CS Influence Decay

[Stalker0]

There has been discussion in the past around the difficulty for high level players to secure CS allies against the AI.

The high level AI is able to generate diplo units very quickly, due to its production and gold advantages. As a consequence, AIs can sometimes amass 1000s of influence in a CS, much more than is economically wise for a human player to compete with. Human players therefore rely on Spheres of Influence to gain and hold CS allies.

One idea that came out of the discussion was on CS Influence Decay. We already have a sliding scale (the more influence you have, the more you lose per turn), so the thought was, scale up the decay even higher as your influence increases. This would lower overall CS influence levels, giving human players a better chance to flip a CS to an ally.

The current formula is: 1.5 + X/100 (X is rounded down to nearest 100s). Note that CS types can change this slightly (from 1 to 2), so we used 1.5 as the base average for this discussion. Example: At 220 influence, you lose 1.5 + 220/100 -> 1.5 + 200/100 -> 1.5 + 2 = 3.5 influence per turn. At 500 influence, you lose 6.5.

One idea was to use the square: 1.5 + X*X / (100 * 100), X is still rounded down to nearest 100s. At 220 influence, you lose 5.5 influence. At 550 you lose 26.5.



The advantage of this method is its focused at higher difficulties. Lower difficulty AIs are not generally getting into the high influence numbers, and so wouldn't be affected. This would be a scalpel change for higher difficulties.

It also remains simple to calculate. A square is still fair easy as opposed to a more complex formula, so people could check their own decay numbers more easily than if we used a full formula.

Ultimately this change would not affect influence up to 199, that would stay the same. Its at 200+ you would start to see a noticeable difference in how fast influence drops. And around 400+, you would see a very sizable difference.


So time for discussion. What do people think of changing the decay rate, and do you like the square approach? Is there an alternate approach you think would work better?

 

[pineappledan]

So, ignoring the 1-2 base decay, which you aren't talking about changing and doesn't really factor in when influence levels are really high anyways, this is what that looks like?

Influence level __ Current __ New
0-99 __ 0 __ 0
100-199 __ 1 __ 1
200-299 __ 2 __ 4
300-399 __ 3 __ 9
400-499 __ 4 __ 16
500-599 __ 5 __ 25
600-699 __ 6 __ 36
700-799 __ 7 __ 49
800-899 __ 8 __ 64
900-999 __ 9 __ 81
1000-1099 __ 10 __ 100

So basically, between 0 to 199, it's identical, at 200-299 it's still bearable, but past that, decay would smack you back down within a dozen or so turns.

This is interesting, because the Statecraft Influence per trade Route tops out at +5 per turn, so that means your "equilibrium", where you stopped building influence passively with the old system was 499 (-1.5 & -4 decay vs your +5 from trade). Now that same equilibrium is only at 299. This means that bursting a few CS for WC quick allies for non-Statecraft civs is much more doable, since it takes fewer diplomats to close the gap, but diplomats after that point hit a very big, very hard wall. Trying to sustain 700+ Influence for any amount of time is just throwing your production/gold into a fire.

That means the competition is all about who can tread water in that 300-600 influence range, and how well you can burst a few diplomats to clinch those allies for a vote on a well-timed, but quickly vanishing lead in the 700+ influence zone.

 

[Stalker0]

The "oddity" with integer rounding in the equation is you have some scenarios where passive decay can "flip" a CS ally.

An example:

I am at 499 influence, and you are at 502. I lose 16 influence, you lose 25. I am now at 483, and you are now at 477. So I have gained a CS ally through passive decay.

This can kind of happen today just in a narrower range. If I'm at 499 and your at 500, I would lose 4 and you 5....and we would now be tied in influence. So the CS ally is lost, not flipped, but its a similar concept.

If people consider this a big issue, there are a couple of ways off hand to stop it.

Solution 1: "Buffering"

You have two numbers, the decay maximum (defined by the equation above). And the decay minimum, which is the decay maximum from the previous level.

