The seeding decisions as it could be read on FIFA WWW service is extremely problematic as well as the drawing procedures carry another mistake which could be corrected easily. To be precise, here are the facts:
1) The seeding seems logical but the consequences are a blow to the
world cup hopes of especially Nigeria, but also of Brazil, Argentina and
Mexico and so the hopes of three continent confederations. In the same
moment it boosts Europes prospects to deliver the world champion although
particular teams (England, Bulgaria and a possible victim by 'accident')
face similar problems.
Why? Here are the mathematics:
First an evaluation has to be taken on the teams. Although one can argue
about this evaluation, the problem will remain even after a moderate reevaluation!
The teams can be classified, to make it easier only into three categories,
after their assumed real strength (This classification neglects the knowledge
of the seeding that was taken by FIFA):
likely to qualify for second round (70%):
Brazil, Argentina, Germany, England, Italy, Bulgaria, France, Netherlands,
Spain, Rumania, Nigeria
50/50 chances (50%):
Denmark, Norway, Yugoslawia, Belgium, Croatia, Austria, Scotland, Mexico
less likely to qualify for second round (30%):
Columbia, Paraguy, Chile, Cameroon, South Africa, Morocco, Tunisia,
Saudi-Arabia, South Corea, Japan, Iran, USA, Jamaica
(Due to the structure of the classification the values have to be corrected
to 71,8%, 51,3% and 30,8 % but this makes no real difference)
It should be clear that a fair balanced group adds up to 200% (because
two teams make it to the second round).
For example: Brazil, England, South Corea, USA or Brazil, Mexico, Austria,
Iran
An unbalanced group now is possible: Brazil, England, Nigeria, Japan.
This group adds up to 240%. So it has to be weight down. The chances for
Brazil, England and Nigeria decrease from 70% to (70*200/240=) 58%. This
means a 17% cut of hopes! Everybody knows what part luck plays and that
there only can be two of England, Brazil or Nigeria to advance from such
a combination, neglecting the impossible task for the fourth power.
Now you might say what is the problem, it could happen to anybody.
The answer is no, it is much more likely to happen to Brazil or Argentina
and it is even more likely to happen to Nigeria:
Even a group with 4 70%-teams (Nigeria, Brazil, England, Bulgaria)
is possible. This cannot happen to European teams topseeded. Their chances
now increased as the following calculation proves.
i) The chances for an Europan top seat are: 1/8 to get Nigeria (a team evaluated 70%), 1/8 to get Mexico (50%), 6/8 to get a 30% team from this pot. 2/9 to get a 70% Europe team, 7/9 to get a 50% Europe team. That leaves the following chances:
| to get a 240% group: 1/8*2/9=2/72=2,8% |
| to get a 220% group: 1/8*2/9+1/8*7/9=9/72=12,5% |
| to get a 200% group: 1/8*7/9+6/8*2/9=19/72=26,4% |
| to get a 180% group: 6/8*7/9=42/72=58,3% |
ii) The chances for Brazil and Argentina are: to get Nigeria 1/8, to get Mexico 1/8, to get a 30%team: 6/8. To get a 70% European team 2/9, to get a 50% European team 7/9. For the fourth team it is 50/50 whether it will be an Asian team or an European team. That means: The chances to get an European 70%er are 1/2*2/9, a 50%er are 1/2*7/9 and an Asian 30%er 1/2. That leads to the following:
| to get a 280% group: 1/8*2/9*(1/2*2/9)=0,3% |
| to get a 260% group: 1/8*2/9*(1/2*2/9)+1/8*7/9*(1/2*2/9)+1/8*2/9*(1/2*7/9)=2,5% |
| to get a 240% group: 1/8*7/9*(1/2*7/9)+1/8*2/9*1/2+1/8*2/9*(1/2*7/9)+1/8*7/9*(1/2*2/9)+6/8*2/9*(12*2/9)=9,2% |
| to get a 220% group: 1/8*7/9*1/2+1/8*2/9*1/2+1/8*7/9*(1/2*7/9)+6/8*2/9*(1/2*7/9)+6/8*7/9*(1/2*2/9)=23,0% |
| to get a 200% group: 1/8*7/9*1/2+6/8*2/9*1/2+6/8*7/9*(1/2*7/9)=35,9% |
| to get a 180% group: 6/8*7/9*1/2=29,2% |
iii) The chances for Nigeria are: 2/9 to get an European
70%er, 7/9 to get an European 50%er as let's call it seat2. For seat1 it
is 1/4 to get Brazil or Argentina. Following this it is 1/2 to get an Asian
team as third opponent 12*2/9 to get an European 70%er, 1/2*7/9 to get
an European 50%er. 3/4 are the chances to get an European top seat. Then
it will be a 30%er as fourth opponent. This leads to the following:
| to get a 280% group: 1/4*2/9*(1/2*2/9)=0,6% |
| to get a 260% group: 1/4*2/9*(1/2*7/9)+ 1/4*7/9*(1/2*2/9)=4,3% |
| to get a 240% group: 1/4*2/9*1/2+1/4*7/9*(1/2*7/9)+3/4*2/9=27,0% |
| to get a 220% group: 1/4*7/9*1/2+3/4*7/9=68,1% |
iv) The chances for Mexico are structured the same. Due
to the fact Mexico was evaluated only to be a 50% team all values have
to be decreased by that difference:
to get a 260% group: 0,6%, to get a 240% group: 4,3%, to get a 220%
group: 27,0%, to get a 200% group: 68,1 %
Also it has to be seen that for Bulgaria and England similar problems
occur although their chances to have to play against Nigeria are smaller
than that of Nigeria has to play against one of those two. They only can
face each other when playing against Brasil or Argentina. As a package
they are avoided for any European top seat. When success is compared continentwise,
the Europeans have the edge here by victimising those two powers.
