Euro 2020 group stage ... (1) What's the highest number of pts a team can have and still fail to progress? & (2) ...

[iancrumpy]

If you were initially attracted to this thread because of the "Euro 2020" in the subject, but you really have no interest in Mathematics, then I apologise for taking up about 20 seconds of your time.

I also apologise for starting a thread that has absolutely nothing to do with life in the TR of NC. I think Soner will forgive me for it though.

Now down to the questions:
(1) What's the highest number of points a team can have in the group stage and yet still fail to progress to the knock-out stage?
(2) What's the least number of points a team can have and yet still go through?

For those those not interested in the footy, but who maybe like a challenge, let me tell you a little about Euro 2020:
- there are 24 teams in 6 groups of 4
- 1st and 2nd from each group go through, but also "the best four 3rd-place teams".
- there are 3 points for a win and 1 point for a draw
- the first of the criteria used for deciding which team progresses is of course points
- then the greatest goal difference is used

There are of course other criteria used by UEFA, but those are not relevant for these two questions.

For both of these answers it would require scorelines, that though quite likely individually, in a series are incredibly unlikely. However, as it stands at the moment, both of the scenarios required for the two answers could happen in the group stage. But, and here's a clue, one of the answers will be impossible if there's another draw today.

[EnjoyingTheSun]

This is the problem with these now bloated tournaments. The tournament lasts for a month and the majority of that month is spent losing 8 teams before we get down to the last 16 when we ask the teams to play 4 games in a little over a week.

As to the question I've known teams go out with 3 points and go through with 2 points.
From a mathematical point of view as the points given out per group can vary from a maximum of 18 to a minimum of 12 then it is possible that a team could score 6 points (eg 2 wins and a loss) and not go through if all groups ended up with 3 teams gaining 6 points each. Then it would go down to goal difference I believe and if you had won your 2 games 1-0 each but lost your other game 6-0 then you are probably going home.

So my answer is you can qualify with as little as 2 points based on empirical knowledge and technically get knocked out with 6 which has never happened and will never happen imo

[iancrumpy]

As to the question I've known teams go out with 3 points and go through with 2 points but from a mathematical point of view I'll try and give it some thought

Yep, you'll need to give a bit more thought on both of those.

[EnjoyingTheSun]

Yep, you'll need to give a bit more thought on both of those.

I actually edited my post and came up with "my answer is you can qualify with as little as 2 points based on empirical knowledge and technically get knocked out with 6 which has never happened and will never happen imo"
So 6 is possible to get knocked out but I'd be amazed if anyone can qualify with less than 2 points

[EnjoyingTheSun]

OK full answer is as follows;

There are 4 groups of 3.

Each team will play the others in the group once making 6 games in total, 3 for each team.

3 points are allocated for a win but only 1 for a draw so we have games where 3 or 2 points may be allocated.

So it is possible that all games produce a result, eg no draws in which can the group will have a total of 6 wins and 6 losses and so produces a maximum of 18 points.

On the other side of the coin it is possible that every game in the group ends in a draw so each team will end up with a total of 3 points so the group produces a maximum of 12 points.

So if all the groups had the following results;
Team A beats team D and team B but loses to team C
Team B beats team D and team C but loses to team A
Team C beats team D and team A but loses to team B
Then the table will have teams A,B and C on 6 points and team D on no points.

So it will all depend on goal difference to decide the order of teams as in how many they won their matches by and how many they lost their match by.

So you would have teams go out on 6 points depending on goal difference.

However if all the teams had these following results.
Team A draws with team B and team C but beats team D
Team B draws with team A and team D but beats team C
Team C and D draw in their game

Then you have teams A and B topping the table with 5 points and teams C and D third and fourth with 2 points and it will again come down to goal difference

So you will have teams going through with 2 points and without actually winning a game going through on goal difference

[iancrumpy]

I actually edited my post and came up with "a team could technically get knocked out with 6 which has never happened and will never happen imo"

Yeah, it would be virtually impossible, but 6 is indeed the answer, so well done! - If five of the groups were to finish with 3 teams having 6 pts (with of course one team in each of those 5 groups having zero points), then the team to go out would be the one team (out of those fifteen 6-pointer teams) that has the worst goal difference or, if that doesn't sort them out, the least goals scored, or failing that, the worst disciplinary record in the tournament. By the way, in this scenario, it is actually possible, in the group not considered thus far, for 1st and 2nd to go through both with less than 6 points.

