USA-MEX 2nd round in 06: what are the odds?

[SoulflyTribeFC]

I've been kicking this around for a while but I am a neophyte when it comes to analyzing stats.

What are the chances that the US and Mexico are drawn in groups such that they could face each other in the second round?

I was just wondering because it has happened twice in a row. Remember in France 98 had the US won their group and Mexico finished second or vice versa, they would have played each other in the round of 16. Obviously it happened in 2002.

Does it stand to reason that it won't happen because the odds are stacked against it happening three times in a row? Is there even a way to figure it out?

I don't know how it was in 94 but there was a different format in place back then. 98 was the first time there were 32 teams in the World Cup.

[scaryice]

USA and Mexico can't be in the same group. Once one team is drawn, then the other one must be in the correct other group in order to set up a matchup. There are seven other groups, so I believe it's 1 out of 7 odds. (right?)

[voros]

Well simplisticly, if we assume every team has equal chance of advancing and equal chance of advancing in 1st or 2nd place, and we know the US and Mexico won't be in the same group then:

Chance of US meeting any single specific team not in its group should it make the second round is: 1/28 (there are 28 teams outside of the US group of which one is Mexico)

Chance of US making the second round is: 1/2

So the chance of meeting Mexico given above conditions is: 1/28 * 1/2 = 1/56

If you want to factor in team quality it obviously becomes a hell of a lot more complicated.

[JohnR]

Well simplisticly, if we assume every team has equal chance of advancing and equal chance of advancing in 1st or 2nd place, and we know the US and Mexico won't be in the same group then:

Chance of US meeting any single specific team not in its group should it make the second round is: 1/28 (there are 28 teams outside of the US group of which one is Mexico)

Chance of US making the second round is: 1/2

So the chance of meeting Mexico given above conditions is: 1/28 * 1/2 = 1/56

If you want to factor in team quality it obviously becomes a hell of a lot more complicated.

Slightly less simplistically, let's say that there is a 50% chance that both the U.S. and Mexico advance. That's probably a bit optimistic but hey, we're CONCACAF homers, right?

Then, the odds are 1/2 x 1/14 = just under 4% for a first round match-up. 46% of the time they each play in first round but don't meet, 50% the whole exercise is moot because one or the other fail to advance out of the pool.

Again being optimistic let's say that if they don't meet, each has a 50% chance of advancing from the first round. So in the second round, then we would have that 46% chance x 25% chance (both advancing) x 1/7th chance = another 2% chance of meeting in the second round. So we're up to 6% overall. If I repeat the exercise for the semis & finals, I guess we'd get up to 7% to 8% in total, using these fairly generous assumptions.

[scaryice]

You guys are thinking too much. He simply wanted to know the probably of being drawn in the groups that could make that matchup possible.

[SoulflyTribeFC]

Thanks for the info.

Myself, I think that the odds would be against the US and Mexico meeting each other so soon because it has happened twice in a row already. But does that have any bearing? And does the fact that Mexico could get a seed have any affect?

[Sagy]

Since you are asking about the odds of US and Mexico being drawn into groups that will meet each other in the 2nd round (not actually meeting each other) the answer is 1/7. The fact that this happened the last two times does not change the odds at all. The fact that Mexico is a seed doesn't have any impact either.

Before the 1998 draw, the odds of the US and Mexico being drawn into such groups 3 times in a row (ignoring the qualification issue) was 1/343 (~0.3%), but since this already occurred in 1998 and 2002 (odds of 1/49) we are left with a 1/7 chance of this occurring again.

[JohnR]

Before the 1998 draw, the odds of the US and Mexico being drawn into such groups 3 times in a row (ignoring the qualification issue) was 1/343 (~0.3%), but since this already occurred in 1998 and 2002 (odds of 1/49) we are left with a 1/7 chance of this occurring again.

Simple enough, but still a public service. It always surprises me how many people get confused by this, and assume either that the odds are higher than 1/7 or lower than 1/7 (depending upon their particular heuristic) because the draw happened to come out this way for the past 2 Cups.