The French football team, reigning world champions, will meet their opponents on Friday evening in the first round of the World Cup, which will take place from November 21 to December 18 in Qatar.
The draw for the group stage – from 6 p.m. in Doha – will be based on four pots per level: the top seven teams in the FIFA rankings and host country Qatar are placed in pot 1, the next eight in pot 2, etc. Since the 2018 World Cup, FIFA has abandoned geographical pots (a process of which I had pointed out the limits).
Pot 1: Qatar, Brazil, Belgium, France, Argentina, England, Spain, Portugal
Pot 2: Mexico, Denmark, Netherlands, Germany, Switzerland, United States, Croatia, Uruguay
Pot 3: Senegal, Iran, Morocco, Japan, Serbia, Poland, South Korea, Tunisia
Pot 4: Canada, Cameroon, Ecuador, Saudi Arabia, Ghana + the winners of play-offs 1, 2 and 3
Dam 1: (Australia or United Arab Emirates) – Peru
Dam 2: New Zealand – Costa Rica
Play-off 3: (Scotland or Ukraine) – Wales
FIFA maximizes intercontinental matches
Each of the eight groups will consist of one team randomly drawn from each pot. The use of pots by level and the new FIFA ranking calculation method introduced in August 2018, which better reflects the value of the teams, should have guaranteed very balanced groups for the first time this year.
But, since FIFA automatically placed the winners of the June play-offs in Pot 4, teams such as Wales, Peru or Ukraine, which would have been placed in Pot 3 by virtue of their FIFA ranking , virtually end up in pot 4.
This could generate a strong France – Germany – Senegal – Peru group, which despite everything seems less ” deadly “ than the death bands of the past. The presence of Qatar in pot 1 also leaves the door open to a “group of life” of the Qatar – United States – Tunisia – Wales type.
As usual, FIFA maximizes intercontinental matches. Thus, a group cannot contain two teams from the same continent (North America and South America are two distinct continents), with the exception of Europe which has 13 qualifiers: each group must contain at least one and at most two European teams.
This legitimate geographical constraint explains why FIFA used geographical criteria for more than sixty years to form the pots: it then became easy to satisfy the constraint during the draw, but to the detriment of fairness and the balance of groups.
The Blues’ most likely opponent in Pot 2 is Uruguay
If we empty the pots sequentially, from pot 1 to pot 4, to form the groups without paying attention, we risk violating the geographical constraint. As I suggested here, to avoid this, FIFA uses an algorithm of backtracking which places the drawn team in the first eligible group in alphabetical order (group A to group H). This is less obvious than it seems, since you have to go through the tree of possible future draws to make sure that the draw will not end in a dead end.
We can calculate the probabilities of clashes between teams from pots 1 and 2. Since Qatar is automatically placed in group A, since pot 2 does not contain any Asian team, and since placing the first team drawn from pot 2 with the Qatar does not generate any future stalemates, Qatar will be paired with the first team drawn from pot 2.
Each team in pot 2 therefore has a one in eight chance (12.5%) of facing Qatar, hence the first column of the table above. The last line can be deduced from this: Uruguay, which cannot face either Brazil or Argentina, has an 87.5% chance of falling against one of the five European teams in pot 1.
By symmetry (countries from the same continent in the same pot are interchangeable), Uruguay has an 87.5/5 = 17.5% chance of facing each of these five teams.
The most likely opponent of the Blues in pot 2 is therefore Uruguay (17.5%), all other opponents being equally probable (11.8%). There is still an 82.5% chance that France will not fall on Uruguay!
More likely to find an Asian team than an African team
Calculating the probabilities is more complex for pots 3 and 4. I simulated the draw 100,000 times following the official procedure for estimating these probabilities; this is called the “Monte Carlo method”. The sampling error, around 0.3%, due to the fact that only a finite number of draws are simulated, explains the slight fluctuations observed for opponents that are nonetheless interchangeable.
Here are the results for France.
- Deschamps’ men are slightly more likely to run into an Asian side than an African side in Pot 3.
- The Blues are unlikely to fall on Serbia or Poland in pot 3. Indeed, if they fell against one of the five European teams in pot 2 (59% probability), they cannot welcome a third European team , as shown in the first table below. They have even less chance of falling against the European team of pot 4 (Wales, Scotland or Ukraine, 4%), for the same reasons.
- France’s most likely opponent is the winner of the play-off between Peru and the winner of Australia-United Arab Emirates (20%), in pot 4. Ecuador (16.4%) is also a fairly likely opponent for the Blues in pot 4. However, as the last table below shows, if France drew Uruguay in pot 2 (17.5%), they could not fall either on the Ecuador nor on the winner of this play-off, which could be Peru, another South American team.
[insérer graphe CondProb_2022WCdrawFIFA_TUN3_CAN4_EURpot1_NApot2 ici]
Finally, the tables above show how the probabilities will update once the opponents of the Tricolores in pot 2 are known. Note that the winner of the Peru-Australia-United Arab Emirates play-off becomes very probable (over 30%) for the Blues if they fall on Mexico or the United States in Pot 2.