You first remove influence = the decay minimum. Then, if you have crossed the 100s place, you stop. If you haven't, you continue to remove 1 influence at a time until you either cross the 100s place, or you hit the decay maximum, whichever comes first.

That's probably very confusing in text so let me show it using the example above.

At 502, my decay maximum is 25, and minimum is 16 (aka what it was at 400-499). First, I lose the 16, putting me at 486. Since I dropped a hundredths place (from 500 to 400 level), I only lose the 16.

Now lets say I was at 520. Again I lose the 16, putting me at 504. I am still at the 500 level, so I lose 5 more, dropping me to 499. I have now crossed from the 500 level into the 400 level, so I don't lose anymore.

If I was at 550. I lose 16, going to 534. I am still above 500, so I keep losing....all the way up to 25 total lost (which is my maximum decay), which puts me at 525.

It is a more complex calculation, but one people could probably still do in their head, though its mechanism is more complex.

Solution 2: Non-Integer Calculation
We use the same formula but we don't round down until the very end.

Example:
Current Decay: 525 becomes 500. 500 * 500 / (100 * 100) = 25
Alternate: 525 remains 525. 525 * 525 / (100 * 100) = 27.5625 -> 27 decay

This has less method steps, its still just one formula, but it would be harder for a human to calculate without assistance.

 

[Heinz_Guderian]

I play on Immortal/deity and I agree it is somewhat of a problem on deity but not on immortal imo. I think some other way of restricting diplomatic units would be better like a diminishing return for using a diplomatic unit on the same city states many times or decreased influence gained from diplomatic units if your influence is already high. Not sure though

 

[pineappledan]

I play on Immortal/deity and I agree it is somewhat of a problem on deity but not on immortal imo. I think some other way of restricting diplomatic units would be better like a diminishing return for using a diplomatic unit on the same city states many times or decreased influence gained from diplomatic units if your influence is already high. Not sure though

If you go that route, what you are saying is that you want to specifically punish Influence based on the source of the influence. If you make Diplomats have a reduced rate of return, or have lower impact the more you train, then Influence from quests and other things like Trade Routes or Instant boosts (CERN, etc.) are made comparatively stronger.

So then is the problem with diplomats exclusively? Or is it with high amounts of influence in general? I personally think it's the latter.

 

[Stalker0]

I think some other way of restricting diplomatic units would be better like a diminishing return for using a diplomatic unit on the same city states many times or decreased influence gained from diplomatic units if your influence is already high. Not sure though

I'll use an example so I make sure I understand your idea.

Decreased Influence: So lets say at 1000 influence, I have a 50% penalty. So normally my diplo unit would provide me 100 influence lets say, but if I were to use it in that 1000 influence CS, it would only gain me 500. And since I can see how much influence a diplo unit delivers when I hover over its spread command, I would assume the UI would be updated to show the new number.

The nice thing about this is its very user friendly. A user can very clearly see how much influence they are going to get out of their unit, and the impact is immediate (immediate boosts are easier for users to understand than slow behind the scenes processes).

As PAD already mentioned, this would be a diplo unit only change, meaning that other forms of influence would get stronger in this model. Whether that's good or bad I leave for debate.

It would also means that high influence units (aka ambassador vs envoys) would be sliiightly stronger. If I use 1 envoy and crossed into a new threshold, my second envoy would be a bit weaker. However, one ambassador would get its full value even if it crossed into a higher threshold, so I would ekk out a few more influence. I doubt that this effect would be strong enough to matter much, and some may consider it a benefit, as higher diplo units cost more paper, so giving them a little bit more advantage may be considered a good thing.


Ultimately my main issue with the idea is that its not continuous, and therefore I don't think it would be powerful enough. Stronger decay forces a civ to utilize more resources to maintain that very high level, its a continuous payment for the privilege of having such a large gap over your opponents. With this model, while it would take more resources to get to that high level, ultimately the gap would remain the same over time, and a second person wanting to catch up would still have to cross those same thresholds and spend just as much resources to ultimately close the gap.... so the human would still have a large disadvantage compared to the AI.

