Dusted off, and back for another outing.
Recap
WCMC_2022 is back for another round - nothing has really changed since the 2018 iteration so I won’t go over the model again and instead get straight into the predictions.
This initial post is being published before the group stage. It will be progressively expanded after the groups, the round of 16, the quarter and semi finals to fill in the updated predictions based on mid-tournament knock out information.
Tuning The Model in 2022
The input data to WCMC_2022 are:
- A ranked list of countries in the tournament, FIFA rankings, 6 October 2022.
- The 2022 tournament group structure.
- The goal outcome of all 64 WC matches from both 2014 and 2018 (after extra time), as training data.
The model’s free parameter, the goaliness range, was again trained by minimising the sum of the \(\chi^2\) over the total-goals and goal-difference distributions from the training sample with respect to many thousand pseudo-2022-group-stage simulations for each point in the parameter space.
The initial coarse tuning placed the global minima somewhere in the range low: (1.0-2.0), high: (1.1-2.1).
A finer grained tuning pass then identified the optimal span of goaliness to be very near to the diagonal: 1.53 - 1.54. Tighter than in 2018 where the optimised range was 1.52 - 1.79, but also in good agreement with the overall shape of the minimisation surface (something I didn’t think to plot last time).
Here then is the outcome of running WCMC_2022 over 1,000,000 pseudo-tournaments using the trained goaliness, the \(\chi^{2}\) per degree of freedom for the MC prediction with respect to the data for the total goals is 1.6, and for the goal difference it is 0.9. Once the data are available (i.e. the games have been played), the 2022 results will be compared to the training dataset.
Before The Tournament
These predictions are published prior to the start of the tournament.
The Group Stages
England are in Group B this time, here’s the WCMC_2022 probability distributions for the outcome of all games in this group over the pseudo-tournaments. The most likely outcome (most populous bin) is shown in the caption. The most probable outcome is more often than not 1-0 or 1-1, there will of course be outlier results at the tournament but we don’t know when they’ll happen. The most extreme predictions for the most-probable outcome are Saudi Arabia 0 - Argentina 2, in Group C and Cameroon 0 - Brazil 2, in Group G.
Predictions of this nature are made for all of the groups: A, B, C, D, E, F, G and H.
These scores feed into the probability of each team passing their group stage, as shown below. England are given 40% odds on winning their group, and a 25% chance in coming second (either are needed to progress). For Wales it’s more of a coin-flip at 45% stay, 55% go.
Knockout stages
Going into the knockout the teams are plotted according to their FIFA rank, so any effect on the tournament structure to advantage or disadvantage each team will show up as bumps or dips on an otherwise smoothly decreasing probability. The Netherlands is in a particularity easy group and this is highlighted here, they are the only team to have over an 80% predicted chance of passing the group stage despite them being ranked 7th overall in the tournament.
England (ranked 5th) are pretty unlucky, with a probability equal to Denmark (ranked 9th). Senegal also have a way better chance than their rank of 16th would dictate, roughly twice the chance of Iran (ranked 18th) - like with the Netherlands, this boost to Senegal is another Group A effect. Uruguay are also benefiting from the group structure.
After the round of 16 Senegal’s lucky streak ends, but Uruguay’s continues. Belgium (rank 2nd) are by a small margin the team with the highest probability of getting through the round of 16, but it is close. All of the top-9 teams have between a 40-60% chance of progressing beyond this stage.
After the quarter finals things subdivide further, the top-four each have a 30-40% chance, whereas 5th-8th (which includes England) each have closer to a 20-30% chance. Any team ranked 15th (USA) or lower are at a sub-10% chance to make it into the semi finals.
Looking at who will pass the semi-finals, the curve is smoothing out with the favourites, Brazil, top of the pack at 25%. At this stage the lucky outliers are France, Portugal and Uruguay (still!).
And finally, WCMC_2022 predicts… Brazil to be the most likely winners at 15% or roughly 1-in-7 tournaments. Followed by Belgium at 13%, France at 10.5%, Argentina at 9.5%, Portugal at 7.5% and England at 6.5% (or roughly 1-in-15).
Comparing to WCMC_2018 from prior to that tournament’s start back in 2018, Germany were top at 17%, England’s chances were under half as good as 2022 (at 3% in 2018). The eventual winners, France, started out at 5%.
Bonus metric - goals per team. Brazil also tops this at an expected 9 goals.
