Here's an obersvation: not all hospitals are created equal. Someone above said it was advisable to upgrade them asap. Hmmm, doesn't really seem like it tbh.
My first hospital, now at L5, next upgrade costs 61M. Stats:
L5 Retain ₳50K armies when territory is close, and ₳25K when the territory is far away
L6 Retain ₳58K armies when territory is close, and ₳29K when the territory is far away
And my most recent hospital, at L1, next upgrade costs 144M. Stats:
L1 Retain ₳3.13M armies when territory is close, and ₳1.56M when the territory is far away
L2 Retain ₳4.69M armies when territory is close, and ₳2.35M when the territory is far away
So 61M for a 4K savings per captured territory, or 144M for 790K savings per captured territory. For just over double, get over 100x the benefits. And that's after 4 upgrades to get the first one to L5 ... so kind of want my money back for those upgrades, LOL.
Especially with the 2 hr upgrade for hospitals, upgrading the first few doesn't really seem to make sense. Essentially, if you're going ot spend money on upgrading a hospital, you should also stop capturing until the hospital is ready, but the value from upgrading the early ones just doesn't seem to be there tbh.
So hold out for those later ones. They're still a decent bonus in the early game, just don't waste money on them when you could put it into market items, or upgrade for army camps or mines.