How am I still in Crystal III League if the minimum trophies for crystal are 2000 while I just have 1981 trophies?
I guess it works like this:
Trophy range: 2000 - 2199
Demoted to a lower league if trophy count drops to 1900
Promoted to a higher league if trophy count rises to 2200
When you are placed in a league, you are in that league until you graduate or flunk. You graduate by gaining the required number of trophies for the next league, and you flunk by dropping below the current #100 player in your league OR dropping below 100 trophies less than the required number for your current league.
Source: Personal experience, @Ellesedil