Draw Probabilities

[songjim]

I just ran all the probabilities of the draw. Gory details at the bottom.

Draw probabilities for Brazil and Argentina:

Angola : 0.166666666666667
Australia : 0.166666666666667
Costa : 0.103174603174603
Croatia : 0.125
Czech : 0.125
Ecuador : 0
Ghana : 0.166666666666667
Holland : 0.125
Iran : 0.0892857142857143
Ivory : 0.166666666666667
Japan : 0.0892857142857143
Korea : 0.0892857142857143
Paraguay : 0
Poland : 0.125
Portugal : 0.125
Saudi : 0.0892857142857143
Serbia : 0.333333333333333
Sweden : 0.125
Switzerland : 0.125
Togo : 0.166666666666667
Trinidad : 0.103174603174603
Tunisia : 0.166666666666667
USA : 0.103174603174603
Ukraine : 0.125

Draw Probabilities for Mexico:

Angola : 0.111111111111111
Australia : 0.111111111111111
Costa : 0
Croatia : 0.125
Czech : 0.125
Ecuador : 0.166666666666667
Ghana : 0.111111111111111
Holland : 0.125
Iran : 0.166666666666667
Ivory : 0.111111111111111
Japan : 0.166666666666667
Korea : 0.166666666666667
Paraguay : 0.166666666666667
Poland : 0.125
Portugal : 0.125
Saudi : 0.166666666666667
Serbia : 0.333333333333333
Sweden : 0.125
Switzerland : 0.125
Togo : 0.111111111111111
Trinidad : 0
Tunisia : 0.111111111111111
USA : 0
Ukraine : 0.125

Draw Probabilities for seeded UEFA team:

Angola : 0.111111111111111
Australia : 0.111111111111111
Costa : 0.158730158730159
Croatia : 0.125
Czech : 0.125
Ecuador : 0.166666666666667
Ghana : 0.111111111111111
Holland : 0.125
Iran : 0.130952380952381
Ivory : 0.111111111111111
Japan : 0.130952380952381
Korea : 0.130952380952381
Paraguay : 0.166666666666667
Poland : 0.125
Portugal : 0.125
Saudi : 0.130952380952381
Serbia : 0
Sweden : 0.125
Switzerland : 0.125
Togo : 0.111111111111111
Trinidad : 0.158730158730159
Tunisia : 0.111111111111111
USA : 0.158730158730159
Ukraine : 0.125

Draw probabilities for Serbia and Montenegro:
Angola : 0.148148148148148
Argentina : 0.333333333333333
Australia : 0.148148148148148
Brazil : 0.333333333333333
Croatia : 0.125
Czech : 0.125
Ecuador : 0.0555555555555556
England : 0
France : 0
Germany : 0
Ghana : 0.148148148148148
Holland : 0.125
Italy : 0
Ivory : 0.148148148148148
Mexico : 0.333333333333333
Paraguay : 0.0555555555555556
Poland : 0.125
Portugal : 0.125
Spain : 0
Sweden : 0.125
Switzerland : 0.125
Togo : 0.148148148148148
Tunisia : 0.148148148148148
Ukraine : 0.125


Draw probabilities for all Asian teams:

Angola : 0.121031746031746
Argentina : 0.0892857142857143
Australia : 0.121031746031746
Brazil : 0.0892857142857143
Croatia : 0.125
Czech : 0.125
Ecuador : 0.136904761904762
England : 0.130952380952381
France : 0.130952380952381
Germany : 0.130952380952381
Ghana : 0.121031746031746
Holland : 0.125
Italy : 0.130952380952381
Ivory : 0.121031746031746
Mexico : 0.166666666666667
Paraguay : 0.136904761904762
Poland : 0.125
Portugal : 0.125
Spain : 0.130952380952381
Sweden : 0.125
Switzerland : 0.125
Togo : 0.121031746031746
Tunisia : 0.121031746031746
Ukraine : 0.125

Draw probabilities for all CONCACAF teams (except Mexico):

