Game theory in practice: scheduling the FIFA World Cup group stage

The 2010 World Cup is on and occupying more of my time than I’d like to admit.

The first part is my favorite segment of the tournament. There are always quality matches, and every game affects a teams chance to advance.

In case you’re unfamiliar, the first part is known as the group stage. There are four teams in each group that play each other in a round robin tournament. A team gets three points for a win, one point for a draw, and no points for a loss. The top two teams advance past the group stage and the bracket continues with single-elimination games.

The most exciting part is the final day of the group coverage. All four teams in the group play simultaneously and each team cares not only about its performance but also the result of the other match which can affect their chances of advancing. Often a team can celebrate even in loss. In 2002 the U.S. squad lost its match to Poland but ended up advancing anyway since South Korea beat the favored Portugal squad.

And yet, it was not always this way.

Through 1982 the final group stage matches were not played simultaneously and they were played sequentially. Certain matches happened first and that gave some teams perverse incentives to perform. Someone was going to game the rules and make an embarrassment of the World Cup.

An infamous example

That someone was the West Germany squad. The apparent match-fixing is described on Wikipedia:

A more recent example occurred in the 1982 FIFA World Cup, West Germany played Austria in the last match of group B. A West German victory by 1 or 2 goals would result in both teams advancing; any less and Germany was out; any more and Austria was out (and replaced by Algeria, who had just beaten Chile). West Germany attacked hard and scored after 10 minutes. Afterwards, the players then proceeded to just kick the ball around aimlessly for the remainder of the match. Algerian supporters were so angered that they waved banknotes at the players, while a German fan burned his German flag in disgust. By the second half, the ARD commentator Eberhard Stanjek refused any further comment on the game, while the Austrian television commentator Robert Seeger advised viewers to switch off their sets.

Highlights of the match

Someone uploaded a video with highlights of the match so you can see how West Germany gave a poor effort after the first goal:

Link to Youtube video

Even the commentator was disgusted on the spot. Here’s a quote from the video:

Players on both teams made little attempt to attack, or shoot, or tackle, and indeed there wasn’t a single efforted goal. The crowd, not surprisingly, reacted angrily, shouting “surrender” and “cowards”…

It is difficult to prove that 22 footballers weren’t trying, or that these two countries might have gotten together and decided that a one-nil scoreline was in their best interest for both of them, but that is certainly the way it looked.

And it is difficult to imagine that FIFA won’t do something to stamp out the memory of an afternoon that was an insult to the crowd and an embarrassment to football.

FIFA takes action

FIFA saw a bad situation and realized it had to take drastic action.

Rather than tweaking some minor rule or implementing an unenforceable penalty on bad play, it decided used the powerful tactic of changing the game.

FIFA scheduled the tournament’s last matches of group play so that all teams played simultaneously. And thus we have our current format which tries to preserve fairness and leads to some fantastic soccer games.