[Vote] (2-34) Change Border Growth Cost Reductions To BGP Modifiers

[azum4roll]

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VP Congress: Session 2, Proposal 34
Now that we have removed additively stacking per-turn tourism penalty from number of cities, the only other additively stacking reduction mechanisms are historic event tourism, which is a much more complicated matter, and border growth cost.

Let's list out the sources of border growth reductions, shall we?

Sovereignty - reduces the exponent by 20%. Out of scope for this change.

Component name	Type	Percentage reduction
Monument/Stele	Building	25%
Ger	Unique Building (Mongolian)	25%
Siberian Riches	Unique Ability (Russian)	25%
Angkor Wat	World Wonder	25%
God of the Expanse	Pantheon	25%

That's it. You can get a maximum of -75% reduction with most civs, and -100% with Russia or Mongolia (or Rome), except it caps at -80%.

The additive nature makes getting more of these reductions always better than getting the previous one. For example, when you build a monument, it effectively speeds up your border growth by 33% (1/0.75 = 1.33). If you stack God of the Expanse on top of it, that speeds up your border growth by 50% (0.75/0.5 = 1.5). Adding Angkor Wat on top of that is a speedup of a whopping 100% (0.5/0.25 = 2), doubling your border growth and any instant yields that come with it. And the last reduction you add is only a multiplier of 0.25/0.2 = 1.25. It's unfortunate that there needs to be a cap to limit this. Or does it?

The policy Fiefdom doubles border growth points gained while the city is in a WLTKD. That column is hardcoded to double BGP, but we can always change that to accept any modifier value and add that column to buildings, beliefs and traits. Since modifiers always stack additively, each of these components effectively give the same benefits regardless of how many of them you already have, and there isn't a need for a cap to avoid division by zero.

The Proposal:
Monument, Stele and Ger increase BGP in the city by 34%.
God of the Expanse increases BGP globally by 34%.
Angkor Wat increases BGP globally by 50% (it's a world wonder after all).
Russian UA stays the same, but the text needs to be changed to clarify that it's a cost reduction. This will be the only border growth cost reduction in VP, and makes Russia and Mongolia no longer share a unique component.

 

[Stalker0]

I don't get why the desire to leave Russia as the odd woman out here. Make it 34% just like everything else.

Also is Fealty staying at 100% BGP?

 

[nekokon]

Agreeable change based on the nature of stacking cost reduction. I also don't mind Russia being the exception if it would be the only source of cost reduction for uniqueness.
Wonder if there's any other stackable cost reduction bonuses somewhere else that should get the same treatment. Iirc pentagon get -50% cost reduction for aircraft or something, which might get too good if there's other stackable source (from VP or other mod mod). Might worth changing them all to future proof (new civ or leader mods, or extra unique components mods)

 

[rkkn]

If they still stack additively, this makes each successive bonus less impactful than the last, yes?
If you've already got a +34%, then adding another one increases that 1.34x to 1.68x, which is 1.68/1.34 = 1.25x

However, most civs only have access to two* three of these anyway, and one is Angkor Wat, which, as proposed, is a larger bonus. +50% added on top of +34% comes out to 1.37x, so that's probably fine. So it's only an issue for Russia and Mongolia.
If Russia's UA stays a cost reduction, then it avoids this issue. Mongolia would still have the issue, but I think Mongolia is less invested in border growth than Russia is.
It is still a nerf to Russia and Mongolia, but having asymptotically stacking bonuses is generally bad design. I can definitely support getting rid of it.

* edit: I somehow forgot there's both monument and god of the expanse, in addition to Angkor Wat. Doesn't change what I said by too much, but it does makes the stacking worse.

I don't get why the desire to leave Russia as the odd woman out here. Make it 34% just like everything else.

Russia's UA would go from having a strong synergy with additional border growth bonuses to having a bit of anti-synergy, with border growth modifiers being relatively smaller than what other civs get instead of larger. That would feel pretty bad.

 

[Stalker0]

UA would go from having a strong synergy with additional border growth bonuses to having a bit of anti-synergy, with border growth modifiers being relatively smaller than what other civs get instead of larger. That would feel pretty bad.

it’s the same thing you today. As you showed, the first discount is effectively 33%, the next one takes it to 50 total (meaning the 2nd one is worth 17).

So this how Russia works today, no reason not to move it into the new system.

