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As for the diplo anexation cost policy, I didn't check last time I used it, but the diplo anex ideas reduce the total cost, thus giving you a huge increase in the anexation % when you take them, I'd assume the policy does the same (since you lock them for at least 10 years, there's no way to abuse it anyways).
If you really plan to anex 6 vassals together though, you might not want the diplomatic reputation, as 2 vassals together can already easily bring you to a -12 DIP per month, which is already hard to keep up.
In all the other cases you will anex faster, 1 point faster per month, at the cost of 2 dip.
* It is an ADM policy
* It *does* affect annexations that have already started
* It immediately reduces the amount of DIP needed to finish annexation
* It does not alter the DIP points already spent toward annexation
* have a big stack of diplo power, the annexation drains from your current MP, not your monthly income
* if you have no MP left the annexation pauses so you get nothing of worth but stuck diplomats
* admin efficiency reduces annex cost too! so getting another level of adm tech can help tons
* 60% adm efficiency, 25% from influence ideas, and 20% from the policy can give you max reduction (which I read from the wiki is 87.5%). They reduce the final cost, so you dont have to start with max reduction, just get it by the very end.
* diplo rep increases the "pipe" youll be draining mp with, since you are draning for multiple vassals, you dont need dip rep at all (maybe if you get a malus) all in all that dip rep policy is not worth it at all unless you ABSOLUTELY need it to progress the annexation (you got a huge malus). Would be better if dip rep worked as "free" points you got monthly towards annexation, if it worked like that then it would be an investment of points to get more points back, and actually useful.
* the "first" vassal (no idea which is first) drains first from your pool, followed by the second vassal and so on, so having multiple annexations does nothing if your pool of MP cant handle it, if it cant then only this first vassal will finish annexation as it will be the only one draining MP (and leaving it empty), and only then, the second will start, then the third and so on.
edit : i m speaking of the influence idea "integrated elites" giving 25% on diplo annex, dunno if the policy work.
now getting diplo rep for admin or military points is ok I guess, as you are basically trading one point for the other
savoy devlopment level:
18+26+37+23+22+31+12+18+20+12+24+18+26+36+22+31+25+22+26+37+31+41+21+40+21+
49+14+20+27+15+27+16+27+33+40+35+30+8+14+20+21+20+20+14
=1090
game states I need 4194 points, i have 26 adm tech, im at 2.3% progress and I got 97 points in (so the number 4194 is correct)
devel * cost per devel * modifiers (adm tech, adm tech, influence)
expected: 1090*8*(1-0.2-0.2-0.25)=3052 so not at all, they use capped arithmetic on every % calc except here, figures
possible modifiers:
adm+adm+inf = 0.35
adm*adm*inf = 0.48
(adm+adm) * inf = 0.45
adm+adm, no inf = 0.6 (influence doesnt work)
adm*adm, no inf = 0.64
(adm*adm) + inf = 0.39
4194 / (1090*8) = 0.4809633027522936
so im leaning towards multiplicative and some rounding, and influence is working, it just isnt as strong as expected (still strong)
now the wiki says the maximum is 87.5 reduction, but i dont see how you can ever hit that number unless they used arithmetic %s
if all the modifiers are multiplicative the best modifier you could get as austria is 0.29376, far from 0.125
maybe adm3 or the policy dont use multiplication to make it possible
Not sure how NIs factor in, but i suspect they will stack additively with Influence and policy and then multiplicative with admin efficiency.
I also suspect that diplo annexation currently does not work as intended since the estimated cost you get on the diplomacy screen is lower than the actual cost indicating that admin efficiency probably should stack additively as well allowing any country to reach the cap.
(adm+adm+adm)*inf = 0.3
adm*adm*adm*inf = 0.384
3283 is 0.3764..., so i think its just plain multiplication so far (as you said)
adm*adm*adm*(inf+p) = 0.2816 that would be a non austrian max reduction
austria would still be far from the cap even if it is additive with inf and p, at 0.2048
also the rounding is weird, because 0.384 is very far from 0.3764, and no matter the rounding schemes I tried I couldnt come up with it. I got a lower number once so it is within possibilty I guess, math fail from the devs, doing several lossy operations instead of a single one at the end.
I hope the policy is additive I might be able to annex them all right by the end of the game :3, now my leaders die... the game has started giving me lose diplo or admin "your choice" events so that can start to happen more often too :(
Admin efficiency is just one number. So the cost will be 22% without NIs.
when I had adm2 the number also was closer to "separate, multiplicative"
I checked the cost in game and adm*(Inf+p) is an accurate formula.
E.g. (1-0,6)*(1-0,25-0,2)=0,22 for maximum reduction.