2018 World Cup: mathematical model analyzes score probabilities
应用数学
13 六月 2018

2018 World Cup: mathematical model analyzes score probabilities

FGV’s School of Applied Mathematics (EMAp) has recently launched a website that renders probability analyses of all matches to be held during the first phase of the tournament, based on goals scored and taken by all of the 222 teams affiliated to FIFA in every match for the last four years, across more than 1 million simulations.

The ball will start rolling in the 2018 World Cup tomorrow, with the opening match between the host Russia and Saudi Arabia. The World Cup is always a special event for Brazilians, when friends and family get together to watch the games and set up the popular sweepstakes. That’s exactly when math can become quite handy to predict scores. FGV’s School of Applied Mathematics (EMAp) has recently launched a website that renders probability analyses of all matches to be held during the first phase of the tournament, based on goals scored and taken by all of the 222 teams affiliated to FIFA in every match for the last four years, across more than 1 million simulations.

Based on this model, EMAp’s researchers drew a comparison between teams and ran simulations of possible scores. The study’s goal is not to predict who will win the World Cup, but it is reasonable to assume that the model’s results are reliable on average. The goal is to take the back-and-forth debate among friends to a whole new level by providing arguments based on numbers.

The study shows that Brazil shouldn’t have any problem making it to the second phase of the World Cup. Neymar, Philippe Coutinho, Marcelo and the rest should win all three starter matches in Group E against Switzerland (1x0), Costa Rica (2x0) and Serbia (2x0). The other tournament favorites should also breeze through the first phase: According to the analysis, Germany, France and Argentina should wrap up the first phase without a single loss. Spain should also come up in first place, but the team will likely reach a draw in its match with Portugal and lead the group with seven points. Combined, the teams selected as the tournament’s favorites have a 64% chance to win the World Cup with no huge upsets.

“This year, the Brazilian national team has a 21% chance of winning the 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.

Moacyr points out that the study caught the attention of students, who put their efforts into helping build the model. For the general public, these types of studies represent a great opportunity to understand how these estimates are made and what each probability represents.

“The model is all about probability. We realize that it won’t get every prediction right. In fact, the model will get more scenarios wrong that right, but the study shows results with no surprises”, said the professor in an interview with FGV Chat.

The study will be updated constantly until the end of the World Cup. All mathematical projections are available for consultation on the website.