I'm writing an app to simulate a sports league. For simplification I have following definitions:
There are 4 Teams A, B, C and D. Every team plays only once with each other in every season (6 matches). Winner gets 1 point. Loser gets 0 points. On draw each team gets 0.5 points. The team with the lowest points will not pass to next season. If there is the case that the last 2 teams have even points there will be a coin flip procedure.
I want to know the minimum points which have to be archived to definitely pass to the next season and highlight the according team.
Since all teams can have the average number of points (if all games are a draw) and it’s clearly impossible to have more than the average number of points and yet have the least number of points, the minimum number of points to guarantee that a team makes it to the next season is $\frac12$ more than the average, that is, $2$.