Angola : 0.122574955908289
Argentina : 0.103174603174603
Australia : 0.122574955908289
Brazil : 0.103174603174603
Croatia : 0.125
Czech : 0.125
Ecuador : 0.132275132275132
England : 0.158730158730159
France : 0.158730158730159
Germany : 0.158730158730159
Ghana : 0.122574955908289
Holland : 0.125
Italy : 0.158730158730159
Ivory : 0.122574955908289
Mexico : 0
Paraguay : 0.132275132275132
Poland : 0.125
Portugal : 0.125
Spain : 0.158730158730159
Sweden : 0.125
Switzerland : 0.125
Togo : 0.122574955908289
Tunisia : 0.122574955908289
Ukraine : 0.125

Draw probabilities for Ecuador and Paraguay:

Argentina : 0
Brazil : 0
Costa : 0.132275132275132
Croatia : 0.125
Czech : 0.125
England : 0.166666666666667
France : 0.166666666666667
Germany : 0.166666666666667
Holland : 0.125
Iran : 0.136904761904762
Italy : 0.166666666666667
Japan : 0.136904761904762
Korea : 0.136904761904762
Mexico : 0.166666666666667
Poland : 0.125
Portugal : 0.125
Saudi : 0.136904761904762
Serbia : 0.0555555555555556
Spain : 0.166666666666667
Sweden : 0.125
Switzerland : 0.125
Trinidad : 0.132275132275132
USA : 0.132275132275132
Ukraine : 0.125

Draw probabilities for African teams and Australia:

Argentina : 0.166666666666667
Brazil : 0.166666666666667
Costa : 0.122574955908289
Croatia : 0.125
Czech : 0.125
England : 0.111111111111111
France : 0.111111111111111
Germany : 0.111111111111111
Holland : 0.125
Iran : 0.121031746031746
Italy : 0.111111111111111
Japan : 0.121031746031746
Korea : 0.121031746031746
Mexico : 0.111111111111111
Poland : 0.125
Portugal : 0.125
Saudi : 0.121031746031746
Serbia : 0.148148148148148
Spain : 0.111111111111111
Sweden : 0.125
Switzerland : 0.125
Trinidad : 0.122574955908289
USA : 0.122574955908289
Ukraine : 0.125

Draw Probabilities for all non-seeded UEFA teams except Serbia and Montenegro:

Angola : 0.125
Argentina : 0.125
Australia : 0.125
Brazil : 0.125
Costa : 0.125
Ecuador : 0.125
England : 0.125
France : 0.125
Germany : 0.125
Ghana : 0.125
Iran : 0.125
Italy : 0.125
Ivory : 0.125
Japan : 0.125
Korea : 0.125
Mexico : 0.125
Paraguay : 0.125
Saudi : 0.125
Serbia : 0.125
Spain : 0.125
Togo : 0.125
Trinidad : 0.125
Tunisia : 0.125
USA : 0.125


Assumptions -

1. Serbia can only be drawn with Mexico, Argentina and Brazil seeds.
2. All of Korea's pot cannot be drawn with Serbia
3. 2 teams from the same federation cannot be drawn in the same pot except UEFA

Methodology -

Each team's probability to draw a particular seeded team was calculated manually. For instance, Serbia's probability of drawing Brazil is 1/3. Korea's probability of drawing Mexico is 1/6 because:

If Serbia draws Brazil or Argentina, USA, Trinidad and Tobago and Costa Rica all cannot be drawn with Mexico, and thus, one of the 4 Asian teams must be drawn with Mexico. Hence, Korea draws Mexico 1/4 of the time in that case. Since Serbia draws Brazil or Argentina 2/3 of the time, the total probability of drawing Mexico is 2/3 * 1/4 = 1/6

The same calculations can be made for every non-seeded country vs. seeded country.

Next, to calculate probabilities of two non-seeded teams being in the same pot (say, Angola and Korea):

1. We take the probability that Korea gets drawn with a particular seeded team (say, Brazil).
2. We then take the probability that Angola also gets drawn with the same seeded team (in this case, Brazil).
3. We multiply the two together to get the probability they will both draw Brazil.
4. We sum over all the seeded teams to get the probability that Korea will be in the same pot as Angola.

