More number chugging
Based on the November FIFA rankings:
the strongest possible group is Argentina, Italy, USA, Portugal
the weakest possible group is Belgium, Cameroon, Australia, Russia
Based on the SPI rankings:
the strongest possible group is Spain, Chile, USA, France
the weakest possible group is Switzerland, Algeria, Australia, Croatia (could you imagine?)
Based on the ELO rankings:
the strongest possible group is Brazil, Netherlands, USA, England
the weakest possible group is Belgium, Algeria, Honduras, Bosnia-Herzegovina
Based on the average of the 3 rankings organizations:
the strongest possible group is Spain, Chile, USA, Netherlands
(side note if you just rank the teams in the tourney, that average has the above tied with Argentina, Netherlands, USA, Portugal)
the weakest possible group is Switzerland, Algeria, Australia, Croatia
Some other thoughts.
The average group strength, ranking them 1 to 32, would be 66 for the group (great number btw).
What we can consider "fair" can be looked at in two ways:
1) What is the average of the rank of all the other 31 teams? That number times 3 could be considered 'fair' - well for the #1 team the average of everyone else is 17, for the #2 team the average is 16. So for team #1: 1+17+17+17 = 52 is a "fair" group and for team #32 32+16+16+16 = 80 is "fair". By this measure, the USA, which has an average rank of #14.5 this works outs to a "fair" group including them as having a total of 64.19.
2) What would the average rankings of the other teams be if we used a serpentine method?
In this case fair for #1 is to get teams 16, 17, and 32 (a total of 66 and a fair group, but one where the other teams are ranked a total of 65), for #32, "fair" is to get teams 1, 16, and 17 (again a total of 66 for a fair group, but one where the other teams are ranked a total of 33).
So for the USA, "fair" by this measure is opponents with a total ranking of 51.5 (on the serpentine they would get either 2, 18, 31 or 3, 19, 30)
The median strength for the USA group is about 56 (for an average ranking of 13.83 for the other 3 teams in their group) Basically the sum of rankings less than 56 is a "bad luck" scenario for the USA.
In terms of the two key measures above.
79.9% of the possible groups for the USA have a total rankings combined of less than 64.19 - that is there's an 80% chance basically that we will get a group tougher than we "deserve" by measure 1.
82.9% of the possible groups for the USA have a total rankings combined of less than 66 - the other measure I mentioned.
1.5% of the possible groups for the USA have a combined rankings of 66 on the nose.
So just 15.6% of the possible groups have a combined ranking above 66.
There's a 4.167% chance that the USA will be the top ranked team in its group based on average rank.
There's a 37.847% chance that the USA will be the 2nd ranked team in its group based on average rank.
There's a 49.306% chance that the USA will be the 3rd ranked team in its group based on average rank.
There's an 8.681% chance that the SUA will be the 4th ranked team in its group based on average rank.
There's a 17.361% chance all 4 teams in the USA group will be ranked in the top 16 based on average rank.
There's a 4.167% chance that the other 3 teams will ranked in the top 10 based on average rank.
There's a 37.5% chance that we get a bottom 8 team in our group.
There's a 5.556% chance that we get two bottom 12 teams in our group.
So there you go.
-QG