UEFA versus FIFA
A RWTH doctoral candidate investigated the regulations of the Union of European Football Associations, UEFA, and the Federation of International Football Associations, FIFA, in a research paper – with surprising results.
Many football fans find it exciting that near the end of the group phase during world and European championships, a team's own game is not the only thing that counts, but rather the results of other matches. Other people feel this is a great injustice.
Yannick Berker, doctoral candidate at the Institute of Experimental Molecular Imaging at RWTH posed the question: Should a game between two football teams influence the order of two other teams? Berker took up this question in a research project – and found surprising results. There are questionable situations in about ten percent of the groups, if one applies UEFA regulations to the final rounds of the European Championship. When applying the corresponding FIFA regulations, which are used during the final rounds of the World Championship, this number sinks to less than 0.1 percent.
Coincidence or System?
The reason for the investigations was the events in Group A during the final round of the UEFA EURO 2012. During the halftime of the last game day, Russia was listed in live league tables as the first in the group ahead of Greece, qualifying for the final round. The Czech Republic and Poland would have to go home. However this situation was extremely close, and the single goal that the Czech Republic made against Poland during the second half turned everything upside down. Russia was suddenly behind Greece in third place and was eliminated from the championship: Greece and Russia switched places, without another goal being made during a game between them. Berker calls this "non-autonomous relative ranking", because the order of both teams was influenced by a game, in which neither participated.
He investigated a hypothesis claiming that the championship mode, or rather the regulations have a decisive influence in the event that teams have the same number of points. He simultaneously wanted to assess how often these situations can be realistically expected. "A mathematical approach would have been a lot of work. For this reason I used a computer to roll millions of game results, summarized them into final tables, and searched them for traces of non-autonomous relative ranking," he explained.
He primarily found something when throwing dice for the European Championships, namely in ten percent of the groups. He was also able to confirm that the mode hat a deciding percentage: According to UEFA regulations, the direct comparison between two teams carries more weight than the difference in goals. The FIFA regulations for the World Championships are the exact opposite.
Extensive Consequences for Sports Competitions
Discussions about the mode of football competitions are not new. However, for the first time, there are tangible arguments for one of the two ruling varieties. Relationships in social choice theory prove that support for "autonomous relative ranking" isn't made up out of thin air, which Berker also illustrates in his paper.
The doctoral candidate prefers the FIFA regulations. "Even if they aren't perfect, they are better at decisive moments – additionally, I find them much more intuitive." Through their introduction at the European Championship, the manipulability of final tables, such as through game fixing, can be reduced. This is not an unimportant consequence for sports betting.
Work in Medical Imaging
For Berker, football fan and scientist, two worlds collide in such cases: One of passionate regular discussions and one of tangible data and facts. "It can be exciting sometimes to combine both." The paper offered a great deal of interesting conversation material for his colleagues in the work group "Physics of Molecuar Imaging Systems,," headed by Univ.-Prof. Dr.-Ing. Volkmar Schulz. Normally the researchers focus on the integration of two medical imaging modalities, magnetic resonance tomography, MRT, and positron emissions tomography, PET, as well as magnetic nanoparticle imaging, MPI.