Will Groups of 3 Ruin the World Cup?

18 Pages Posted: 20 Jun 2018 Last revised: 3 Jun 2019

See all articles by Julien Guyon

Julien Guyon

Bloomberg L.P.; Columbia University - Department of Mathematics; New York University - Courant Institute of Mathematical Sciences

Date Written: April 21, 2019


In 2026, the FIFA World Cup will for the first time gather 48 men's national teams. It will consist of a group stage made of 16 groups of three, with the best two teams in each group advancing to the knockout stage. Using groups of three raises several fairness issues, including risk of match fixing and schedule imbalance. In this article we examine the risk of collusion. The two teams who play the last game in the group know exactly what results will let them advance to the knockout stage. Suspicion of match fixing occurs when a result qualifies both of them at the expense of the third team of the group, and can seriously tarnish the tournament. We quantify how often this is expected to happen and explain how to build the match schedule so as to minimize the risk of collusion. We also quantify how the risk of collusion depends on competitive balance. Moreover, we show that forbidding draws during the group stage (a rule considered by FIFA) does not eliminate the risk of match fixing, and that surprisingly when draws are forbidden the 3-2-1-0 point system does not do a better job at decreasing the risk of collusion than the 3-0 point system. Finally we describe alternate formats for a 48 team World Cup that would eliminate or strongly decrease the risk of collusion.

Keywords: sports, tournament design, FIFA World Cup, groups of 3, match fixing, collusion, point system

Suggested Citation

Guyon, Julien, Will Groups of 3 Ruin the World Cup? (April 21, 2019). Available at SSRN: https://ssrn.com/abstract=3190779 or http://dx.doi.org/10.2139/ssrn.3190779

Julien Guyon (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Columbia University - Department of Mathematics ( email )

3022 Broadway
New York, NY 10027
United States

New York University - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

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