Mathematics
16 May 2018

# Study analyzes probabilities of national teams winning World Cup

The study shows that Brazil is a favorite to win the 2018 World Cup.

After the draft of players representing Brazil in the World Cup was released, less than a month away from the tournament, this topic has been gaining increasingly more coverage in the news. A mathematical model developed by FGV’s School of Applied Mathematics (EMAp) will cheer up Brazilian fans who want the country’s sixth title. The study shows that Brazil is a favorite to win the 2018 World Cup. To reach that conclusion, the researchers observed the goals scored and conceded in each match of the 207 national teams affiliated to FIFA in the past four years, across more than 1 million simulations.

“This year, the Brazilian national team has a 21% chance of winning the 2018 World Cup. Spain comes next with 13%, followed by the current champion, Germany, with 11%. The figures show that it will be a very balanced tournament”, said EMAp professor Moacyr Alvim, who coordinated the study alongside professor Paulo Cezar Carvalho.

According to the EMAp professor, it was possible to simulate the matches between teams based on attack and defense data from each of them. “It is much more likely that Brazil wins its first match against Switzerland, but there is a low probability that the European team wins. The simulations capture more or less what our common sense tells us about what is typical and what is unexpected. But we know that atypical events are not so rare in soccer”, said Alvim.

Moacyr Alvim points out that the Brazilian national team’s figures could even be a little better. The defeats under former coach Dunga ultimately made Brazil’s odds worse. “However, it is important to note that Brazil was also a favorite in the 2014 World Cup, with a 28% chance of taking the trophy, but the team didn’t win.  That atypical match took place in the semifinals, and we forgot that there was a 72% chance of us not winning the tournament”, said the EMAp professor, who recognizes: “This year, we have a 79% chance of not ranking first”.

1st phase – EMAp’s calculations show the odds in the group stage of the national team under coach Tite. According to them, the Brazilian team should be undefeated, conceding no goals. The results presented are: the first match will have a tight score, 1 to 0 against Switzerland, then 2 to 0 in the match against Costa Rica, and the same score against Serbia.

The full study, with the expected results for the first phase and the odds of all national teams, will be available soon via a special World Cup hotsite.