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There's over 2 months until the next matchday so this will probably come in handy several times.
This is a general mathematical proof, allocating all remaining points as best as possible. You can ignore specific match results as the proof doesn't need them.
After Andorra draw with Slovakia, the table would look like this:
Team | Pld | Pts |
---|---|---|
Slovakia | 6 | 11 |
Russia | 5 | 10 |
Republic of Ireland | 5 | 10 |
Armenia | 5 | 8 |
North Macedonia | 5 | 4 |
Andorra | 6 | 1 |
Now with the best case scenario, Andorra win all their games. I'm keeping them bottom of the following table for simplicity:
Team | Pld | Pts |
---|---|---|
Slovakia | 6 | 11 |
Russia | 6 | 10 |
Republic of Ireland | 6 | 10 |
Armenia | 6 | 8 |
North Macedonia | 6 | 4 |
Andorra | 10 | 13 |
In order for Andorra to have a chance of winning the group, ALL other teams have to be kept below 14pts.
Slovakia, Russia, Ireland, and Armenia all play each other once. That's 6 matches, and the absolute minimum of points that therefore HAVE to be distributed amongst these 4 teams is 12pts. Ignoring specific match combinations, and therefore giving Andorra the best possible chance, we can distribute them as follows:
Team | Pld | Pts |
---|---|---|
Slovakia | 9 | 13 |
Russia | 9 | 13 |
Republic of Ireland | 9 | 13 |
Armenia | 9 | 12 |
North Macedonia | 6 | 4 |
Andorra | 10 | 13 |
Any 3 of those 4 teams will be on 13 points, with the remaining one on 12pts (which happens to be Armenia in this example). Macedonia play each of those teams, and will HAVE to defeat the teams on 13pts in order to stop them getting 14 or more, and being out of Andorra's reach:
Team | Pld | Pts |
---|---|---|
Slovakia | 10 | 13 |
Russia | 10 | 13 |
Republic of Ireland | 10 | 13 |
Armenia | 9 | 12 |
North Macedonia | 9 | 13 |
Andorra | 10 | 13 |
The one remaining match is between the team with 12 points, and Macedonia. It is impossible for this match to be settled without one of those teams getting 14 or more points, meaning that Andorra cannot win the group.
At each stage of this proof, I have given Andorra the best possible chance and given them the best outcomes. Still, it is impossible for them to finish on top of the group if they should draw against Slovakia. Aheyfromhome ( talk) 17:46, 28 March 2011 (UTC)
just curious why the standings do not agree with what the three way tie-breaker table shows. is it simply because UEFA lists the standings that way? seems peculiar. 18abruce ( talk) 23:28, 4 June 2011 (UTC)
According to UEFA, this is how the table is supposed to be (I'm leaving out Macedonia and Andorra):
1. Rep Ireland W:4 D:1 L:1 GF:11 GA:6 GD: 5 PTS: 13
2. Russia W:4 D:1 L:1 GF:9 GA:4 GD: 5 PTS: 13
3. Slovakia W:4 D:1 L:1 GF:6 GA:4 GD:2 PTS: 13
4. Armenia W:2 D:2 L:2 GF:10 GA:7 GD:3 PTS: 8
Not the one we have! It seems UEFA is rather ranking teams by goals scored rather than Goal Difference of head-to-head record.
Source: http://www.uefa.com/uefaeuro2012/standings/round=15171/group=700958/index.html GuyWithoutAUsername ( talk) 19:57, 5 June 2011 (UTC)
If Macedonia loses vs Russia, they can max get 14 points, with Russia already at 14, and games between Rus-Svk, Rus-Irl and Irl-Svk yet to be counted. No matter how things end up in those 3 matches, Macedonia gets eliminated.
If Macedonia draws Russia, they get eliminated too:
The three games between Russia, Slovakia and Irland means that at least one team ends up at 15 points or more, and the only way for the runner-up team not to beat 14 points is for Russia to defeat the other two teams, while Slovakia-Irland ends in a draw. This also requires Armenia to beat Slovakia and Ireland, causing a four-way tie. Even in that scenario, Macedonia gets eliminated, because they lose the tie. (Which would be Irl 11p, Arm 10p, Mac 7p, Svk 5p.)
If Macedonia wins, they can still win the group, but only if Ireland-Slovakia ends in a draw. That way Rus-Irl, Rus-Svk and Svk-Irl can all end in draws, leading to Macedonia winning with 16 points ahead of Rus, Svk and Irl at 15. (Assuming all remaining games go Macedonia's way.)
If Ireland or Slovakia win their game, Macedonia can still qualify but not win the group.
If either Svk or Irl win, they reach 16 points and need to lose all remaining games. Them losing their game vs Russia leads to Russia reaching 16 points, meaning they need to lose vs the other team of Svk and Irl to remain below 17 points. This leads to a four-way tie with Russia, Slovakia, Ireland and Macedonia all at 16 points. Macedonia would lose this four way tie though. (The results would be Irl/Svk 10p, Rus 9p, Mac 6p.) Lejman ( talk) 03:56, 6 June 2011 (UTC)
Armenia can't become unable to win the group. Even if they lose vs Andorra, Russia defeat Macedonia and Ireland defeat Slovakia, a four way tie where Russia, Slovakia, Ireland and Armenia all end up at 17 points can still occur, leading to Armenia winning the group on better head-to-head record. Lejman ( talk) 04:26, 6 June 2011 (UTC)
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There's over 2 months until the next matchday so this will probably come in handy several times.
