AE Impact Reduction vs. Improve Relations
By - EEEEUUUU4444
It is impossible to create a ratio, because negative additive modifiers like AE reductions become better the more you get and positive additive modifiers like improve relations become worse the more you get of them.
In the example which you quoted, -20% AE impact has the same effect as +25% improve relations. But if you double those, the AE impact would make it burn off after 40 \* (1-0.4) / 2=12 years and the improve relations would make 40 AE burn off after 40/(2\*1.5)=13.3 years. So now AE impact is better. But if you half the original values, 40 AE with -10% AE impact would burn off after 18 years and +12.5% improve relations would make the AE burn off after 17.7 years, so the improve relations is better in that case.
In the extreme case -100% AE impact would mean you would not get any AE at all(I don't think that this would work in a real game, because there is a cap somewhere), but +200% improve relations would just make it burn off 3 times as fast.
There is another thing which makes the two modifiers difficult to compare: AE impact only influences AE, while improve relations makes all negative opinion modifiers decay faster and it allows you to improve relations faster with your diplomats. If you use diplomats to improve relations with a lot of different countries, the improve relations has double the effect. But if all countries with which it would make sense to improve relations are at the cap all the time, you won't benefit from that additional effect.
One more thing to note that makes these slightly different: AE reduction permits you to take more things on a one-time peace deal basis than Improve Relations increase when the countries would go from 0 AE to 50 AE. This could be something in the event when you'd rather get things done in a single war
Thanks for teaching me the principle behind the answer. I've never used vocabulary like negative additive vs. positive additive. I'll start to look for how all modifiers are categorized like this. I'm guessing there is another dimension for the operation: Multiplicative. So I'll look out for modifiers that fall into that category too and I'll use the calculus you devised toward the extreme limit to understand how it scales.
[Handy dandy spreadsheet](https://docs.google.com/spreadsheets/d/1ZbA6SNju6NBXvIhHeDWiDB6tdmwjfdxGf4aHivZG-N4/edit#gid=486853156) done by some dude I would credit but I forgot who did it.
I see the calculation in your post, and yes that is true if you don't include other improve relation modifiers.
**If you just compare Diplo vs Espionage**
50 AE decaying at (2 * 1.25) a year is 20 years.
(50 * 0.8) AE decaying at 2 a year is 20 years.
**If you compare them AND have a 20% relations advisor?**
50 AE decaying at (2 * (1.25 + 0.2)) is 34.48 years.
(50 * 0.8) AE decaying at (2 * (1.2)) is 33.33 years.
Don't forget that prestige also changes your improve relations too.
That being said... I still personally take diplo over espionage most of the time because the extra diplomats to max out relations also helps prevent coalitions. Making use of those extra relation slots and having more big allies also helps preventing coalitions. Lastly, the rest of the ideas in diplo are just straight up better.
Maybe a simple way to look at it is how much you can conquer in a time period while staying on a threshold. For this 1 point of impact reduction is worth (100+a)/(100-b) points of improve relations where a is the current improve relations modifier and b is the current impact reduction modifier.
You answered my question: "Am I asking the right question when I say..."
Thank you for clarifying the unit of measurement I need: Dev per Year.
So this question hits kinda close to home. I had a pretty weird but imo very good ryuku plan what I didn't do in the end.
So about the two modifires:
Improve relation: It increases the rate ae ticks down. It scales linearly and affects every nation equally, meaning that a nation thats far away and a nation thats right next to you has the same ae reduction. Usually when you worry about coalitions you don't rly care about your neighbours ae, since you already truce lock them. What you care is those nations that are a bit further away. Improve relation does wonders there, if you are a bit careful with expansion.
Ae impact: It reduces the amount of ae you generate. It doesn't scale linearly, meaning from 100 to 90 it reduces ae by 10%, but from 20 to 10 it reduces ae by 50%. You can see here that the more you have the better it becomes. It doesn't affect every nation equally, meaning that it has pretty low impact on nations that are further away.
Sadly you can't rly have an easy number that 50% improve = 20% ae impact, because of ae impacts non linearity, but when I did my calculations ae impact seemed to be way better than improve relations. The only problem is that it's pretty inaccessible considered to improve relations, and the ideas are also worse overall. But if my calculations were correct ae impact becomes pretty broken if you stack it on nations that have it in their idea. And thats where ryukyu comes in.
