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And you are exaggerating. If you need 20 years to annex a vassal it's not "some tiny vassal" but at least a medium regional power (120+ total development).
That means you annex at 5 a month(base 1 + dip rep 3 + same religion 1). Annexing costs 8 dip points per development.
so in order for an annex to take 15 years it would mean their development is at:
totTime (in years) = (dipAnnexCost * development) / (annexPerMonth * 12 months)
15 y = ( 8 * dev) / (5 * 12)
15 * 60 = 8 * dev
900 = 8 * dev
dev = 112.5
that is hardly a small country
Little comment:
The base annexation is 2 per month and base diplomatic reputation is 0 - before anyone believes he should have +3 diplomatic reputation without any modifers ;)
Diplo-Annex is also referred to as "integration" within the game ("integration is a slow process" pop-up after annexing a vassal). In either case he's talking about manually annexing a vassal or PU, because he has a shortage on diplomatic points.
This vassal annexing crazyness really seems to make WC impossible now.
10 years for denmark + you have spare diplo points = you probably don't have any diplomatic or influence idea.
Why do you complain about integration of vassals if your country isn't specialized? Do you complain about combat if you don't have any military ideas at all?
The problem is, if you don't have a direct border, the religious CB is not granted, hence the need of vassal integration. I only have about 100 years left and need to integrate denmark to continue with scandinavia, I need to integrate the balkans (hungary, a giant fed bosnia and a giant fed mentese) to continue into africa / middle east / india. I got Poland/Lithuania in a PU under me and fed most of russia to them. I also need to integrate France to get their overseas colonies in asia, portugal is in a PU under me but Colombia in South America separated and is independant. And as if all that wouldn't be enough, I still need to hope that Spain will get a weak heir so I can finally claim throne on them and force them into a PU as well, they got a giant colonial realm and there's no other way I could get all that in the remaining time.
It just feels like every time I integrate something to open new borders to expand into, I'm locked out of any significant conquereing for 10-15 years because I can't save up enough diplo points for war demands to make it worth it. Going to war for just 1-2 provinces isn't worth the truce timer afterwards really.
I don't know, maybe I've got the wrong approach altogether or I'm missing anything, I only read some world conquest AARs / guides from very old EU IV versions and most of the glitches used there don't work any more by now.