When exactly do players move between leagues?

I see this article that says

After a hidden period of time, their skill level will be reevaluated.

Has anyone been able to determine how this work? I now reached 1st place in my league and am eager to pass on to the next. I was already promoted a league once, how long do I wait before being promoted again? Does a higher score grant me a better/sooner chance of being upgraded, or does it simply happen at random time period if I have enough score?

The score you see doesn't matter and it's mostly there so you feel like you're making progress and hence continue playing.

See this question for more details on that. I've been told it's evaluated every so many games (I heard 30 before, but I can't say how definite that is).

You'll get promoted faster if you consistently beat players that are ranked higher than you (in the hidden ranking, not the visible points you see)