World Cup 2022: Winning 2 out of 3 Group Matches but Failing to Advance?

Unlikely, but mathematically possible… and it’s happened before!

Russell Lim
4 min readNov 22, 2022
Image source: Tasnim News via Wikipedia commons

In the group stage of the world cup, countries are placed in groups of 4 and play one match against each of the 3 other countries in the group. The 2 top ranked teams from each group then proceed to the knockout stage. You would think that winning 2 out of 3 of these group matches would be enough to keep your country safe, right?

Well, actually… no!

First, here’s a little more detail on how the group stage rankings are decided. A win earns 3 points, a draw earns 1 point, and a loss earns no points. If 3 teams have equal points, then goal difference is used to select the top 2 teams. (There are further rules if goal differences are also equal, but this is enough for our purpose.)

Consider what happens if one team loses all 3 matches. This immediately means that the 3 other teams in the group have at least one win. Now, if these 3 teams all win one more match in a “triangle”, they are now ranked equal with 2 wins (6 points) each.

The top 3 teams win 2 matches out of 3

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Russell Lim

I teach high school mathematics in Melbourne, Australia. I like thinking about interesting problems and learning new things.