[Joelzinho]

What is this a statistics class...All I am seeing is decimal points.

We here at big soccer appreciate the effort that you put into that post. But my man, god damn I didnt put nothing together from that with the exception of your conclusion....

[tamachan]

What is this a statistics class...All I am seeing is decimal points.

We here at big soccer appreciate the effort that you put into that post. But my man, god damn I didnt put nothing together from that with the exception of your conclusion....

0.1356789999999 means a 13% chance.

If there are eight girls and one has AIDS and you shagged one theres a 13% chance youre gonna get screwed twice. Get it now :D

[tamachan]

Anyway Songjim this is partly useless because Serbia can be drawn against any of the teams in pot 4 including South Korea. They are going to alternate the pickings between pots 3 and 4. Dont believe other people because its true you'll see.

[songjim]

Okay, there are 7 teams in pot D (Asia + CONCACAF). How is Serbia going to be in the same group as one of those teams? If they are, that means there are 2 teams in that group plus one team from pots A, B and C (all of which have 8 teams each) for a group with 5 teams, which is impossible.

And guys, it's a useful table, if you want to see it formatted better, just ask.

[NBlue]

.

If there are eight girls and one has AIDS and you shagged one theres a 13% chance youre gonna get screwed twice.


Why didn't you just say that in the first place? It all becomes clear now.

[tamachan]

Okay, there are 7 teams in pot D (Asia + CONCACAF). How is Serbia going to be in the same group as one of those teams? If they are, that means there are 2 teams in that group plus one team from pots A, B and C (all of which have 8 teams each) for a group with 5 teams, which is impossible.

And guys, it's a useful table, if you want to see it formatted better, just ask.


Serbia can only be drawn in a pool that is headed by a NON-EUROPEAN seed(Brazil, Argentina or Mexico) They are certain to get drawn with an african team or 1 from group D. Do you understand now?

Group 1 is already drawn
Group 2 gets drawn

So now pots 3 and 4 get drawn alternate which leaves 1 group with only 3 teams. That group will be a group with either 1 european representative or 1 Group D representative. Do you see it?

[Shahryar]

I just ran all the probabilities of the draw. Gory details at the bottom...


Thanks, that was a lot of work. :) reps.

Good luck to Korea and to rest of the Asian teams.

[songjim]

Serbia can only be drawn in a pool that is headed by a NON-EUROPEAN seed(Brazil, Argentina or Mexico) They are certain to get drawn with an african team or 1 from group D. Do you understand now?

Dude, Serbia gets drawn with Brazil, Argentina or Mexico, that much is clear.

Now what about the other two teams in the pot?

1 has to come from pot B (UEFA non-seeded pot) since there are 8 teams and none of those 8 can be in the same group (definition of a pot).

1 has to come from pot C (Angola/Togo/Ivory Coast/Tunisia/Ghana/Paraguay/Ecuador/Australia) since there are 8 teams and none of those 8 can be in the same group (definition of a pot).

Hence, they CANNOT be in the same group as Korea/Iran/Japan/Saudi Arabia/USA/Trinidad and Tobago/Costa Rica.

Do YOU understand now?

[titanicsmarty]

Serbia can only be drawn in a pool that is headed by a NON-EUROPEAN seed(Brazil, Argentina or Mexico) They are certain to get drawn with an african team or 1 from group D. Do you understand now?

Wow!!!

You are having problems with this, aren't you.

We have eight top seeds.

We have eight Euros, placed in a pot.

We have another pot, with a total of eight from Africa, Oceania, and South America.

That leaves eight more.

Of those remaining eight, Serbia cannot be placed in a group that already has two Euros.

Therefore, Serbia must be placed in a group headed by Brazil, Argentina or Mexico.

When that business is taken care of, the remaining seven countries are allocated to the remaining seven groups.

It is impossible for Serbia to be drawn together with another of those last seven.

