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Monday, December 10, 2018

2020 UEFA EURO qualification: 10000 simulations (10 december 2018)

The ten qualification groups for EURO 2020 were drawn last week. Now it's possible to simulate the complete match schedule, including the play-offs in March 2020 for the last 4 spots at the EURO's. These play-offs are a second chance for the group winners of the Nations League if they can't qualify directly by finishing first or second in their qualification group.

For each of the four leagues there is one EURO berth to be contested. These are the 16 group winners from the Nations League 2018:
league A: Switzerland, Portugal, Netherlands, England
league B: Bosnia-Herzegovina, Ukraine, Denmark, Sweden
league C: Scotland, Norway, Serbia, Finland
league D: Georgia, FYR Macedonia, Kosovo, Belarus

However, when a group winner qualifies directly their spot in these play-offs goes to the next best ranked, not directly qualified, team in their own league. When there are not enough teams in a league available to fill all empty spots (vacated by directly qualified group winners), best ranked and not directly qualified teams from the overall Nations League ranking can occupy the empty play-off spot. All this under the restriction that a group winner can not compete in a play-off against teams from a higher league.

When the 16 participants for the play-offs are determined (in the order from league D to league A) the four play-off paths are populated in the same order of leagues and under the following conditions:

  • a group winner can not be in the same path as a team from a higher league;
  • when there are 4 or more teams from a league under the participants, a path of 4 of them has to be formed by drawing from all teams of the specific league;
  • there is a special case when host-countries of EURO 2020 are destined to be paired together in a path, when UEFA will perform a seeded draw to separate these teams.

All in all a somewhat complex procedure to determine the composition of the four play-off paths. 
Each of the four play-off paths consists of two (one-off) semi-finals and a final with the winner qualified for EURO 2020.

Here are the probabilities (in %) -generated over 10.000 simulations- for each UEFA team to qualify for EURO 2020, directly (Qdirect) or via the play-offs (po-semi, po-final and po-win). In column Qtot the total probability to qualify for EURO 2020 as the sum of Qdirect and po-win. Teams are ordered by this last column.

team   Qdirect  po-semi   po-final    po-win        Qtot
France 99,08 0,92 0,77 0,57 99,65
Belgium 97,34 2,66 2,23 1,67 99,01
Spain 94,20 5,79 4,65 3,31 97,51
Germany 90,79 8,95 6,90 4,93 95,72
Portugal 86,84 13,16 10,02 6,34 93,18
England 87,40 12,60 8,42 4,85 92,25
Croatia 83,85 15,91 11,48 7,33 91,18
Netherlands 83,68 16,32 11,86 7,23 90,91
Denmark 78,78 21,22 15,02 10,46 89,24
Italy 81,33 18,52 11,79 6,19 87,52
Switzerland 77,26 22,74 16,66 9,39 86,65
Poland 75,82 23,86 11,84 4,98 80,80
Serbia 52,44 47,56 34,08 23,04 75,48
Sweden 58,94 41,06 25,11 15,36 74,30
Bosnia-Herzegovina 63,13 36,87 21,60 9,61 72,74
Austria 66,66 33,24 13,60 5,37 72,03
Ukraine 58,51 41,49 25,52 13,17 71,68
Wales 54,26 45,31 26,03 13,92 68,18
Russia 56,55 43,43 22,30 10,70 67,25
Scotland 42,04 57,96 40,54 21,96 64,00
Slovakia 47,55 50,02 25,92 13,52 61,07
Turkey 50,76 44,85 18,63 8,96 59,72
Czech Republic 42,44 55,99 20,07 7,32 49,76
Bulgaria 35,44 63,45 27,02 12,67 48,11
Republic of Ireland 35,79 54,76 24,03 11,35 47,14
FYR Macedonia 18,64 81,36 53,95 27,12 45,76
Iceland 35,36 62,23 25,64 8,96 44,32
Georgia 8,17 91,83 55,43 30,68 38,85
Finland 23,78 76,22 30,79 13,52 37,30
Romania 31,36 16,43 8,49 5,32 36,68
Norway 15,28 84,72 43,30 18,70 33,98
Belarus 4,52 95,48 47,68 26,59 31,11
Greece 28,02 2,78 1,31 0,74 28,76
Montenegro 28,36 0,16 0,08 0,02 28,38
Northern Ireland 18,53 57,76 19,95 7,09 25,62
Slovenia 24,16 0,00 0,00 0,00 24,16
Hungary 12,78 47,46 15,79 6,34 19,12
Kosovo 6,36 93,64 32,87 12,48 18,84
Israel 13,12 72,78 18,23 5,01 18,13
Albania 14,15 0,80 0,33 0,10 14,25
Armenia 3,67 4,37 1,79 0,86 4,53
Luxembourg 1,25 32,83 8,16 2,25 3,50
Cyprus 3,01 0,02 0,00 0,00 3,01
Estonia 2,48 0,00 0,00 0,00 2,48
Latvia 1,60 0,00 0,00 0,00 1,60
Azerbaijan 1,56 0,44 0,10 0,02 1,58
Kazakhstan 1,06 0,05 0,02 0,00 1,06
Lithuania 0,96 0,00 0,00 0,00 0,96
Moldova 0,64 0,00 0,00 0,00 0,64
Faroe Islands 0,21 0,00 0,00 0,00 0,21
Liechtenstein 0,07 0,00 0,00 0,00 0,07
Malta 0,01 0,00 0,00 0,00 0,01
Andorra 0,01 0,00 0,00 0,00 0,01
Gibraltar 0,00 0,00 0,00 0,00 0,00
San Marino 0,00 0,00 0,00 0,00 0,00

