### Logical mistakes of the qualifying rounds of World and European Championships

In the qualifying rounds of these world competitions the participating national teams are sorted into 9 groups.   As the number of the participant teams (53) and that of the qualifying teams (14 and 13) did not give the organisers a mathematical chance for a clean arrangement, they chose the following method:
In the 8 groups there were 6 participant teams, in one there were 5,
The winners qualified (this meant 9 qualifying teams),

In case of 14 qualifying teams the winner teams qualified (this meant 9 qualifying teams),
and also the best second team (as the 10th qualifying team),
and four more from the other 8 second best teams (determined by pair matches),
thus a total of 14 teams qualified.

In case of 13 qualifying teams the winners,
from the 9 second best the worst team drops out, and from the remaining eight four more qualify based on the results of pair matches, this means 4 more besides the 9 winners.

The logical mistake is the following:
Out of the 9 groups there were 6 participant teams in 8 of the groups, every one of these teams played 10 matches, and a maximum of 30 points could be reached by the winners and a maximum of 27 points for the second bests. There were 5 teams in the ninth group, every team played 8 matches, so the winners could reach 24 points, the second ones could reach 21 points.  The second team in this group would be at a disadvantage - according to the organisers, and finally they are right in that  - therefore, in order to establish a ranking between the second teams, they decreased the score of the second teams in the other groups by the score of the match against the weakest team of the group, as if they had not played against that team.
The result of this measure was that the score of the team that lost points against the weakest team of the group was decreased by fewer points, which is - in my view - incorrect.  The team that could not win against the weakest team of the group in both matches is privileged.

This mistake is clearly visible in the qualifying rounds of current world championships:
Iceland’s matches against the weakest team of the group, Cyprus: 2-1 and 0-1, thus their score was decreased by only 3 points, and they got into a better position than Denmark, who won 2 matches (6 points) against the weakes team of the group.  Originally Denmark had 16 points, Iceland had 15 points, yet it is Iceland who can play on to qualify for the world championship.