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

--

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

Only 2 teams can proceed, so the team with the least goal difference will, despite having won 2 out of 3 group matches, be sent home in tears to watch the knockout stage on FOX Sports.

It’s happened before!

1994 — Maradona’s final world cup

The last country to suffer this unhappy fate was Argentina in the 1994 World Cup, led by the controversial legend Diego Maradona. Argentina won their first 2 group matches, and in fact were at the top of the group rankings right up until the dying minutes of their 3rd match.

Source: Google World Cup results

But in a crazy twist of fate, Argentina lost their 3rd group match against Bulgaria in extra time. Maradona did not play in this losing match, as he had been thrown out of the tournament after…

--

--

Russell Lim

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