UEFA Eliminates Russia

The first major upset in Euro 2012 happened on Match Day 3 of Group A when Russia lost 0-1 to Greece and was eliminated.  Under the tie-breaking rule used in European Championships, Greece went through to the quarterfinals as runners-up in Group A, because both teams had 4 points from three games behind Czech Republic's 6 points but Greece ranked above Russia by the head-to-head result. As noted by a few commentators, it would be Russia, instead of Greece, that would have gone through under the tie-breaking rule used in the World Cup, because Russia had +2 goal difference to Greece's 0.  Incidentally, Czech Republic became the first team in the history of European Championships to emerge winners from a 4-team group with a goal difference of -1, as it lost to Russia 1-4 in the opening game.  

After the elimination at the feet of Greece, the Russian press rightfully pointed out that nobody but their own players and coach was to blame for the early exit.  But I was surprised that apparently no analyst or commentator picked up an anomaly in applying the tie-breaking rule of UEFA (Union of European Football Associations) in this case.  Deep in the injury time of the Czech-Republic-Poland game, Jakub Blaszczykowski of Poland had an angled effort on goal that escaped the Czech goalkeeper Petr Cech but was cleared off the line by the defender Michal Kadlec.  Had Poland scored the consolation goal, Czech Republic would have the same 4 points as Russia and Greece.  In the resulting "mini-league" of the three teams, Czech Republic would have been eliminated and Russia would have advanced from the group as winners ahead of Greece due to the superior goal difference.

This can't be a fair way of ranking the teams---the final relative ranking between Russia and Greece changed according to the result of a game that neither team was involved in!   

The anomaly was a direct consequence of UEFA's tie-breaking rule.  Depending on the result of the Czech-Republic-Poland game, the mini-league of the teams with the same 4 points may or may not have included the Czech Republic.  Which way it went affected the relative ranking between Russia and Greece because the two had different results against the Czech Republic.  But this would not have happened under the tie-breaking rule used by FIFA (Federation Internationale de Football Association) in the Word Cup, which first considers the goal difference and goals scored in the entire group stage of the teams tied in points.  Russia would have been ahead of Greece no matter what happened in the Czech-Republic-Poland game.

But many football fans also hate the tie-breaking rule used in the World Cup.  Match Day 3 of Group C offers an illustration.  Going into the last day of the group competition, both Spain and Croatia, with 4 points from defeating Ireland and tying Italy and a goal difference of 4 and 2 respectively, would play each other, while Italy had 2 points and would play Ireland.  Under FIFA's tie-breaking rule, regardless of the result of Spain vs Croatia, Italy would guarantee a quarterfinal berth by beating Ireland 3-0 or more, and the first place finish from Group C and thus avoid meeting Group D winners and a potential semi-final date with Germany, by beating Ireland 5-0 or more.  That would have gotten the reigning European and World champions slightly worried, especially considering that Ireland had an Italian coach.  More to the point, many football enthusiasts would consider the situation fundamentally unfair, as an already eliminated Ireland would be potentially deciding which two of the three teams tied with 5 points would advance from the group. The same people are happy with UEFA's tie-breaking rule, under which the Italy-Ireland result would be irrelevant if Italy, as expected, defeated Ireland.  Indeed, going to Match Day 3, it was the Italians who were worried about another "biscotto," as Catholic brethren Spain and Croatia would have both advanced with a 2-2 or higher scored draw by the number of goals scored in the 3-team mini-league.  

So, the choice between the two tie-breaking rules comes down to which situation is "more" unfair---the relative ranking between Russia and Greece and hence which team would advance could depend on the result of the Czech-Republic-Poland game in Group A, or an already eliminated Ireland could throw the game to Italy and decide which two of three superior teams would advance in Group C?  But before anyone tries to choose the lesser evil between the two, some game theorist should convince us that there is no tie-breaking rule that can escape both.