The lecture here describes how to tell if a given team is excluded from topping a baseball league using max-flow. For baseball, the team with the most wins tops the league and every game can either be a win or a loss.
In this way, an integer programming problem is converted to something that can be formulated as a linear program. The inputs are the number of points for the team in question, those above it and the number of games remaining among all these teams. At a high level, there is one node per each combination of these teams and all of them are connected to a source. These in turn are connected to one node per team (capacities being games remaining) and finally a sink with capacities being the number of wins a team can win without crossing the maximum possible wins for the team in question. The idea is that if all the capacity going out of the source can be utilized, it's possible for the team in question to win.
I was wondering if it would be possible to extend this approach to a soccer league. Typically, these are points based and a team gets 3 points for winning, 0 points for losing and 1 point for a draw. The problem becomes that the total number of points (unlike the wins for baseball) isn't a conserved quantity. So, the total number of points at the end depends on the actual outcomes of the games. I tried solving this problem by adding a dummy node with the two-team-combination nodes connected to it with infinite capacity. This didn't work however as some flow possibilities emerged that don't correspond to any game combinations.
I was wondering it there is some other trick to extend the baseball elimination with max-flow to soccer.
There is a paper, "Football Elimination is Hard to Decide under the $3$-Point-Rule," by Bernholt, Gülich, Hofmeister, and Schmitt, that shows that under the three-point rule, deciding whether or not a team has been eliminated is NP-complete.
Therefore, there is no way to solve the problem with max flow, (at least not if we assume that it takes only polynomial time to convert the schedule of remaining games to a max flow problem.)
EDIT
I should mention that the abstract says that the problem is NP-complete even if each team has at most $3$ games remaining! (I haven't read the paper yet.)