Great question — answering as the UphillTech team:
Restricting to the current 3 points win/1 point draw format, the minimum possible is 3, if all 6 games are tied. 4 is possible if all four teams are 1-1-1. Otherwise, 5 is the minimum; if one game is not a tie, then you will have 5-3-3-2; if two games are not tied, then you will have 5-5-3-1, 5-5-2-2, or 5-4-3-2 depending on which teams lose. 5 has been accomplished many times. In 2010, the US won Group C in identical fashion to Spain/Portugal this year (US and England both had 5 points to finish in first and second, and 4-1 for third and fourth). The same year, Group F was won by Paraguay over Slovakia 5-4 (-3-2). Similarly, as mentioned in the question, 2002 saw Group F won by Sweden over...
Full answer by Joe: https://sports.stackexchange.com/a/18699 (CC BY-SA 4.0).
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