The following facts are correct even if you corrected the evaluation
for the teams up to some acceptable extend*:
Nigeria has no chance at all to get into an easy group. Their hopes
are cut because the probability they advance is smaller than that of any
other comparable team if they play the same strong. In other words: They
have to be much stronger than others to achieve the same.
European topseeds can expect much easier groups than South-American
teams. Only about 10% probability for a heavy group. The worst case, a
group of four superstrong teams cannot happen to them at all.
Nigeria, carrying the hopes of a continent and the hopes of fans all
over the world for exitement are the losers and can only hope that luck
lowers the damage. Already in 1994 Cameroon had to pay for this kind of
seeding. In a last minute change their success in 1990 was regarded less
important than the idea to put the African teams into one pot to avoid
they played against each other. It had a similar effect on Cameroons chances
then. The result was they were getting drawn into the 'group of death'
as it was called after the draw, but there was still the hope for the third
of each group to qualify. Because Cameroon was weaker than 1990 it was
not such a shame than it is now for Nigeria.
(*three examples:
If you say Bulgaria is not a 70% team, there will be only a moderate
change in the probability values but no change in the structure you can
see above.
If you say Brasil is stronger than 70% you have to distinguish more
cases: you will have to add some cases worse than the ones described above.
If you say, there are 30%ers among the Europeans (Austria), you will
find an extra case with the possibility of a 200% group for Nigeria, although
only with a small probability value. But in the same moment you will have
the possibility of a 160% group for an European top seat as well. The tendency
always remains the same unless you made Nigeria and Mexico 30%teams. But
this they are not.)
2) The drawing (a minor problem but it can easily be solved):
The drawing does not allow South Americans to play against Asians,
it does not allow Central/North- Americans to play against Africans. As
we know from the past ceratain teams to easier against certain others.
So an exclusion is always unfair. Also the battle of concepts is one of
the great things to watch in FIFA world cup. This problem can easily be
solved by a modifikation:
First it is drawn into which group the ninth European team is drawn
into: Brazil or Argentina. The next, it is drawn into which of the European
groups the three remaining CONBEBOL teams are drawn into. (You don't need
to draw the names yet! It makes it even more thrilling to have the confederations
first, the names then!)
The next step is, you have a pot that decides on from which of the
remaining confederations (CONCACAF, AFC, CAF) the remaining teams come
from. Now you have 4 groups with already three teams and four with two.
From here on it is easy. First you have to determine a succession in
which no confederation succeeds itself and which allows all combinations,
for example: CAF, AFC, CONCACAF, AFC, CAF, CONCACAF, CAF, AFC, CAF, CONCACAF,
AFC, CAF.
Then you draw the group where to start (for example E is drawn, then
those teams will be drawn from left to right: E, F, G, H, A, B, C, D),
or you determine each group by drawing the number from a pot. Then one
team from the confederations is drawn in the succession as determined above.
It sounds more complicated than it is and is still possible to have
any succession you like whether to draw the European teams first or not.
This information is brought to you by **###
institut für universelle zusammenhänge, The
Shot that passed right through the Net. More information on how African
teams were put at a disatvantage until 1990 with mathematical evidence
you can find at http://www.informatik.uni-frankfurt.de/~wille/WOM/BALL/afr_st_e.html
(in Deutsch: http://www.informatik.uni-frankfurt.de/~wille/WOM/BALL/afr_stat.html)