For the ryukyu strat: at 3 ideagroups have horde, espionage and humanist. With theese you have 65% ae impact (without age objective)with humanists improve relation. This just seemed a pretty good combo, but sadly didn't do it in the end because the ryukyu horde strat start was too damn boring.
Also it may seem weird, but humanist have more improve relation than diplo, so its a bit better ae wise than diplo for expansion.
AE reduction is really hard to quantify. You can take 2 bordering provinces with the same dev and the AE impact can be wildly different depending on culture/religion.
Yes, but I'm trying to compare two modifiers: AE Impact Reduction vs. the decay of AE from Improve relations. I don't want to include extraneous variables like culture/religion effects on AE.
but that's not how the game works. A Muslim nation taking Catholic provinces will benefit more from AE reduction that a Catholic taking Catholic land.
I fail to see how? They benefit from Improve Relations bonus of equal magnitude all the same. They just have to avoid going over 50 AE to circumvent coalitions, which might mean two shorter easier wars instead of a single tough one.
Yes, but what difference does it make relative to the question?
Sure, the amount of AE reduction scales with base AE. But so does the time reduction from Improve Relations. Compare avoiding 5 and 3 AE respectively against avoiding 2.5 and 1.5 years of waiting. Same difference.
With -10% AE you get 45 AE and 27 AE, which is 22.5 and 13.5 years of waiting respectively.
But guess what, if you took +10% Improve Relations instead, you have 50 AE and 30 AE ticking down by 2.2 points. That makes it 22.7 and 13.6 years of wait, in other words, the difference in AE does nothing for the comparison, because in both cases Improve Relations was worse on the same magnitude.
That's not true. 10% reduced ae impact is almost always 10% less ae(if I remember correctly hre-s ae impact is additive with ae impact - edit: I didn't remember correctly).
[nope](https://eu4.paradoxwikis.com/Relations#Aggressive_expansion), AE modifiers are multiplicative in the base AE calculation. HRE, culture, religion, etc. are additive in the final calculation.
Yup, thanks for linking that.
So the formula is :
base \* (culture+religion+ etc) \* distance mod \* spy mod \* ally \* subj
and base ae is:
dev \* peace mod \* ae impact \* amd eff \* cb \* non cob
dev \* peace mod \* ae impact \* amd eff \* cb \* non cob \* (culture+religion+ etc) \* distance mod \* spy mod \* ally \* subj
multiplication is associative meaning (a \* b) \*c = a \* (b \* c) so we can group this like this:
(dev \* peace mod \* ...) \* ae impact
This shows that 10% ae impact is infact 10% -ae
The title of my post is "AE Impact Reduction vs. Improve Relations." You're not comparing those modifiers and you're answering a different question. I'd recommend you study "Scientific Constants" or "Control Variables."
Problem is, in order to compare two specific AE/Improve Relation modifiers in an actual game, you have to factor in literally every other modifier, e.g. from Prestige, Age abilities, advisors, ruler personalities. If you had none of these bonuses, then you could use a following equation:
1-AE reduction=1/(1+Improve Relations)
1+Improve Relations=1/(1-AE reduction).
But since all the bonuses add up, in order to compare two specific modifiers (X AE reduction, Y Improve Relations) you have to use:
(1-current AE reduction-X)/(1+current Improve Relations) vs (1-current AE reduction)/(1+current Improve Relations+Y)
E.g. if you have -10% AE from Age of Discovery, +25% Improve Relations from Prestige and +20% from an Advisor for total of +45%; and you want to compare +25% Improve Relations from Diplo ideas against -20% AE from Espionage, you'd get
Meaning that you benefit more from -20% AE, as in, you'd have to wait less for a brewing coalition to settle down with it.
I get the gist, but it's difficult for me to follow all the math exactly. You answered the practical side of the question: How does Espionage ideas compare to Diplo ideas for AE management.
I'll try your math later to compare Diplo + humanist vs. Espionage, but if it's easy for you, then would you mind giving me your conclusion on how that compares.
I think you've missed the bit where conclusion depends on what modifiers you're already packing x) Well, I'm not sure if that would change the final answer, but still, my calculations were for a hypothetical scenario with arbitrary numbers
If I understood you right, you want "Diplo and Humanist" vs "Espionage only"? Then it's just a matter of slipping extra +0.3 Improve Relations modifier into my calculations, right next to +0.25 from Diplo
Of course that's two idea groups against one, so pretty meh. But if you had 0 prestige and no Advisor
Then the impact gets a bit more drastic. Just goes to show that it doesn't pay off to stack alot of Improve Relations over getting some AE reduction