You might want though want to rethink your answer to the 2nd question.

[EnjoyingTheSun]

Yeah, it would be virtually impossible, but 6 is indeed the answer, so well done! - If five of the groups were to finish with 3 teams having 6 pts (with of course one team in each of those 5 groups having zero points), then the team to go out would be the one team (out of those fifteen 6-pointer teams) that has the worst goal difference or, if that doesn't sort them out, the least goals scored, or failing that, the worst disciplinary record in the tournament. By the way, in this scenario, it is actually possible, in the group not considered thus far, for 1st and 2nd to go through both with less than 6 points.

You might want though want to rethink your answer to the 2nd question.

Team A draws with team B
Beats team C & D
Team B draws with team A and beats C & D
Teams C & D both lose to teams A & B and draw with each other so both end up with 1 point each so it comes down to goal difference.

I think we can agree it is virtually impossible to get knocked out with 6 points but if anyone ever manages it it’s almost certainly going to be Scotland!!

[iancrumpy]

Team A draws with team B
Beats team C & D
Team B draws with team A and beats C & D
Teams C & D both lose to teams A & B and draw with each other so both end up with 1 point each so it comes down to goal difference.

Well done ETS. Yes a team could in theory go through on just 1 point.
To sum it up, it would take just three groups to finish as;
1st : 9 pts
2nd : 6 pts
3rd : 1 pt
4th : 1 pt
or as in the example given by ETS;
1st : 7 pts
2nd : 7 pts
3rd : 1 pt
4th : 1 pt
Unbelievably one of the three 3rd-placed teams would have the right to go through ... with just 1 point.

[iancrumpy]

If five of the groups were to finish with 3 teams having 6 pts, then the team to go out would be the one team (out of those fifteen 6-pointer teams) that has the worst goal difference or, if that doesn't sort them out, the least goals scored, or failing that, the worst disciplinary record in the tournament.

The answer to the first question is indeed 6 pts, but the method I used there isn't quite right. Firstly they would decide the five 3rd-placed teams using the criteria given. Then they would use the same criteria to determine which of those five 3rd-place teams should be eliminated ... it would though come down to the same team in the end.

[EnjoyingTheSun]

If five of the groups were to finish with 3 teams having 6 pts, then the team to go out would be the one team (out of those fifteen 6-pointer teams) that has the worst goal difference or, if that doesn't sort them out, the least goals scored, or failing that, the worst disciplinary record in the tournament.

The answer to the first question is indeed 6 pts, but the method I used there isn't quite right. Firstly they would decide the five 3rd-placed teams using the criteria given. Then they would use the same criteria to determine which of those five 3rd-place teams should be eliminated ... it would though come down to the same team in the end.

I remember Uruguay going through to the second round in 1986 with only 2 points. They drew 1-1 with Germany, lost 6-1 to Denmark and then kicked their way to a 0-0 draw with Scotland.
So they got into the second round with a goal difference of minus 5 and after having 2 players sent off and 6 booked. Hungary went home with 2 points actually having won a game. This was back in the days of 2 points for a win.
You have to question a system that let's a team like Uruguay playing like that through.

That said, In 1982 before the best third place nonsense Italy got through the first round and went on to win the whole thing without winning a game in the first round whereas Algeria went home having won 2 games.

[iancrumpy]

the best third place nonsense

UEFA doesn't have much choice ... seeing as they don't have 16 or 32 teams. Here's a format though with 24 teams that you might like - 8 groups of 3 ... only the winners progress to the knock-out stage, which would be the quarter finals.
(1) It would halve the number of group-stage matches, which you felt made the whole tournament somewhat "bloated"
(2) It would almost certainly stop teams playing for a draw ... as, using your example, Uruguay did in 1986.
(3) It would still allow all the teams to play at least two matches in the tournament.

By the way, your memory of such tournaments is impressive.

[EnjoyingTheSun]

UEFA doesn't have much choice ... seeing as they don't have 16 or 32 teams. Here's a format though with 24 teams that you might like - 8 groups of 3 ... only the winners progress to the knock-out stage, which would be the quarter finals.
(1) It would halve the number of group-stage matches, which you felt made the whole tournament somewhat "bloated"
(2) It would almost certainly stop teams playing for a draw ... as, using your example, Uruguay did in 1986.
(3) It would still allow all the teams to play at least two matches in the tournament.

