### With the group stage of the men’s soccer World Cup in Qatar now complete, the paths to the final for the remaining 16 teams are clear. ‘Scorecasting’ economists make Brazil the favorites to win the tournament with a probability of 28%, while England’s chance of taking the trophy home is 8.7%.

The first phase of the men’s soccer World Cup has been completed after much drama and excitement. Two of the most favored countries, Belgium and Germany, have already been knocked out of the tournament, and another, Spain, survived a qualifying scare.

Now that the starting 32 teams have been whittled down to 16, it’s a good time to review the forecasts made at the start of the tournament. The removal of some of the biggest teams, along with the default draw structure, means that much more is now known about how the tournament will play out.

The sense of anticipation of events yet to occur drives much of the interest in an event like the World Cup. Research using Google searches for events where the winner is often known before the schedule is complete lends credence to this: once the winner is known, search volumes drop.

How can we make better predictions? Predictions can be as basic as gut instinct, or judgment forecasts, as they are often called in statistical research, or they can be based on established statistical methods.

Bookmakers use statistical models to set odds, for example, while former footballer Chris Sutton on BBC Sport makes critical forecasts. Here we present a simulation-based statistical method for forecasting. We simulated the match results of each of the 64 World Cup matches and looked at what might happen.

Our simulation method consists of extracting a random number from a statistical distribution: a Poisson distribution, known for approximating variables that are counts, such as the number of visits to the doctor, the number of absences in the workplace or the number of goals . The distribution has a mean (average), the expected number of goals a team will score, and a variance, how varied that number is.

The idea is that the generated scores (for example, 3-1, 2-4 or 1-1) are such that, on average, *Look* as real and plausible football results. The most common score in soccer history is a 1-1 draw (around 11% of the hundreds of thousands of matches stored on www.soccerbase.com end 1-1), with a 1-0 home win as the the second most likely place. . But on average, the home team scored 1.7 goals and the away team 1.2, and therefore rounding up, a score of 2-1 is also relatively common (about 9% of all matches).

We model the expected number of goals a team will score depending on how strong they are and how strong their opposition is. We measure how strong the opposition is based on what are called Elo ratings. These have been used to model the results of soccer matches, as well as other sports.

It is a convention to start Elo ratings at 1000 when a team plays their first match and then update after each match based on the team strengths of the two teams involved. The adjustment factor can be made larger (louder ratings) or smaller (less quickly reflecting the changing strengths of teams).

To create these ratings, a conservative adjustment factor of 20 has been used. Spain is the second best team after Brazil, followed by Argentina and France.

Outside of this top four there is a group of European nations: England, Germany, the Netherlands, Belgium and Portugal. With a few exceptions, these ratings are the same as those built by the www.eloratings.net website, which increases the adjustment factor for the biggest matches, up to 60 for World Cup final matches.

When Brazil, with an Elo of 1400, faces Cameroon, which has an Elo of 1130, they are expected to win. In fact, the Elo prediction would be around 0.83, which implies that Brazil has an 83% chance of winning (not taking into account the possibility of a draw), so the loss of Cameroon in the phase of groups in this World Cup was very unexpected. If Brazil faces Spain, the prediction is 0.57 or 57%.

Our simulation method draws random goals for each team according to the strengths of the two playing teams and thus generates complete World Cup scenarios. The results of the group can be inferred from the simulated results and the routes of progression to the later stages. We use a correction for home advantage that is well known in international sports and soccer.

Table 1 lists the chances of each country reaching each knockout stage of the tournament and ultimately winning the competition, as calculated at the start of the tournament. Brazil was almost certain to reach the last 16 (95%), as was Argentina (87%). Belgium (79%) and Germany (71%) are the two most surprising outings of the tournament so far.