 

[Heinz_Guderian]

That was just a top of mind thing honestly, but yes I do feel like the problem is mostly due to diplomat spamming because of absurd production for deity AIs. You could still increase decay exponentially but maybe not by that crazy amount that PD listed above. Even with tweaked decay, wouldn't the AI still keep the alliances if their behavior is the same? I would maybe rest around 100-200 influence and they would rest at like 400+ because they are gaining like 30 influence/turn because of how much they are spamming diplounits

 

[pineappledan]

That was just a top of mind thing honestly, but yes I do feel like the problem is mostly due to diplomat spamming because of absurd production for deity AIs. You could still increase decay exponentially but maybe not by that crazy amount that PD listed above. Even with tweaked decay, wouldn't the AI still keep the alliances if their behavior is the same? I would maybe rest around 100-200 influence and they would rest at like 400+ because they are gaining like 30 influence/turn because of how much they are spamming diplounits

I think the difference would be that it shifts diplomacy to being more about sprinting for a big spike of influence around vote time, rather than the current situation, where you and the AI fill a massive bucket of influence. High amounts of influence decay too fast and are too costly to maintain for less reward. and you can maintain higher levels of influence for at least a bit of time still -- It takes 11 turns for 400 influence to decay to 300 -- but the equilibrium for votes won't be in the thousands anymore, which allows human players to still punch up influence with a burst of diplomats for a short amount.

 

[Hinin]

And overall, it makes endgame diplomacy a lot more reaction-based : only CStates targeted by WCongress will be locked diplomatically. The others will be a lot more swingy, and that's a net plus I think. Makes Diplomatic Victory less about pure stacking and more about strategizing and gives a rubber-band mechanic for CS diplomacy.

 

[Solic]

I'd be wary of affecting lower difficulties negatively.

Also mechanics that halt influence decay (I'm thinking cold war resolution and Austria marriage) should be taken into account.

 

[azum4roll]

An exponential factor of 2 is too radical a change. We also shouldn't restrict ourselves to just integers.

Let k be the influence decay (constant) when the influence is between 1 and 100, and x be the current influence.

Current decay:
k + floor(x / 100)

Suggested decay:
k + floor((x^2) / (100^2))

My suggestion:
k + (x^n) / 100, and we tune n to get the best value.

 

[Stalker0]

An exponential factor of 2 is too radical a change. We also shouldn't restrict ourselves to just integers.

Let k be the influence decay (constant) when the influence is between 1 and 100, and x be the current influence.

Current decay:
k + floor(x / 100)

Suggested decay:
k + floor((x^2) / (100^2))

My suggestion:
k + (x^n) / 100, and we tune n to get the best value.

View attachment 605715

View attachment 605722

a nice tight graph, thank you.

So the first question, is there an influence level we want things to “cap at”. Right now how level AIs can get into the 3-5k range pretty trivially (and that’s 5k from me, no idea what that total influence actually is).

right now the current numbers aren’t really providing a cap, so is there a range we really want to see influence stop growing at? That gives us a high point to look at.

As the goal is to mainly adjust for high difficulties, I guess one question, what are influence numbers reaching for king/emperor level difficulties? Ideally we don’t want to affect that range too much.

 

[azum4roll]

At Emperor, each non-Statecraft AI usually picks one nearby CS to spam diplo units on, and wouldn't bother with friendly civs' allies. Around 2k influence at end game.

Statecraft AI usually wants to ally with more CS and would aggressively use diplo units on other civ's allies (influence depends on how fierce the competition is - they stop once they successfully ally these), in addition to the 1-2 CS (2k influence) that they won't let go of.