Well they have 55 teams which they have wheedled down to 24 with 2 years of qualifying games!
So I guess they can amend the qualifying groups to give us 16 or 32.

The problem is political and dates back to Joao Havelange and FIFA in the early 70s.
Football up to then had pretty much ignored any other associations bar Europe and South America, Africa for example wasn't even allowed a representative in the 66 World Cup.
Anyhow Havelange wanted to get control of FIFA and realised that if he could appeal to the associations in Africa, Asia and Central America etc then he could gain control. EG Qatar doesn't have much of a football pedigree but their vote counts just as much as say Italy's.
So if he expanded the Word Cup places and offered more places to the lesser nations then he'd be elected to run FIFA.
So we went from having 16 teams in the World Cup in 1978 to the 32 we now have.
I'm guessing the same tomfoolery goes on with UEFA. North Macedonia??
From one point of view it has made the game more global, without Havelange I doubt the likes of South Korea or South Africa would have hosted world cups or the likes of Senegal, Cameroon and Ghana made such an impact but it does give you a hell of a lot of meaningless games.
The other problem with straight knock out is the bigger countries are one bad game away from going out very early so like the champions league they get a couple of bites of the cherry and it isn't sh%t or bust.
Lessens the excitement but gives the marketing men the final they want.

By the way, your memory of such tournaments is impressive.

A wrecked memory prompted by google.

[EnjoyingTheSun]

(2) It would almost certainly stop teams playing for a draw ... as, using your example, Uruguay did in 1986.

Not 100% sure it would tbh. In theory yes but by the same token any team losing would certainly go home.

The other problem is;
Team A plays team B and beats them.
Then what?
Team B is now playing team C in a very important game to the other countries which means zero to them because they are almost certainly going home. So now if they put out the reserves and/or don't try then team C will win easily and would probably have a goal difference advantage over team A and play for a draw in their game.
Of course team A could play team C next but that would mean that the remaining game between team B and C would be lucky to draw two men and a dog to watch it as it's in all likelihood meaningless, the group has already been decided.

[iancrumpy]

Team B is now playing team C in a very important game to the other countries which means zero to them because they are almost certainly going home.

Good point. The 4-team-group format is probably best.
Here in Ağırdağ we loved that 2nd Czech goal ... poor old Scotland!

[EnjoyingTheSun]

Good point. The 4-team-group format is probably best.
Here in Ağırdağ we loved that 2nd Czech goal ... poor old Scotland!

The Scots played quite well tbf but that goal was worthy of winning any game.
Re 3 team groups you often see these plans to encourage more attractive football do just the opposite. The golden goal being a case in point

[Brinsley]

What a ridiculous question about a ridiculous sport. On 'round robin' knockout qualifying league all teams draw their respective games 0 - 0 except one game which draw at 4 - 4, all teams get 1 point but the 4 - 4 draw teams go through on goal difference.
Best stick to real ball games as in rugby & cricket!

[iancrumpy]

On 'round robin' knockout qualifying league all teams draw their respective games 0 - 0 except one game which draw at 4 - 4, all teams get 1 point but the 4 - 4 draw teams go through on goal difference.

Firstly you mean goals scored, and not "goal difference". Secondly in your scenario all four teams would have 3 points, which as pointed out in messages 7 and 8 is not the lowest number of points for a team to have but still progress.

Maybe though it was a ridiculous question ... hey ho ...

By the way, after the draw between Spain and Sweden this evening, it's no longer possible in this tournament for a team to go out at the group stage on 6 points.

[EnjoyingTheSun]

What a ridiculous question about a ridiculous sport. On 'round robin' knockout qualifying league all teams draw their respective games 0 - 0 except one game which draw at 4 - 4, all teams get 1 point but the 4 - 4 draw teams go through on goal difference.
Best stick to real ball games as in rugby & cricket!

Err no.
4 minus 4 is??

As for real ball games, yes rugby and cricket are nice pastimes for those who can't play football.
How many attend the home games of the best rugby union club side in England? About ten thousand?
Some football clubs in the fourth tier get that many. And cricket clubs dream of even getting a quarter of that.