Context

I'm a baseball fan. As the regular seasons comes to an end, some teams clinch their spot in the postseason and others are guaranteed to not make it. Most of the times I see that a team was eliminated (as an /r/baseball post) it was someone doing the problem by hand. I'm trying to find a generic algorithm, and one that can run in a reasonable amount of time. Maybe this is more of a programming problem, but I'm asking here since the math is pretty tough.

Problem

Major League Baseball has 30 teams split into two leagues (American League and National League), each split into three divisions (East, Central, West). Teams enter the playoffs when they a) have the best score in their division (winning the division) or b) have the best or second best score in their league among teams not winning their division (wildcard). Given the current standings and remaining schedule, find the teams that are assured a place in the playoffs and those that are assured elimination.

Alternatives

It's much easier from a probabilistic approach. This is what FanGraphs does. They simulate the rest of the reason (as coin flips or a more informed way) 10,000 times and then report the percentages. This is how teams can have a 100% post season chance on their site while not yet being mathematically locked in. It's just they made it in 10,000/10,000 simulations.

Attempts

I tried brute force, with at least considering remaining matchups as one number. Teams that play each other 7 times have 8 ways to share the wins, rather than 128 (2**7) unique orderings. Still, the combinatorial space is just way too high. I'd estimate 10**40 was the best I could do. The splitting of division winners and wildcards made narrowing the space beyond my abilities.

Prior Work

I found a paper, some slides and a blog post. All of them take the approach of looking at it as a max flow graph problem, which I think is the way to go. The downside is they all take on calculating not winning the division, a much easier problem! The wildcard is the wildcard.