 

[pineappledan]

So the first question, is there an influence level we want things to “cap at”. Right now how level AIs can get into the 3-5k range pretty trivially (and that’s 5k from me, no idea what that total influence actually is).

right now the current numbers aren’t really providing a cap, so is there a range we really want to see influence stop growing at? That gives us a high point to look at.

As the goal is to mainly adjust for high difficulties, I guess one question, what are influence numbers reaching for king/emperor level difficulties? Ideally we don’t want to affect that range too much.

I think a good "cap" is 1,000. @azum4roll's highest cap -- n=1.1 -- is still only -28 influence lost per turn at 1300 total influence. that's only a little more than 2x the current rate of -13 per turn. On top of not going far enough it's way more complicated and difficult to describe to a player. Influence decay would just be a black box to most users if the exponent isn't a whole number.

If you put influence decay at ( Influence) / 100)^2, then decay per turn at 1,000 is 100, which means you drop to 900 (and a decay of 81) in 1 turn. That keeps a 1,000 points of spread, still a considerable amount, but diplomacy civs don't go into having leads on other civs 4 digit leads. It doesn't even make competing for city-states feel possible, much less worth it.

I play a lot of King, and at that level you will have civs with high diplomacy flavours have 3-4 city-states with 1,000+ influence, but there's usually 8 or so that are just in the 200-500 range.

I do want to emphasize that the comfort that people feel with 500+ total influence with all city-states is a product of the Statecraft policy that gives Influence per turn via trade routes with City-states. That policy allows you to freeze decay up to that point. The late game diplomacy units, especially when paired with Autocracy, allow you to blow past that equilibrium into the thousands. The decay mechanics offer no counter to the way that Ambassadors become so cheap and give so much influence in the late game.

 

[AndreyK]

I think that cap at 1000 is too low, in this case you wouldn't put any effort at keeping or gaining alliances, everyone will be at 1000 influence, so that will be left to random. Then human player will have advantage by using diplo units right before WC vote.

 

[Stalker0]

Keep in mind that it’s a true “cap” per say, it just becomes exceptionally hard to keep influence at that rate, so in general rates will be lower overall.

 

[vyyt]

Wouldn't an AI malus for diplo units production fix the problem?

 

[Stalker0]

Wouldn't an AI malus for diplo units production fix the problem?

the issue with that is it creates imbalances with AIs thst are focused on diplo units, as they effectively consume more hammers.

But that’s another valid option to consider

 

[vyyt]

the issue with that is it creates imbalances with AIs thst are focused on diplo units, as they effectively consume more hammers.

But that’s another valid option to consider

Sorry, I don't understand. If the problem is that because of the AI bonuses, AIs gain humongous influence over CSs, which hooman player can compete with only by forcing spheres of influence, then wouldn't exempting/decreasing the AI bonus for Diplo units solve the problem?

The CS/Diplo focused AIs could still focus on CSs, and given that bonuses for other production stay in, they will still have more hammers left to assign for Diplo units, no?

 

[Stalker0]

Sorry, I don't understand. If the problem is that because of the AI bonuses, AIs gain humongous influence over CSs, which hooman player can compete with only by forcing spheres of influence, then wouldn't exempting/decreasing the AI bonus for Diplo units solve the problem?

The CS/Diplo focused AIs could still focus on CSs, and given that bonuses for other production stay in, they will still have more hammers left to assign for Diplo units, no?

Your right in that it’s a effective solution to the problem, it just also creates a new problem.

For sake of argument let’s say that a nondiplo AI spends 10k hammers on diplo units over the game, and a diplo AI spends 20k. So the diplo AI is paying 10k more of its diplo advantage.

If we made diplo units 50% more expensive, than the numbers would be 15k and 30k. Both are paying more, and the diplo AI has an even wider pay gap than before.

So In theory this change would reduce the AI production bonus overall, and especially weaken diplo AIs.


So that’s why decay was looked at first, but if decay is not a good way to go I do think this method would be the next best