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And that doesn't always make sense if you want to have the region later.
That's more for barbarians or when you realize that you have no chance and take what you can!
It seems that many, if not all, are destroyed even if there was no army there.
But I could be wrong!
It's not their base income :P
The basic formula for vassal income is pop x prosperity / 100. Tile, improvement and bonus income from spirit/government are all factored into that for each resource, so the actual formula for any given resource would be (population + bonus income) x prosperity / 100. So even a basic 5 pop vassal at 100% prosperity with no bonus IP income is still generating 1 improvement point per turn.
Where do you find that information?
How do you calculate 1 IP from that? From the formula it looks like (5population + bonusincome) X 100prosperity / 100 = 1 would require that bonusincome = -4, if no bonusincome then the formula yields 5. Details please :)
I used the term "base" without defining it, in a common way intending to exclude the IP from Improvements under discussion. Is the term defined for the game in this situation?
I'm confident I've seen Improvements in the Razed state when no units had been present to Raze them. Maybe there is some Improvement damage when a Vassal or Region is captured for example. I don't know exactly.
"Vassals grant a base amount of Income by default. That income is supplemented by what terrain is within the Vassal's territory, and is multiplied by the Vassal's Population and Prosperity, divided by 100"
I didn't, it just looks to be the minimum :P I suspect it would actually add five (5 x 100 = 500, divided by 100 puts us back at 5) but they're a bit inconsistent with how they apply multiplier, sometimes (and given the fractional input from tiles plus the notion sub 100 prosperity is bad I believe it to be the case here) it refers to an actual multiplication so less than 100% is effectively a penalty. Other times it actually refers to addition, so 100% means 'double the number'.
You can get damaged improvements when capturing a city. It's also not particularly good at notifying you when enemy units - especially barbarians - have wandered into a vassals territory, and given their camps tend to spawn fairly close to neutrals if you're not paying attention it's quite possible for a barbarian stack to wander in, burn down a farm and wander off.
In general the higher the prosperity of a vassal, the faster it usually grows and builds own stuff.
You can take over the vassal, build all the stuff (buildings, improvements) you want them to have and then turn them into a vassal again. Doing this with one vassal at a time should not stress your culture income too much. Just check prosperity after releasing the vassal. I think when I last did this (in a previous game version) a prosperity 300 vassal was back to 100, so I had to place a merchant there again. If you use specific vassal based National Spirits, they may recover prosperity fast on their own.
My two points again:
1.) Improvements should only be destroyed intentionally.
For this to happen, the enemy army must be on site (like the player)!
2.) The vassal whose improvement was destroyed should use all work points and improvement points to repair it (work points for improvement points)!
If that's the case, then everything is fine (but I don't think so ;)
It'd put strain on the IP income early game when you're only generating a handful per turn though. The main problem is that vassals don't benefit from improvements the same way the player does so the costs would be out of whack - it makes no difference to the vassal what improvement is in a tile, just whether an improvement is there or not (it's one of the reasons they end up spamming clay pits and hunting camps).