This is a general mathematical proof, allocating all remaining points as best as possible. You can ignore specific match results as the proof doesn't need them.
After Andorra draw with Slovakia, the table would look like this:
Team | Pld | Pts |
---|---|---|
Slovakia | 6 | 11 |
Russia | 5 | 10 |
Republic of Ireland | 5 | 10 |
Armenia | 5 | 8 |
North Macedonia | 5 | 4 |
Andorra | 6 | 1 |
Now with the best case scenario, Andorra win all their games. I'm keeping them bottom of the following table for simplicity:
Team | Pld | Pts |
---|---|---|
Slovakia | 6 | 11 |
Russia | 6 | 10 |
Republic of Ireland | 6 | 10 |
Armenia | 6 | 8 |
North Macedonia | 6 | 4 |
Andorra | 10 | 13 |
In order for Andorra to have a chance of winning the group, ALL other teams have to be kept below 14pts.
Slovakia, Russia, Ireland, and Armenia all play each other once. That's 6 matches, and the absolute minimum of points that therefore HAVE to be distributed amongst these 4 teams is 12pts. Ignoring specific match combinations, and therefore giving Andorra the best possible chance, we can distribute them as follows:
Team | Pld | Pts |
---|---|---|
Slovakia | 9 | 13 |
Russia | 9 | 13 |
Republic of Ireland | 9 | 13 |
Armenia | 9 | 12 |
North Macedonia | 6 | 4 |
Andorra | 10 | 13 |
Any 3 of those 4 teams will be on 13 points, with the remaining one on 12pts (which happens to be Armenia in this example). Macedonia play each of those teams, and will HAVE to defeat the teams on 13pts in order to stop them getting 14 or more, and being out of Andorra's reach:
Team | Pld | Pts |
---|---|---|
Slovakia | 10 | 13 |
Russia | 10 | 13 |
Republic of Ireland | 10 | 13 |
Armenia | 9 | 12 |
North Macedonia | 9 | 13 |
Andorra | 10 | 13 |
The one remaining match is between the team with 12 points, and Macedonia. It is impossible for this match to be settled without one of those teams getting 14 or more points, meaning that Andorra cannot win the group.
At each stage of this proof, I have given Andorra the best possible chance and given them the best outcomes. Still, it is impossible for them to finish on top of the group if they should draw against Slovakia. Aheyfromhome ( talk) 17:46, 28 March 2011 (UTC)
just curious why the standings do not agree with what the three way tie-breaker table shows. is it simply because UEFA lists the standings that way? seems peculiar. 18abruce ( talk) 23:28, 4 June 2011 (UTC)
According to UEFA, this is how the table is supposed to be (I'm leaving out Macedonia and Andorra):
1. Rep Ireland W:4 D:1 L:1 GF:11 GA:6 GD: 5 PTS: 13
2. Russia W:4 D:1 L:1 GF:9 GA:4 GD: 5 PTS: 13
3. Slovakia W:4 D:1 L:1 GF:6 GA:4 GD:2 PTS: 13
4. Armenia W:2 D:2 L:2 GF:10 GA:7 GD:3 PTS: 8
Not the one we have! It seems UEFA is rather ranking teams by goals scored rather than Goal Difference of head-to-head record.
Source: http://www.uefa.com/uefaeuro2012/standings/round=15171/group=700958/index.html GuyWithoutAUsername ( talk) 19:57, 5 June 2011 (UTC)
If Macedonia loses vs Russia, they can max get 14 points, with Russia already at 14, and games between Rus-Svk, Rus-Irl and Irl-Svk yet to be counted. No matter how things end up in those 3 matches, Macedonia gets eliminated.
If Macedonia draws Russia, they get eliminated too:
The three games between Russia, Slovakia and Irland means that at least one team ends up at 15 points or more, and the only way for the runner-up team not to beat 14 points is for Russia to defeat the other two teams, while Slovakia-Irland ends in a draw. This also requires Armenia to beat Slovakia and Ireland, causing a four-way tie. Even in that scenario, Macedonia gets eliminated, because they lose the tie. (Which would be Irl 11p, Arm 10p, Mac 7p, Svk 5p.)
If Macedonia wins, they can still win the group, but only if Ireland-Slovakia ends in a draw. That way Rus-Irl, Rus-Svk and Svk-Irl can all end in draws, leading to Macedonia winning with 16 points ahead of Rus, Svk and Irl at 15. (Assuming all remaining games go Macedonia's way.)
If Ireland or Slovakia win their game, Macedonia can still qualify but not win the group.
If either Svk or Irl win, they reach 16 points and need to lose all remaining games. Them losing their game vs Russia leads to Russia reaching 16 points, meaning they need to lose vs the other team of Svk and Irl to remain below 17 points. This leads to a four-way tie with Russia, Slovakia, Ireland and Macedonia all at 16 points. Macedonia would lose this four way tie though. (The results would be Irl/Svk 10p, Rus 9p, Mac 6p.) Lejman ( talk) 03:56, 6 June 2011 (UTC)
Armenia can't become unable to win the group. Even if they lose vs Andorra, Russia defeat Macedonia and Ireland defeat Slovakia, a four way tie where Russia, Slovakia, Ireland and Armenia all end up at 17 points can still occur, leading to Armenia winning the group on better head-to-head record. Lejman ( talk) 04:26, 6 June 2011 (UTC)