There is always a chance that losing a match during a sports tournament such as this year’s World Cup in Brazil could work to a team’s advantage. Dr Marc Pauly from the University of Groningen recently proved his theory in a publication in the journal Social Choice and Welfare.
During the 1982 World Cup in Spain, Germany played Austria in Gijón. With the score at 1-0, both teams had enough points to qualify for the second round and agreed a ‘truce’. They stopped making an effort and the fans had to sit through a disappointing match. To prevent a repeat, FIFA decided that in the future the last matches at the group stage would be played simultaneously. Pauly’s research now shows that even this approach is susceptible to ‘strategic manipulation’: intentionally trying not to win.
The idea behind redesigning a tournament to prevent unsportsmanlike behaviour is entirely understandable. However, the research shows that these solutions will not work as long as there is a group stage whereby the team that finishes second also goes through to the next round. A team’s opponent in the second round depends on whether it comes first or second in the first-round group. The idea is that the winner of a group has an advantage in the next round, as it plays the team that came second in another group. But sometimes, the players would rather play the team that won that group. In a case like this, it could be better to lose a match in your own group. Even then it will not work: If Brazil ends up second, then both Chili and the Netherlands will have an incentive to lose the game if they want to avoid Brazil.
The thing that makes Pauly’s proof unique is his use of a computer to substantiate part of his evidence. Pauly converted the tournament designs and the criteria applying to a tournament into mathematical formulas. He then asked the computer to check which tournament design complied with the various criteria. It turns out that all sports tournaments organized along the same lines as the World Cup in Brazil are susceptible to strategic manipulation.
So does this mean that a sports tournament can never be entirely fair? Absolutely not, says Pauly. But it seems that the way a tournament is organized is closely connected with the question of whether it satisfies our ideas of sportsmanship. This could be the subject of more research in the future. As for the World Cup in Brazil, football fans will simply have to hope that the teams themselves prefer a resounding win to a strategic loss.
Contact: Marc Pauly, researcher and lecturer
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