A sport tournament is replete with incentives. Ideally, incentives promote fair play and the integrity of sport competition. But not always.

In the recent handball World Championship, we witnessed a situation where the tournament design could have played a crucial role in determining the qualifiers to the semifinal. Before the last game of the second group round, Denmark and Norway had 8 points each and Sweden 6 points. The two first teams would qualify to the semifinal. The last game was between Denmark and Sweden. In case of a Swedish win, three teams would have had 8 points and the tiebreaker rule determines that the teams should be ranked according to head-to-head points. However, this rule could not determine the best teams, since Denmark won against Norway 30-26 and later, Norway won against Sweden 30-27. This means that if Sweden won, all the teams would have had 2 points in head-to-head games.

If this happened, the next rule to decide the winner was head-to-head goal difference. Now things became interesting, because if Denmark and Sweden agreed, they could control the outcome. If Sweden beat Denmark with a difference of four goals, Denmark and Sweden would both qualify to the semifinal. Norway would be eliminated. In this situation, Sweden would have had a goal difference of +1, Denmark would have had a goal difference of 0 and Norway would have a goal difference of -1.

Fortunately for the the sport spirit, Denmark beat Sweden and Norway advanced to the next stage.

Disgrace of Gijon

However, fair play is not a given and badly designed tournaments may lead to it’s breach and unforgettable shame. One of the most memorable examples is the “Disgrace of Gijon”. This title was given to the match that took place in the 1982 FIFA World Cup between West Germany and Austria, played in Gijon, Spain. It was the last match of the group stage. The situation was similar to the previously described handball game. A win by one or two goals for West Germany would qualify both teams, and eliminate Algeria. West Germany scored after 10 minutes and after that, none of the teams tried to change the result. Both sides were accused of match-fixing, although FIFA ruled that neither team broke any rules. After the tournament, FIFA decided that the last two games of a group must take place simultaneously.

However, FIFA now plans to extend the World Cup to 48 participating teams, starting from the 2026 FIFA World Cup (if not earlier). To avoid a situation that a team may play more than seven games in a tournament (as it is now), one of the suggestions is to have 16 groups of three teams each. This means that by definition, it is not possible to have simultaneous matches in the last round. Accordingly, the teams who play in the last game will have an advantage of knowing which results may qualify both of them. Let us hope there will be another solution to allocate 48 teams into groups that will satisfy the fair play principles that FIFA seemingly supports.

Barbados vs. Grenada

While the Disgrace of Gijon was bad, harmful tournament designs have had even worse effects, where teams actually try to lose in the purpose of winning. This may sound crazy and not realistic, but it is true. The best example is the 1994 Caribbean Cup qualification match between Barbados and Grenada that took place exactly 25 years ago. None of us would have taken care of this match, was it not for the bizarre situation that the teams wanted to score own goals, which was a pretty rational reaction because the organizers of the tournament had decided that all the games must have a winner. In the case of a draw after 90 minutes, there was an extra time of 30 minutes, and the first goal scored in the extra time not only won the match, but also counted as double.

To qualify for the next stage Barbados needed to win by a margin of at least two goals. However, several minutes before the end of the 90 minutes, the score was only 2-1 in favor of Barbados. What would you do? You will attack and try to score the third goal, right? No! In this situation it was more rational just to score an own goal (which is easy) to force an extra time where you could get the two-goal winning margin by scoring one goal, thanks to the tournament design. This is exactly what Barbados did. They scored an own goal.

However, this is not the end of the story. May be players of Grenada did not take a game theory class, but they also had their strategy. Grenada would qualify by losing or winning by a margin of one goal. Should they try to win or to lose by one goal? They tried both. Half of the Barbados team defended their goal and the other half defended the goal of Grenada. They needed a goal, but it did not matter in which goal! End of story was that the game went into extra time where Barbados scored a golden goal and qualified for the next stage.

These examples emphasize the role of incentives. Badly designed incentives may have an adverse effect on aspects such as efforts and fairness, virtues that are highly valued and has a direct effect on our passion toward sports. So, sports authorities, please think carefully through the tournament design.

If not, you may score an own goal.

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Professor Alex Krumer, HiMolde:

When I was 6 years old, a strange table with many numbers in my father’s newspaper caught my eyes. I tried to understand the meaning of all these different numbers, which seemed to me as an impossible mission, but I did not give up. It turned out to be a usual table from a sport league that described the number of points, goal difference, etc. Since then, different combinatorial structures and rules of tournaments have fascinated me.