Random ponderance about 4-team group stages

[Shwafta]

So the Euros got me wondering
1) What is the highest number of points a 3rd place team could get? Along with that, what's the lowest number of points a team in 2nd needs to get to confirm advancement
2) What's the highest number of points a 4th place team can get? As well, what's the lowest number of points a 3rd place team needs to confirm potential qualification?
3) What are all the permutations that a group stage can have?

As such, I created a small javascript program that ran and here are the results I got, filtered for duplicates:

Spoiler

[[0,3,6,9],[1,1,6,9],[3,3,3,9],[1,3,4,9],[0,4,4,9],[1,2,4,9],[2,2,2,9],[3,3,6,6],[0,6,6,6],[1,4,6,6],[1,3,6,7],[3,4,4,6],[0,4,6,7],[1,4,5,6],[2,4,4,6],[1,2,6,7],[2,2,5,6],[3,3,4,7],[0,3,7,7],[1,3,5,7],[2,3,4,7],[0,4,5,7],[1,3,4,7],[1,4,4,7],[2,2,4,7],[1,1,7,7],[1,2,5,7],[2,2,3,7],[3,4,4,5],[2,3,5,5],[3,4,4,4],[4,4,4,4],[2,4,4,5],[1,4,5,5],[2,3,4,5],[0,5,5,5],[1,3,5,5],[2,2,5,5],[2,3,3,5],[3,3,3,3]]

From this, I found the following:
1. The highest number of points for a 3rd place team is 6, meaning that to guarantee at least second place, the second place team has to get 7 points, aka two wins and a draw. There is a possibility that even after winning two games, a team is NOT guaranteed second place!
2. The highest number of points the 4th place team is... 4! to confirm not last, 3rd place must get at least 5 points.
3. Here are all the permutations. Seeing as it's impossible to get 8 points, the only way to guarantee first place in a group is to win all three games. Most likely two wins and a draw can seal the deal on 7 points, but there are a few cases where two teams end up on 7 points, so it's not guaranteed.

I've always wondered what the possible permutations are, and this is fascinating to me so I hope some of you learned anything fun.

As an added bonus, I'm going to leave two more things:
1. The full set of possibilities, with team names connected to the points:

Spoiler

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2. Here is the algorithm I used to find the solutions, if anyone is interested: https://jsfiddle.net/#&togetherjs=g9lJnsbJrI

 

[Gotham Gator]

Good stuff. I like that.

Another one. If the second place team has 7 points, then so does the first place team.

The scenario where a 3rd place team has 6 points has always been interesting to me. Basically, this means that three teams tie at 6 points and the fourth gets zero. The three teams each beat the fourth and then one of the others - rock, paper, scissors style. It nearly happened in the 2018 World Cup, but S. Korea upset Germany in the final game. If Germany had prevailed, it would have been on 6 points with Sweden and Mexico, and Mexico would have been the odd team out based on goal differential. Imagine not advancing with 2 wins, one of them over Germany!

 

[Shwafta]

Good stuff. I like that.

Another one. If the second place team has 7 points, then so does the first place team.

The scenario where a 3rd place team has 6 points has always been interesting to me. Basically, this means that three teams tie at 6 points and the fourth gets zero. The three teams each beat the fourth and then one of the others - rock, paper, scissors style. It nearly happened in the 2018 World Cup, but S. Korea upset Germany in the final game. If Germany had prevailed, it would have been on 6 points with Sweden and Mexico, and Mexico would have been the odd team out based on goal differential. Imagine not advancing with 2 wins, one of them over Germany!

Yeah, that scenario is always nuts! I forgot that happened at the world cup, probably mostly because Germany lost.

I want to see if there's any scenario of the above that have never happened in a group stage, but that's not something I feel like actively trying to research right now lol.