 

[rkkn]

All that said, I think border growth could use some more extensive reworking. The cost ramps up so quickly (without Sovereignty) that having 34% more growth merely comes out to being the difference between having 16 instead of 15 tiles (when you include the first 7), and then in the long run, 33 tiles instead of 30

 

[rkkn]

it’s the same thing you today. As you showed, the first discount is effectively 33%, the next one takes it to 50 total (meaning the 2nd one is worth 17).

So this how Russia works today, no reason not to move it into the new system.

I don't understand what you mean

not sure what you mean, so I'll just clarify what I was saying.

Current scenario:
Most civs, upon taking God of the Expanse, effectively gain a 1.33x growth multiplier.
Russia, upon taking God of the Expanse, goes from needing 0.75x points (effectively a 1/0.75 = 1.33x multiplier) to needing 0.5x (effectively a 1/0.5 = 2.0x multiplier). God of the expanse therefore gives Russia a 2.0/1.33 = 1.5x multiplier, which is larger than what other civs get.

With shifting all the bonuses to +34% additive:
Most civs, upon taking God of the Expanse, gain a 1.34x growth multiplier.
Russia, upon taking God of the Expanse, goes having a 1.34x multiplier to having a 1.68x multiplier. God of the expanse therefore gives Russia a 1.68/1.34 = 1.25x multiplier, which is smaller than what other civs get.

That's what I mean by there is a bit of anti-synergy. Russia would get less relative gain than other civs. while previously/currently they get more relative gain

 

[nekokon]

That's what I mean by there is a bit of anti-synergy. Russia would get less relative gain than other civs. while previously/currently they get more relative gain

This is already established in the first post, stacking cost reduction gives extra gain the more bonus you get, thus Russia would gain the most benefits, thus removing that stacking mechanic would nerf what Russia gets. I don't see it as anti-synergy, just the result of nerfing something that Russia greatly benefits from before. You still get good benefits from going for god of expanse as Russia, and it still gives more than doing it as other civ (1.68 vs 1.33), just not as much as it is right now (2.0 vs 1.33)

 

[rkkn]

You still get good benefits from going for god of expanse as Russia

Russia indeed still gets good benefits since it gains yields on border growth.

But. When talking about only border growth itself,

it still gives more than doing it as other civ (1.68 vs 1.33)

this is incorrect, as I outlined above.
Perhaps we are talking about different things. Are you referring to the pantheon's faith and production output? Rather than the border growth itself.

 

[nekokon]

I don't understand what you mean

not sure what you mean, so I'll just clarify what I was saying.

Current scenario:
Most civs, upon taking God of the Expanse, effectively gain a 1.33x growth multiplier.
Russia, upon taking God of the Expanse, goes from needing 0.75x points (effectively a 1/0.75 = 1.33x multiplier) to needing 0.5x (effectively a 1/0.5 = 2.0x multiplier). God of the expanse therefore gives Russia a 2.0/1.33 = 1.5x multiplier, which is larger than what other civs get.

With shifting all the bonuses to +34% additive:
Most civs, upon taking God of the Expanse, gain a 1.34x growth multiplier.
Russia, upon taking God of the Expanse, goes having a 1.34x multiplier to having a 1.68x multiplier. God of the expanse therefore gives Russia a 1.68/1.34 = 1.25x multiplier, which is smaller than what other civs get.

That's what I mean by there is a bit of anti-synergy. Russia would get less relative gain than other civs. while previously/currently they get more relative gain

It's your math.

Oh ok I got what you mean. But it's also listed in one of the posts above that having multiple bonuses would give you diminishing return. I also don't think this count as anti-synergy, as it would happen to every bonuses in the game (like saying getting +100 gpt when you have 1000 gpt is worse than getting +1 gpt when you have 1 gpt)

 

[rkkn]

All that said, I think border growth could use some more extensive reworking. The cost ramps up so quickly (without Sovereignty) that having 34% more growth merely comes out to being the difference between having 16 instead of 15 tiles (when you include the first 7), and then in the long run, 33 tiles instead of 30

Expanding on this, and thinking about it more, I don't think the current broken stacking is actually as much of an outlier as it seems (big caveat: if Sovereignty isn't taken). Because, as noted above, 34% faster border growth does not come anywhere near equating to 34% more border growths. So the fact that it stacks up to the point where an additional bonus gives 100% faster border growth, which sounds insane, is actually not anywhere near as strong as it sounds. It has rather steep diminishing returns, so the fact that stacking reductions has increasing returns kinda offsets that and is not so bad. Changing the formula to have border growth stack linearly would make border growth stacking extremely weak when you don't take sovereignty.

