The Mathematical Problem of Organizing a 48-Team World Cup

The end of the 2022 World Cup opens a new chapter in football. From 2026, the number of teams participating in the World Cup will increase to 48 teams .

Many fans and experts are concerned that expanding the number of teams will reduce the quality of the tournament. FIFA, the global governing body of football, said it is considering how to organize the rounds to be as perfect and balanced as possible.

The first issue is deciding which teams will compete. The World Cup is primarily about finding the best teams, but FIFA also sees the tournament as an opportunity to develop the game. This is why Europe only has 13 of the current 32 places, despite having 16 of the world's top 32 teams.

Contrasting options

The 16 additional spots will be primarily intended to increase diversity, giving teams from a wider range of countries a chance to qualify for the World Cup, rather than adding spots for the top teams.

The number of Asian and African teams allowed to participate in the 2026 World Cup will nearly double. Europe will get three more spots, but overall the proportion of European teams will decrease from about 40% to one-third.

Next, FIFA must decide on the format of the tournament to determine the winner of the 48 teams. The fairest solution is a round-robin system, which is often used in national football leagues.

Argentina lost to Saudi Arabia in the group stage, but thanks to the competition format, they still have a chance to "make up for their mistakes" in the following matches. (Photo: Nbcnews).

In this format, each team plays against all the other teams, leading to a final ranking. This is the most fair way to play and shows the team's true strength, but it is not practical for the World Cup, because it would require 48 teams to play 1,128 matches within a month, or 36 matches per day. This way of playing would also eliminate the dramatic final match.

The other extreme, the knockout stage, would require much fewer games. With 32 teams, only 31 games would be needed to determine the champion. But this would waste the time and money of many teams and fans who would come to the tournament to play or watch a single game and have their team eliminated immediately.

Football is a game with many variables, and a weak team can be lucky to win against a strong team, so the knockout format is also the most "lucky". In this format, Argentina will not be able to win the World Cup this year, because they lost their opening match to Saudi Arabia.

Therefore, world championships in most sports have a group stage, with teams arranged into small ranked tournaments, and the teams that finish high in their groups advance to the knockout stages.

FIFA's dilemma

This is also the reason why FIFA is in a difficult position with the number of 48 teams. 32 teams can be divided into 8 groups of 4 teams each, with 2 places in the knockout stage. But with 48 teams, it will be very "tricky" to get to 32 or 16 teams to be able to pair up in the knockout stage .

FIFA plans for the upcoming World Cup to have 16 groups of three teams each. The top two teams from each group will advance to the 32-team knockout round.

But this would make some of the final group stage matches meaningless, after the top two spots have already been decided. Worse, it could lead to collusion, with both teams playing in the final match potentially advancing to the next round with a draw.

Messi and Argentina celebrate their World Cup victory. It is not easy to find a fair format for 48 teams without losing the dramatic final match like the one just happened. (Photo: Reuters).

Another solution could be 12 groups of four teams. The top two teams in each group would advance to the knockout stage, plus the eight best third-placed teams, for a total of 32 teams. However, the choice of the eight 'best' third-placed teams in each group would be controversial, regardless of the metric used.

A more radical approach is the Swiss System, a tournament format used for chess and other board games. After each round, the winning teams play each other and the losing teams play each other, and so on until a final ranking is reached. The unlucky losing team still has a chance to redeem itself and climb higher in its group.

According to a study by Laszlo Csato at Corvinus University in Budapest, this format is the most efficient in ranking teams in a short period of time. Starting in 2024, the Champions League will use a variation of the Swiss System for the group stage, with 16 teams from 36 participating teams competing in a knockout round.

However, in football, using the Swiss System for the group stage rather than the tournament as a whole would make it difficult to ensure that each group has a similar level of difficulty, avoiding teams getting through by playing easy opponents in the group stage. Fans and teams may complain or even be angry about the group draw.

If the Swiss System were used for the entire tournament, fans would miss out on the dramatic final, as the highest-ranked team would be the one that wins consistently throughout the tournament, not depending on a particular match.

Any decision FIFA makes will be awkward, especially given the simplicity of the current format. But there was a time when this was only temporary, and football fans would still enjoy the World Cup no matter what format it took. Fans in countries that are playing in the World Cup for the first time will certainly be excited.