There is some confusion over Russia's exit from Euro 2012 in Group A. This isn't surprising as there are different systems for tie-breakers when teams are level on points in the group stages of international football tournaments - one operated by FIFA and the other by UEFA.
Russia have been knocked out because the UEFA system gives priority to the head to head results between the teams equal in the points standings, rather than separating the sides on goal difference in all group games.
So in the case of Russia their 4-1 victory against eventual group winners the Czech Republic, counts for nothing in deciding whether they or the Greeks go through to the next round.
The system operated by UEFA leads to fairly complex calculations and bizarre results regarding who would go through under different scenarios. But the main weakness lies in its essence - in a group stage surely the teams going through should be those who have achieved the best results in all the group games.
With such a limited number of games the best teams, those most deserving to go forward, are more likely to progress if the results in all group matches serve as the main criteria.
The system adopted by FIFA
The system adopted by FIFA will be familiar to football supporters everywhere and is based on the concept of overall goal diffference which is the basis for league football rankings throughout the world.
The ranking of each team in each group will be determined as follows:
a) greatest number of points obtained in all group matches;
b) goal difference in all group matches;
c) greatest number of goals scored in all group matches.
If two or more teams are equal on the basis of the above three criteria, their rankings will be determined as follows:
d) greatest number of points obtained in the group matches between the teams concerned;
e) goal difference resulting from the group matches between the teams concerned;
f) greater number of goals scored in all group matches between the teams concerned;
g) drawing of lots by the FIFA Organising Committee.
8.07 If two or more teams are equal on points on completion of the group matches, the following criteria are applied, in the order given; to determine the rankings:
a) higher number of points obtained in the matches among the teams in question;
b) superior goal difference in the matches among the teams in question (if more than two teams finish equal on points);
c) higher number of goals scored in the matches among the teams in question (if more than two teams finish equal on points);
d) superior goal difference in all the group matches;
e) higher number of goals scored in all the group matches;
f) position in the UEFA national team coefficient ranking system (see Annex I, paragraph 1.2.2);
g) fair play conduct of the teams (final tournament);
h) drawing of lots
Abuse of tie-breaking systems
There have been arguments about how the different tie-breaking systems lead to perceived abuses. One example under UEFA's system was in the 2004 Euros where Sweden and Denmark played to a 2-2 draw, enough to eliminate Italy (who as it turns out would have been eliminated in any case). A famous example of a perceived abuse (never proven) under the FIFA goal-difference system was the 6-0 victory in Argentina v Peru which lead to the elimination of Brazil from the 1978 World Cup.
So both systems can theoretically lead to abuses, but the superiority of the FIFA system lies in its essence in reality, which is to reward the best team overall.
The FIFA system also has the additional benefit that it is likely to reward attacking teams who score goals, rather than defensive-minded teams who may achieve results against the balance of play, based on stubborn defence and counter-attack.