The usual suspects top this list, I would say of course :) 
Great probabilities to qualify for their first EURO for the established teams in the league D play-off: Georgia, FYR Macedonia and Belarus. Kosovo has to pull off a miracle though.
I will keep track of the developments in these qualification probabilities after each pair of qualifiers matchdays next year.

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. Ed, can you give us the currently most probable play-off semi-final pairs in all four leagues?

    1. Hi nogomet, here is a full matrix of all pairs for both the semi finals and the finals:

    2. Hm... How can Iceland have a 22.76% chance of playing in League C play-offs? In fact, all League A teams have a certain probability of playing in League B and League C play-offs. How can that be?

    3. It's not being in league C playoffs, but playing a team from league C.
      In fact there is no guarantee that there will be a seperate playoff for each league (it is guaranteed only if a NL group winner does not quaify from that league)

    4. To elaborate: there were 12 teams in League A. In order for a play-off consisting only of League A teams to be formed, no more than 8 of them should qualify directly. But given the strength of the League A teams, it's likely that at least 9 of them will qualify directly, so the remaining spots in the League A play-offs will be filled by teams from League B.

      But bear in mind that UNL group winners cannot play play-offs against teams from a higher league. So, if in League B there are too few teams that neither won their UNL group nor qualified directly, the remaining spots in the League A play-offs will have to be filled by League C teams.

    5. That is understood. But still, I'm looking for the answer what are the most probable play-off semi-final pairs per league at the moment? I cannot find anywhere the static predictions that would say, e.g. currently the most likely League A play-offs would be: Iceland - Slovakia, Poland - Bulgaria. League B play-offs: Northern Ireland - Austria, Ireland - Israel. And so on all the way to League D.

    6. As I said, it is not even guaranteed that there would be a playoff for each league. If for example exactly 8 teams from leagues A and B would qualify, the other 8 would be mixed in a seeded draw among all of them.
      In the matrix you could see each pairing, it covers all possible options (and the host of the semi finals is the higher ranked in NL overall rankings)

    7. If there are 4 non-qualified teams from League A and 4 non-qualified teams from League B - aren't teams from League A supposed to play together, and teams from League B also together?

      BTW, can you give me the currently projected semi-final parings for all 4 play-off paths?

    8. "If there are 4 non-qualified teams from League A and 4 non-qualified teams from League B - aren't teams from League A supposed to play together, and teams from League B also together?"

      The answer is no, only a NL group winner is guaranteed to play against teams from its league or a lower one.

    9. I can calculate the specific 8 pair combination that is the most likely, but it is very sensitive to small changes (1 team change could change every pairing), and has a lower than 1% chance of happening exactly like that, so I see no point in that...

