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Wednesday, June 13, 2012

MY EURO 2012 GROUP B LOGIC


Firstly, I will denote the countries in Group B by it's first letter
D for Denmark
G for Germany
P for Portugal
N for Netherlands



N obviously needs G's cooperation, although G only requires a draw to be in pole position. As the match happens at the same time, G will expect D fighting hard for the win so a draw in the middle would be dangerous, let's say if D scores late goals and P crushes N.

If N wins against P, G is automatically qualified. And there is no logical dependence on how much G wants to take the advantage to be #1 in the group stage (facing the #2 in Group A), as they can just settle for an easy scoreless (or any) draw and it's a mutualism symbiosis for D and G (provided that N has already won by some goals, and they can monitor the results)

However, even if G beats D, N's chances are still slim. The tiebreakers are as follows :
1) Higher number of points obtained in the group matches played among the teams in question
2) Superior goal difference from the group matches played among the teams in question
3) Higher number of goals scored in the group matches played among the teams in question
4) Higher number of goals scored away from home in the group matches played among the teams in question
5) If, after applying criteria 1) to 4) to several teams, two or more teams still have an equal ranking, the criteria 1) to 4) will be reapplied to determine the ranking of these teams. If this procedure does not lead to a decision, criteria 6) and 7) will apply

Consider the case if N,P and D (they lost to G) have the same 3 points.
1) Pass the 1st tiebreaker as N beats P beats D beats N.
2) For the 2nd point, N will have at least -1, both P and D will have at most -1. If N beats P by more than 1 goal, N will qualify. Otherwise, go the 3rd point.
3) Both P and D already scored 3 goals, while N only got 1. As we arrive here, our assumption is N only beats P with exactly 1 goal difference meaning N will still be 1 goal below P's goals and thus not qualified.

To sum it up, N can only qualify if :
1) G wins against D
2) N wins against P by more than 1 goal.

On the other hand, if N-P's match ended in a draw, it will make life difficult for D, as they can't just settle with a draw with G (see 1st tiebreaker).

But it's another interesting tiebreaker scenario if both P wins against N and D wins against G :
1) Pass the 1st tiebreaker as P beats D beats G beats P
2) P and D will have at least +1, while G will have at most +1. If D beats G with more than 1 goal, G is eliminated. If P beats N with more than 1 goal, P is in pole position and out of the tiebreaker.
3) In any case, for the 3rd point, P score 3 goals (3 vs D, 0 vs G), D score 2+x goals (2 vs P, x vs G), and G score 1+y goals (1 vs P, y vs D). As D wins against G, x > y and thus D's goals are superior to G's.

The only way for G not to be eliminated here is if P beats N by exactly 1 goal (so that they stay in the tiebreaker), and G's goals are not less than P's goals, meaning y >= 2 or in other words G must at least score twice, another miniscule chance right here..

And in case the tiebreaker continues as G scored twice vs D, that makes point 4 identical to point 3 as P and G are not the hosts. That makes we go to point 5, a tiebreaker between only P and G, which is clearly won by G (back to point 1).

To sum it up, G will be eliminated only if :
1) P wins against N
2) D wins against G
3a) D wins by more than 1 goal, or
3b) P wins by more than 1 goal, or
3c) G scored at most 1 goal vs D

It's interesting to see that; by means of pure probability (assuming all teams have even chances to win against each other); it's more probable for G to be eliminated than N to be qualified. Haven't taken into account that the 1st condition for N to qualify is the only one based on sportsmanship.

So, it's correct if someone tweeted that "the stars need to align if Netherlands are to sneak through..."

Yeah that's all, I guess. If you're reading up to this point, thanks for your time =p