Most commonly occurring outcomes
An issue I am going to face when trying to quantify the performance of the model will be in contrasting it to the single outcome of the actual tournament.
Each outcome can be encoded in a character sequence which spells out (in order) the winner, the runner-up, the two teams who got knocked out at the quarter finals, the four who got knocked out at the semis and the eight who got knocked out at the round of 16. The teams in each of these sets can be sorted alphabetically such that their internal ordering does not change the sequence (i.e. we don’t want to also be sensitive to if a team came 1st or 2nd in their group).
For example, the very first England win just happens to occur on the second pseudo-tournament, here the outcome is:
- EN/BR/AU_DE/AR_CA_NL_UY/BE_CH_DK_JP_PL_PT_SN_WA
If we collate unique outcomes together then we find that almost every single one of the 1,000,000 pseudo-tournaments generates a unique result. Which really goes to highlight huge number of ways each tournament could potentially unfold. Only 201 times does any individual outcome repeat itself, and then it obviously only repeats itself once.
If we instead restrict ourselves to the eight teams in the quarter finals and beyond, then we find the five most common outcomes to be these listed below (with five different outcomes all tied for fifth place, each with 15/1,000,000 occurrences). We still have 823,427 of the 1,000,000 outcomes being unique.
- Most common outcome #1 with 21 occurrences: BR/PT/AR_FR/BE_EN_HR_NL
- Most common outcome #2 with 18 occurrences: BE/BR/AR_FR/EN_ES_NL_PT
- Most common outcome #3 with 17 occurrences: BR/PT/AR_FR/BE_EN_HR_US
- Most common outcome #4 with 16 occurrences: BR/BE/AR_FR/EN_ES_NL_PT
- Most common outcome #5 with 15 occurrences: BE/ES/DK_FR/BR_NL_SN_UY
- Most common outcome #5 with 15 occurrences: BR/PT/AR_FR/DE_ES_NL_SN
- Most common outcome #5 with 15 occurrences: BR/PT/DK_FR/BE_DE_NL_SN
- Most common outcome #5 with 15 occurrences: BR/PT/DK_FR/BE_EN_ES_NL
- Most common outcome #5 with 15 occurrences: ES/BE/DK_FR/EN_NL_PT_UY
Finally, by restricting to just the four teams in the semi finals and final we get the five most common outcomes to be:
- Most common outcome #1 with 1,226 occurrences: BR/BE/AR_FR
- Most common outcome #2 with 1,169 occurrences: BR/BE/DK_FR
- Most common outcome #3 with 1,108 occurrences: BE/BR/AR_FR
- Most common outcome #4 with 1,089 occurrences: BE/BR/DK_FR
- Most common outcome #5 with 1,018 occurrences: BR/PT/DK_FR
and now ‘only’ 23,035 outcomes are unique within the 1,000,000 pseudo-tournaments.
After the Group Stages
Most probable outcomes for the Round of 16 (excluding penalties, extra time) come in as: USA 1, Netherlands 1. Australia 0, Argentina 1. England 1, Senegal 1. France 1, Poland 0. Croatia 1, Japan 0. South Korea 0, Brazil 1. Morocco 0, Spain 1. Portugal 1, Switzerland 1.
With the following probabilities for passing the four remaining stages.
Now the modal outcome is BR/ES/AR_FR accounting for 1.17% of all occurrences. The most likely outcome which includes England winning is the 11th most likely overall, it is EN/BR/AR_ES with 0.67% of all outcomes.
Stepping back to include the quarters BR/ES/AR_FR/EN_HR_NL_PT is most likely at 0.25% of all outcomes.
After the Round of 16
Here we have: Brazil 1, Croatia 0, Portugal 1, Morocco 0. Argentina 1, Netherlands 1. France 1, England 1.
Portugal are lucky to be coming up against Morocco at this late stage, the odds have reduced to:
With the modal outcome now BR/FR/AR_PT (no Spain!) at 4.1%, and with England first winning in the 9th most likely outcome - EN/BR/AR_PT (2.1% for this particular outcome).
After the Quarter Finals
Coming to the end with Croatia 1, Argentina 1. France 1, Morocco 0. And around 80% of tournaments expected to finish with France or Argentina winning at this point.
After the Semi Finals
And to finish, Morocco 1, Croatia 1. France 1, Argentina 1.
Source Code
WCMC the World Cup Monte Carlo is written in C++ and uses the ROOT library for plotting.