    10. Amir, there is also the condition that if there are 4 or more teams from a league participating in the play-offs, a play-off path of four of those teams must be formed. In the case of more than 4 teams from a league UEFA performs a draw among all the play-off teams from the specific league to populate the specific play-off path.
      I think nogomet is right in the described example.

    11. You right Ed, I forgot about this rule, so change my example to 3 teams from league A and 3 from league B (none of them group winner) not qualifying directly

    12. Top 5 match-ups in the semi-finals of each play-off path (playing home and away or vice versa is summed). Generated over 10.000 simulations.

      league A

      Iceland - Poland 2,86%
      Iceland - Russia 2,20%
      Iceland - Israel 2,01%
      Iceland - Czech Republic 1,94%
      Iceland - Bulgaria 1,94%

      league B

      Northern Ireland - Bosnia-Herzegovina 4,97%
      Northern Ireland - Ukraine 4,38%
      Republic of Ireland - Bosnia-Herzegovina 3,37%
      Republic of Ireland - Ukraine 3,03%
      Ukraine - Sweden 2,62%

      league C

      Serbia - Norway 11,68%
      Norway - Finland 9,91%
      Scotland - Finland 8,86%
      Serbia - Finland 8,05%
      Norway - Israel 7,65%

      league D

      Kosovo - FYR Macedonia 34,91%
      Georgia - Belarus 33,38%
      Georgia - Luxembourg 11,36%
      Kosovo - Belarus 10,74%
      Luxembourg - FYR Macedonia 3,14%

    13. What do you mean playing home and away is summed? In each matchup, the higher ranked team will always play at home...

    14. You're right Amir, but I was too lazy to check that and just summed both halves of the matrix. I just haven't paid attention to the home and away playing team in each match-up. That's what I wanted to express.

      I also just discovered that the presented percentages for the matchups should be doubled. I thought yesterday that all matchups in a path had to sum to 100% but of course it concerns TWO semi-finals in each path so the division by two was incorrect.
      So f.i. Georgia - Belarus has a 66,76% probability.

    15. Thanks, Ed! Still not quite what I was asking for, but it's a start. :)

      Maybe someone else can calculate what the most proabable semi-final pairs and predicted play-off winners are at the moment, provided that most probable teams qualify via regular qualifiers.

    16. I'm talking about the static predictions, where we assign a 100% probability that the two teams with the highest probability of qualifying in each qualifying group indeed qualify.

    17. Although it's not what you asked exactly (which was: Ed, can you give us the currently most probable play-off semi-final pairs in all four leagues? See above :D ) I understand your question better now. Taking per group the top two with highest probability to qualify directly out of the equation, the following 8 semi-finals in the 4 play-off paths will remain:

      League D (4 group-winners)
      Georgia - Belarus
      FYR Macedonia - Kosovo

      League C (4 group-winners)
      Scotland - Finland
      Norway - Serbia

      Those were the two easy paths to form :)

      Then there remains Iceland (A), Slovakia, Republic of Ireland and Northern Ireland (B) and Bulgaria, Israel, Hungary and Romania (C).
      As there are 4 teams from C they must form a path together, and the remaining teams will form the path for league A:

      League 'B' (actually C)
      Bulgaria - Romania
      Israel - Hungary

      League A (mostly B though)
      Iceland - Northern Ireland
      Slovakia - Republic of Ireland

      No draws required to form these paths.

      Resulting qualifiers for EURO 2020 based on current probabilities: Georgia, Serbia, Bulgaria, Slovakia.

    18. Yes, that's it! Sorry for not being clear enough. :)

      Is it too much to ask that you include these static projections after each update in the main post? I think it provides a clearer picture of what the most probable final outcome is.

    19. This comment has been removed by the author.

    20. @Ed, it is not correct that a draw will not be needed (having group RU having easier path is exactly what UEFA tried avoiding with the complicated rules it set up).
      League C group winners will play against each other as you said, but Bulgaria, Romania, Israel, Hungary, Iceland, Northern Ireland, Slovakia, Republic of Ireland will all be seeded in 4 pots with 2 teams each and be drawn into 2 paths.

