How fast do free players earn pearls?

Achievements have dried up. Gift boxes are randomized and the common one, the white box, doesn't drop pearls every time. The calendar has had mostly item drops lately. Chests, quests, and crates don't drop pearls at all. So most of my pearl income has come down to earning them in matches. Some matches drop a couple of pearls on their own, otherwise I earn 1 pearl if I watch an ad at the end. These don't add up.

Doing some generous and lazy math, let's say I earn 200 pearls a week from matches alone. I get lucky and get 50 pearls from care packages. At 250 pearls a week, it still takes 15.6 weeks to get an Epic Chest, or 109.2 days. Sadly, I don't actually earn that much. Over the past week I think I've only gained about 50 or so, which is 78 weeks, or roughly 1.5 years. I haven't been keeping track, though, so let's be safe and say 100 pearls, which is 39 weeks, roughly 9 months.

Bringing this up because players here often get the advice to save their pearls for the Epic Chest, but no one ever says how long that takes if you don't set aside a few bucks to buy pearls every so often.