#### Table 1: Pre-tournament odds of teams reaching each stage of the 2022 World Cup

Country |
last 16 |
quarterfinalists |
semifinalists |
finalists |
Winners |

Brazil | 95 | 76 | 52 | 38 | 27 |

Spain | 81 | 59 | 3. 4 | 22 | 13 |

Argentina | 87 | 59 | 39 | twenty | eleven |

France | 84 | 55 | 36 | twenty | 10 |

England | 77 | 51 | 28 | 14 | 6 |

Germany | 71 | Four. Five | 24 | 13 | 6 |

Netherlands | 86 | 51 | 27 | 12 | 6 |

Belgium | 79 | 39 | twenty-one | eleven | 5 |

Portugal | 76 | 41 | twenty | 10 | 4 |

Iran | 59 | 33 | fifteen | 6 | two |

Mexico | 58 | 26 | eleven | 4 | 1 |

Croatia | 58 | twenty | 8 | 3 | 1 |

Uruguay | 52 | twenty-one | 8 | 3 | 1 |

South Korea | 54 | twenty-one | 8 | 3 | 1 |

USA | 49 | 25 | eleven | 3 | 1 |

Japan | 38 | 18 | 7 | 3 | 1 |

Denmark | 53 | 22 | 9 | 3 | 1 |

Swiss | fifty | 22 | 8 | 3 | 1 |

Morocco | 46 | 14 | 4 | 1 | |

Australia | 40 | fifteen | 6 | two | |

Senegal | 52 | 19 | 6 | two | |

Poland | 35 | eleven | 4 | 1 | |

Serbian | 3. 4 | 12 | 3 | 1 | |

Tunisia | 24 | 7 | two | ||

Ecuador | 36 | 10 | 3 | 1 | |

Saudi Arabia | twenty-one | 5 | 1 | ||

Cameroon | twenty-one | 6 | 1 | ||

Qatar | 26 | 6 | two | ||

Costa Rica | 10 | 3 | 1 | ||

Welsh | fifteen | 4 | 1 | ||

Ghana | 18 | 3 | 1 | ||

Canada | 17 | 3 | 1 |

Now that the group stages have been completed, we can update these numbers and present the new calculations in Table 2. Here, we have simulated the tournament as of now. A lot of uncertainty is removed now that there are fewer potential winners and each country’s path to the final is much clearer.

#### Table 2: Probability of reaching each stage of the 2022 World Cup, by team in the round of 16

Country |
quarterfinalists |
semifinalists |
finalists |
Winners |

Brazil | 79.9 | 63.7 | 42.7 | 28.0 |

Spain | 75.2 | 49.9 | 29.4 | 15.3 |

France | 77.6 | 46.7 | 25.3 | 12.5 |

Argentina | 75.1 | 46.1 | 23.0 | 12.5 |

England | 71.7 | 37.1 | 18.9 | 8.7 |

Netherlands | 63.4 | 30.8 | 13.7 | 6.7 |

Portugal | 65.5 | 29.2 | 14.4 | 6.0 |

Croatia | 51.0 | 13.5 | 5.2 | 1.8 |

Japan | 49.0 | 12.8 | 5.0 | 1.6 |

USA | 36.6 | 14.1 | 4.2 | 1.6 |

South Korea | 20.1 | 10.0 | 3.8 | 1.3 |

Morocco | 24.8 | 10.1 | 3.5 | 1.1 |

Swiss | 34.5 | 10.8 | 3.6 | 1.0 |

Australia | 24.9 | 9.0 | 2.5 | 0.8 |

Senegal | 28.3 | 9.3 | 2.8 | 0.7 |

Poland | 22.4 | 7.0 | 2.2 | 0.5 |

Despite teams with a combined 16% chance of winning the World Cup being eliminated, and despite knowing how Brazil will reach the final, their probability of winning only changes slightly, at 28% (versus 27). %). Spain also jumps – from 13% to 15%; Argentina from 11% to 12.5%; and France from 10% to 12.5%.

It’s perhaps not entirely surprising that the odds haven’t changed much; after all, none of the four most likely countries came out of their groups unbeaten. Neither team won all three group stage matches, and as such, no team looks unbeatable…yet.

The odds here, with South Korea having a 20% chance of reaching the quarterfinals despite facing the daunting task of playing Brazil, tell us to expect, at the very least, unexpected results in *at least* one in five of the round of 16 matches, therefore around three of them. If anyone from South Korea, Australia, Poland or Morocco wins their matches at this stage, it makes the passage from their quarterfinal opponents, on paper, to the semifinals a bit easier.

### Where can I find more?

Evaluating strange forecasts: the curious case of soccer match scores: a study by James Reade and colleagues.

Going with your gut: the (in)accuracy of forecast revisions in a football score prediction game: another research paper by James Reade and colleagues.

Futbolmetrix Blog: Discussion of football (futbol, calcio, soccer) and numbers.

### Who are the experts on this issue?

Author: James Read

Photo by Rhett Lewis for Unsplash