    21. Maybe that's what confused you:
      "If four or more teams from a league enter the play-offs, a path with four teams from the league in question must be formed."

      That doesn't mean that if 8 teams from a league are in the PO, 2 paths of these teams must be formed.

    22. Amir, it's all about art 16.03 from the EURO 2020 regulations:
      The UEFA administration conducts a draw to allocate teams to the different playoffs path, starting with UEFA Nations League D, subject to the following conditions:
      a. A group winner cannot form a path with a team from a higher-ranked league in the overall UEFA Nations League rankings.
      b. If four or more teams from a league enter the play-offs, a path with four teams from the league in question must be formed.
      c. Additional conditions may be applied, subject to approval by the UEFA Executive Committee, including seeding principles and the possibility of final tournament host associations having to be drawn into different paths.

      In this specific case the teams participating in the play-offs come from leagues:
      A: 1
      B: 3
      C: 8
      D: 4

      I interpret b) as I described: there are 4 teams from C left (after path D and C were formed), so they should be put together in one path.
      You argue that there is already one path formed with teams from league C and that the rest of the league C teams land in a seeded draw together with the A and B teams.
      I have seen sofar one example in an official UEFA document which comes closest to this case, but in that example there were 2 from A, 3 from B and 3 from C remaining. And in that case indeed a seeded draw was performed over all 8 teams to form the paths for A and B.

      So for now, as far as I'm concerned, it remains unclear how UEFA is going to proceed in this specific case with 1 A, 3 B's and 4 C's remaining. Could be what I assumed, could be what you assumed :)

    23. These rules have to be applied in the order from path D to A, so for the composition of each path these 3 conditions should be applied again, given the situation (regarding the remaining teams and the leagues they are from) at the moment the specific path is formed.

    24. This comment has been removed by the author.

    25. Even if you are right, which is very possible, After reading it again I believe a seeded draw would take place to determine how to divide these 8 league C teams into 2 paths.

    26. If Serbia would qualify directly instead of Ukraine for example, then surely all other group C winners would play the same playoff path, to avoid playing team from a better league. That's what I meant earlier that the predictions are not stable... One small change changes a lot

    27. That's right Amir, I think I can agree with your 1:10 PM post :)
      There should indeed be a seeded draw between the 8 C-teams with 4 pots of two teams. Place the teams in order of their league C ranking in the pots. The first two pots contain the 4 group-winners from C and the last two pots contain the four remaining C-teams. First team drawn from each pot goes to path C, the other team from the pot goes to path B. In that way it is assured that the two group-winners in each path play in separate semi-finals against a non group-winner. The fairest solution indeed.

  2. Is the simulation based on Elo or something else? It puzzles me why the Qdirect probabilities don't line up with the Elo ranking. For example Serbia is ahead of Ukraine in Elo, they're in the same group, but Ukraine is more likely to qualify directly. The same happens with Netherlands / Germany, Switzerland / Denmark, Austria / Poland, Israel / Macedonia and Finland / Greece, at least. Additionally, Israel and Slovenia are tied on Elo but Slovenia is 11 %-points more likely to qualify directly?

    I'd get it if it was a tiny difference one way in Elo and a tiny difference the other way in the simulation, that can happen, but some of the differences are sizeable.

    1. Perhaps the fixture schedule is to blame. Serbia start with a bye followed by two toughest away games in their opening three rounds - Portugal and Ukraine. By round four they might be behind Ukraine on Elo points, which is what could give Ukraine the projected edge over them.

  3. Timoteus, the result of each scheduled match is calculated with ClubElo's probability distribution functions for goals scored for each team in the match. These functions are dependent on the win-expectancy of the home team according to elo at the moment the match is played.
    So nogomet is right, the order of matches in a group according to the match schedule influences the home-team win expectancy of the next match a team plays.
    Generally the qualification probabilites should follow the elo-ranking, but small distortions are always possible, because I work with probability distribution functions.
    After all that's the reason why a simulation gives insight in possibilities instead of just predicting the group-standings based on the elo-ranking.

  4. I ran 100K simulations without changimg the Elo between the matches after each simulated result, and therefor my simulations follow Elo more closely: