other, Spain drew with South Korea.

Variant 1b).2 [Standard/Classic Situation]: A and B each deal with C and D relatively comfortably but draw with each other. Expectations are therefore met.

Example: Group F 1998 FIFA World Cup
 United States300315−40

Category 2 : The Love Triangle

A beats B. 
B beats C. 
C beats A.
A > B > C > A...

This creates an apparent logical fallacy in the sense that A is expected to beat C yet in fact loses to C!

The common factor, however, is that D loses to everyone else as D is easily the weakest in the group.

Goal Difference, Goals For and Head-to-head appear to be determinative here in separating 1st, 2nd and 3rd.

Example: Group D 1994 FIFA World Cup.


Example 2: Group F 1994 FIFA World Cup

 Saudi Arabia320143+16

Category 3: Survival of the Second Fittest

In this situation, A is grossly (perhaps even absurdly) dominant; whereas B, C and D are all of comparable strength and must scrap for second place. It just takes 1 key victory amongst teams B, C and D for one to separate from the rest of the pack!

Classic example is Group F 2006 FIFA World Cup

I'd argue that Australia, Croatia and Japan were all of comparable strength in the sense that Japan and Croatia drew and Croatia and Australia also drew. The difference was that Australia was slightly stronger than the other two by pulling off a cool victory against Japan (3-1)!!

Example 2: Group C 1998 FIFA World Cup

 South Africa302136−32
 Saudi Arabia301227−51

Example 3: Group B 2010 FIFA World Cup

 South Korea311156−14
Note that the difference between this group and the others is that 3rd place (Greece) actually wins a game against 4th place (Nigeria).

Variant 3.1 [Tiebreaker Required]: Here, the difference between second and third comes down to Goal Difference or Goals Scored! (by virtue of each team drawing and winning one game each)

Example 1: Group B 2002 FIFA World Cup
 South Africa31115504

Example 2: Group C 2002 FIFA World Cup

 Costa Rica311156−14
 China PR300309−90

Variant 3.2 [Undefeated Second]: This occurs where 2nd place is snatched by not losing to any member of the group (this is extremely rare and is unlikely to be successful - note that New Zealand were undefeated in the 2010 World Cup but failed to proceed to the knockout stage)

Example: Group B 1998 FIFA World Cup
Amazingly, Chile secures progression with three draws!!!

Category 4: Closely contested 

In this category, the points in the group are very evenly spread amongst all teams either because of:

i) An unusually high number of draws (probably due to a large number of defensive or relatively poor teams) OR

ii) What I call a broken love triangle (basically a Category 2 situation where A > B > C > A but the last group member D does NOT score 0 points but manages to draw and win a match).

Example 1:

 New Zealand30302203

Example 2: Group D 2010 FIFA World Cup.

In this case Ghana > Serbia > Germany > Ghana but Serbia loses to Australia and Australia draws with Ghana, hence the broken love triangle.

Example 3: Group C 2010 FIFA World Cup 

 United States312043+15

Example 4: Group E 1998 FIFA World Cup

 South Korea301229−71

Imagine a group where everyone draws all games -- I don't think this has happened from 1994 onwards? (or ever?)

Category 5: "Group of Death"

This category is, strictly speaking, not categorised by final points but by apparent closeness in contest between high-ranking/seeded on the one hand, and seemingly underrated teams on the other, before the competition starts. It is usually a phrase thrown around by the media in anticipation of the World Cup to generate hype.

It often happens when at least 1 "good team" (that has enjoyed previous success) fails to be properly seeded, perhaps because they have not been doing well of late.

To make for a "proper" group of death, there probably ought to be at least 3 strong teams and perhaps 1 average or stronger-than-normal team. Another way of checking to see if there is a Group of Death is to add up the seedings of all the countries - the lower the number, the more likely you have a Group of Death.

One credible World Cup example would be Group C 1982 FIFA World Cup, but this only had 3 members:


I'm not sure whether any credible Groups of Death existed from 1994 and onwards (when the 3-point for a win system was used).

Arguably, Group G 2010 FIFA World Cup fell short of the mark because North Korea was not "average" by any means, though some media outlets thought it was a Group of Death at the time:

 Ivory Coast311143+14
 North Korea3003112−110

However, a good non-World Cup example is Group C Euro 2008 where 2006 World Cup finalists Italy and France were drawn with Netherlands and Romania.


Another good example would be Group C Euro 1996 where the respective world rankings of the groups members were 2, 3, 7 and 10!

 Czech Republic311156–14

Category 6: Seemingly Random Chaos

This category accounts for all the left overs. We are talking about random patterns and oddities here. In other words, this category involves a combination of one of the above categories.

For the time being I can only think of one group that partially (though not completely) fits the bill:

In Group H 2010 FIFA World Cup, whilst Spain and Chile were the dominant teams, Spain somehow lost to Switzerland in its opening match. Spain were "lucky" that Switzerland only drew with Honduras and that Chile did not score more goals against Switzerland.

It is probable that this would fit into the Flawed Duo variant mentioned in Category 1b).1 above, but it doesn't feel completely right categorising this group as such because the top team loses to the 3rd-ranked team.

So that's all for now.
Have I missed anything?
Perhaps more to come later...

Andre Lim

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