Related to this question, what is the minimum points required to guarantee qualification for Euro 2016 in a five or six team group? In a four team group with home and away games and the top two qualify (as in the Champions League) you must have 13 points to guarantee qualification?
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1 Answer
For six teams 25 points, for five teams, 19 points.
If you have six teams there are 30 games, so maximum 90 points to play for. Assuming every game is won by a team where; the bottom team wins none, the second bottom beats only the bottom team (6 points) and the third team beats on the two lower placed team (12 points). That leaves 72 points, to be split between the three top teams who all beat the lowest three teams and each other once.
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In a five team league there are 20 games, so 60 points to play for, same sort of logic applies, working up from the bottom team.
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It feels to me that you should be able to generalise this to
nteams fairly easily at this point.– Philip Kendall ♦Jul 1, 2015 at 11:53 -
1No. If all games are draws, for five teams, then only 8 points will be necessary.– MFornariJul 1, 2015 at 14:43
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1@MFornari that's sort of miss the point, as it is conditional on other results going in the favour of a qualified team. To guarantee qualification you must consider the worst (not the best) possible set of results in all other games.– guyabelJul 1, 2015 at 15:22
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Then in a five teams draw, you could qualify with 10 points, 7 draws and a win... and all other matchs finished ties– gbianchiJul 1, 2015 at 16:57
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3@gbianchi That's still not the point - the question is what is the minimum number of points you need to guarantee qualification even if every other result makes it as hard as possible for you.– Philip Kendall ♦Jul 1, 2015 at 17:28