Sovereignty changes things a lot, however, so it's pretty difficult to have any kind of conversation about border growth balance if it's ignored.

 

[pineappledan]

Keeping Russia as the only cost reducer means that border growth boosting abilities are uniquely stronger with her, but still weaker and less stackable than they are now. I like it.

Monument gives +34% BG and Russia only needs 75% of normal tile cost:
Before monument: 1.00/0.75 = 1.33
After monument: 1.34/0.75 = 1.79
So the monument boosts Russian border growth by 46%
In comparison the current monument boosts Russia’s BG by 67% (0.75/1 vs 0.5/1)

 

[Stalker0]

Keeping Russia as the only cost reducer means that border growth boosting abilities are uniquely stronger with her, but still weaker and less stackable than they are now. I like it.

Monument gives +34% BG and Russia only needs 75% of normal tile cost:
Before monument: 1.00/0.75 = 1.33
After monument: 1.34/0.75 = 1.79
So the monument boosts Russian border growth by 46%
In comparison the current monument boosts Russia’s BG by 67% (0.75/1 vs 0.5/1)

Not quite 46%. For % change, its (New - Orig) / Orig.

Or (1.79 - 1.33) / 1.33 = 34.6%.


Now that said, a better example of this might be to actually look at how many BGP you need to get several tiles (anyone know the formula?). Similar to GPP, where +25% to GPP does not mean +25% more GP (because of the way GP costs scale up), a +50% bonus to tile growth does not mean you will have +50% more tiles necessarily.

 

[pineappledan]

Not quite 46%. For % change, its (New - Orig) / Orig.

Or (1.79 - 1.33) / 1.33 = 34.6%.


Now that said, a better example of this might be to actually look at how many BGP you need to get several tiles (anyone know the formula?). Similar to GPP, where +25% to GPP does not mean +25% more GP (because of the way GP costs scale up), a +50% bonus to tile growth does not mean you will have +50% more tiles necessarily.

Yes quite. This is semantics. I said it boosts by X, and I’m clearly calculating a difference between 2 percentages, not calculating a 3rd percentage off of percentages. I don’t agree that viewing these changes as percentage rates of percentage rates gives as accurate a picture, and prefer to use the base value of 1 BGP as reference.

As for looking at growth rate, sure. That’s why tradition’s bonus is so powerful, because the scaling is so impactful. But just looking at 1 case is enough to show that keeping Russia as a cost reduction is stronger and retains synergy with %BGP-altering effects while still being weaker than the present effects.

In a vacuum, we know that most civs in all games only get 1 of these bonuses: the monument. Without stacking, 25% cost reduction is identical to +33% BGP. So this is only to constrain the power of specific wonder/belief/civ combinations (and to eliminate the need for a hard floor)

 

[Stalker0]

Yes quite. This is semantics. I said it boosts by X

Its not semantics, its how math is calculated.
If told you to "boost" 1.33 by 50%, you would take 1.33 * (1 + .5) = 1.995
Likewise at 46% boost would be 1.33 * 1.46 = 1.9418
A 34.6% boost would be 1.33 * 1.346 = 1.7902, the actual number.

The ability is boosting by 34.6%. Now that doesn't toss out your argument or anything, I am not saying your argument is invalid because the number is lower than what you quoting. But saying 46% boost is simply not accurate, so a simple correction.

 

[pineappledan]

It’s not inaccurate. It’s a preference. The way you guys are layering percentages off percentages and deriving multiple layers of percentages is disorienting and confuses the issue.

 

[Stalker0]

It’s not inaccurate. It’s a preference.

sigh. Ok, I guess going forward whenever you give a proposal that says "increases by 10%" or something, I'll need you to clarify what calculation you are intending to use.

 

[rkkn]

referring to both things as % is what's confusing, imo. Which is why I refer to them as multipliers when doing the multiplicative calculation. It's accurate to say that Russia effectively gets an additive +46% from the monument when you say that it's UA is first giving +33%, and also accurate to say it gets a 1.34x multiplier.

 

[Recursive]

I sponsor this.

Proposal sponsored by Recursive.

 

[BornDownUnder]

What about Shoshone and their UA providing more land when they found a city?