Try it again:
It is impossible for Serbia to be drawn together with another of those last seven.

Get it yet?

[Timanfaya]

I just ran all the probabilities of the draw.

Good stats, cheers.

But there might be details of the draw that distort the values?

I'm thinking of China last time round, who were earmarked for one of three groups, A B or C (i.e. any of the groups playing matches *in* Korea, but not in group D *with* Korea). A team was taken from the pot for Group A. There was a 1/8 chance it would be China, but it wasn't. A team was taken from the pot for Group B - again not China. At this point it was announced that China would have to be in Group C.

By that method, China had a 6/8 chance of being in Group C, whereas before the draw we all would have assumed things would be done sensibly and they'd have 1/3 chance of being in each of groups A, B or C.

Maybe they'll booger it up like this for Serbia/M, for instance? Or in any of the other situations where countries from the same confederation have to be kept separate.

[tamachan]

I must be drunker than i thought! Thanks boys.

[karny9]

You must be from asia to figure out something like that

[locoxriver]

I just ran all the probabilities of the draw. Gory details at the bottom.

I appreciate your time and effort.. But people, relax.. theres just 3 ********ing days till they announce the groups (December 9th).. ;)

[titanicsmarty]

I just ran all the probabilities of the draw. Gory details at the bottom.



Thanks for that, and a lot of hard work.

However, I'm not sure what it tells me specifically.

Take an example for Japan:

Your figures tell me Japan is most likely to be in Mexico's group. Japan has an equal probability of drawing any of the eight Euro teams; and Japan is more likely to get Paraguay/Ecuador than one of the Africans or Australia.

So your figures tell me to expect a group of Mexico, Japan, Paraguay/Ecuador plus one Euro.

But, the same likelihood applies for South Korea or Iran or KSA, so really there's nothing here to help me predict who Japan might face.

The figures are only maningful in terms of federation against federation, not in terms of country against country.

I think you've shown that Mexico's group is likely to include one Asian team, but you haven't told me much about any individual country.

Maybe it would be more meaningful to do a federation by federation breakdown?

[chapulin]

I appreciate your time and effort.. But people, relax.. theres just 3 ********ing days till they announce the groups (December 9th).. ;)

Haha, ur right dude. But, you gotta agree that the hype is just too much!!! :p

[argentine soccer fan]

0.1356789999999 means a 13% chance.

If there are eight girls and one has AIDS and you shagged one theres a 13% chance youre gonna get screwed twice. Get it now :D

Not if you're smart and use a condom. :D

[songjim]

Okay, I've formatted things a bit better. (is there any way to do tables a bit easier here?).

Australia = Australia or any African team
Brazil = Brazil, Argentina
Ecuador = Ecuador, Paraguay
England = Seeded UEFA
Holland = Unseeded UEFA
Korea = Asia
USA = Unseeded CONCACAF


------ Austral Brazil Ecuado Englan Hollan .Korea Mexico Serbia. . USA
Austral 00.00% 16.67% 00.00% 11.11% 12.50% 12.10% 11.11% 14.81% 12.26%
.Brazil 16.67% 00.00% 00.00% 00.00% 12.50% 08.93% 00.00% 33.33% 10.32%
Ecuador 00.00% 00.00% 00.00% 16.67% 12.50% 13.69% 16.67% 05.56% 13.23%
England 11.11% 00.00% 16.67% 00.00% 12.50% 13.10% 00.00% 00.00% 15.87%
Holland 12.50% 12.50% 12.50% 12.50% 00.00% 12.50% 12.50% 12.50% 12.50%
. Korea 12.10% 08.93% 13.69% 13.10% 12.50% 00.00% 16.67% 00.00% 00.00%
.Mexico 11.11% 00.00% 16.67% 00.00% 12.50% 16.67% 00.00% 33.33% 00.00%
.Serbia 14.81% 33.33% 05.56% 00.00% 12.50% 00.00% 33.33% 00.00% 00.00%
. . USA 12.26% 10.32% 13.23% 15.87% 12.50% 00.00% 00.00% 00.00% 00.00%