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Saturday, September 26, 2020

CONMEBOL qualification World Cup 2022 simulations (september 2020)

This week CONMEBOL finally confirmed the plans for their World Cup qualifiers. They will start as expected next month with their 18 match days encompassing qualification. If they play two MD's per FIFA window they will also need the June 2021 window (one week before the start of their postponed Copa America) in order to be able to finish in March 2022. That seems not very desirable  and it remains to be seen if they maybe will follow the UEFA and divert their two June MD's to two other windows in 2021.

Here are the probabilities (in %) of the qualifying schedule for CONMEBOL teams, including the complete Copa America 2021 along the road -generated over 10.000 simulations- with all match results based on ClubElo prediction formula's for goals scored in a match depending on elo home win expectancy.

First the Copa America. This is the first edition in a new format of 2 groups of 6 teams instead of the awkward format of 3 groups of 4 teams. Now simply the group numbers 1 to 4 qualify for the quarter finals. There are again 2 guests, this time Qatar and Australia as the last two Asian Champions.

The group results, ordered by average group position:

To qualify for the quarter finals:

To qualify for the semi finals (in square brackets the probability, given qualification for the quarter finals):

To qualify for the final (in square brackets the probability, given qualification for the semi finals):

To win the Copa America (in square brackets the probability, given qualification for the final):

Then the probabilities to qualify for the World Cup 2022 in Qatar as number one to four in the group or to qualify for the interconfederational play-off as group number 5:

About me:

Software engineer, happily unmarried and non-religious. You won't find me on Twitter or other so called social media. Dutchman, joined the blog in March 2018.


  1. I keep being amazed by the oddity of Colombia being the favorite to win according to the simulations, but we've talked about it in past, so it is what it is :)

    1. Home advantage is key here: the matches in group B are all played in Colombia. And if they end in the top 2 of their group the quarter en semi finals are also in Colombia. And the final is in Barranquilla.
      Plus: Colombia is currently 7th in the elo ranking, 97 elo points behind Brazil, the only CONMEBOL team ranked above them in elo.
      Argentina could have the same advantages in group A and the knock-outs but are a bit further away from Brazil at 9th with 115 points deficit (same as Uruguay).

      You see that in the WC qualifying group with homa and away matches the probabilities for Argentina, Colombia and Uruguay are equal.

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  3. Out of curiosity, what is the Club Elo goals scored formula mathematically? Or is it a proprietary thing?

  4. ClubElo used to have a page explaining their research and also listing the formulaes, so it's certainly in the public domain. But they have removed the page from their site, so I can't direct you to it anymore.
    Another point is that these formulaes are derived on a large resultset from domestic and international CLUB-football. In het meantime I've derived similar formulaes for NT-football where the home field advantage plays a bigger role than in club football. I'm planning to write a comprehensive post about my work soon (before the end of the year) where I will explain the methodology and the resulting formulaes. I will then also start to use my own prediction formulaes in my simulation models.

    The currently used ClubElo formulaes are:
    Hgl is the average number of goals scored by the home team in a match with home team win expectancy We:
    if We < 0.5: Hgl = 0.2 + 1.1 * (We / 0.5) ^ 0.5
    if We >= 0.5: Hgl = 1.69 / (1.12 * (2 - We / 0.5) ^ 0.5 + 0.18)

    Agl is the number of goals scored by the away team in a match with home team win expectancy We:
    if We < 0.8: Agl = -0.96 + 1 / (0.1 + 0.44 * ((We + 0.1) / 0.9) ^ 0.5)
    if We >= 0.8: Agl = 0.72 * ((1 - We) / 0.3) ^ 0.5 + 0.3

    This average number of goals is the only parameter in the probability distribution of the number of goals scored for a team which is Poisson distributed and looks like:
    prob_N = Hgl^N * E^(-Hgl) / N!

    For example:
    the probability to score 2 goals as a home team in a match with We = 0,817
    Hgl = 2,2008 and
    prob_2 = 2,2008^2 * E^(-2,2008) / 2! = 0,2681