Influence Upkeep alternatives

For what's not in 'Top Priority Game Design'. Post your ideas, visions, suggestions for the game, rules, modifications, etc.

Moderator: Oberlus

Message
Author
User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Influence Upkeep alternatives

#1 Post by Oberlus »

Thread to discuss and decide the different influence upkeep equations tailored to different strategies.
Vezzra wrote: Thu Oct 29, 2020 1:56 pm
Issue: current influence upkeep equation does not grow faster than number of colonies or population, and so defeats it's exponential-growth control purpose. Is any developer planning to introduce distance-based influence upkeep (either as the default upkeep, my preferred choice, or as one that can be adopted via policies, as long as the default upkeep is something different from current one).
We reached agreement to try the following, and see how that is going to work:

At the start of the game, IP costs are just based on number of colonies. The formula should be exponential, but scale in a way so that the first few colonies have only moderate IP costs, but after that IP costs should ramp up quite drastically. To address this, the player needs to adopt one of several policies which alter the way IP costs are calculated.

One of these policies could be distance-based (with higher costs for colonies which are not supply connected), maybe two number-based (one better for supply connected empires, one better for distributed supply disconnected empires) etc. All these policies will offer significantly better IP costs. The player would choose policies depending on their situation/intended strategy etc.

The starting formula might be something like this: (# of colonies ^2) * 0.2.

The policies for colony IP costs need to be unlocked by comparatively cheap, early game techs, so players can get them before the default IP costs formula cripples their empire.
There is another thread about influence upkeep, focused on a proposal about weighting influence upkeep with galaxy size, which is not well received by some devs because it implies varying influence costs depending on galaxy settings, which in turn means that the optimal time to set a new colony to influence focus (to compensate for increasing infuence costs) would vary depending on galaxy size.
I don't think that is a problem at all, but we'll be better off if we can get other influence upkeep equations that tackle the same problems (scalable to any galaxy size, hampering snowballing) without presenting that unwanted characteristic of varying influence costs.

So, let's discuss.

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#2 Post by Oberlus »

The starting formula might be something like this: (# of colonies ^2) * 0.2.

Factor = 0.2
Exponent = 2
PlanetsIP upkeep per colonyTotal empire IP upkeep
1 0.2 0.2
2 0.8 1.6
3 1.8 5.4
4 3.2 12.8
5 5 25
6 7.2 43.2
7 9.8 68.6
8 12.8 102.4
9 16.2 145.8
10 20 200
That's brutal. It would require acquiring an influence upkeep policy before almost any other tech, sooner than getting third colony. Otherwise, when you have three planets you need 1.5 set to Influence focus, when you have four planets you need three on influence, and you can't afford a fifth planet even with all colonies set to influence.
I mean, if we are forcing players to get first a policy for a better influence upkeep, we can very well unlock from the start all the influence upkeep alternatives intended for early game.


Factor = 0.2
Exponent = 1.1
PlanetsIP upkeep per colonyTotal empire IP upkeep
1 0.2 0.2
2 0.428709385014517 0.857418770029035
3 0.669673904420343 2.00902171326103
4 0.918958683997628 3.67583473599051
5 1.17461894308802 5.8730947154401
6 1.43547743862158 8.61286463172947
7 1.70073966165469 11.9051776315829
8 1.96983106135187 15.7586484908149
9 2.24231569130793 20.1808412217714
10 2.51785082358833 25.1785082358833
Now policy is mandatory before fifth colony, to allow for more than half of your panets set to non-influence. Still too restrictive.


Constant + Factor (# of colonies)^Exponent.
Constant = 0.5
Factor = 0.1
Exponent = 1.2
PlanetsIP upkeep per colonyTotal empire IP upkeep
1 0.6 0.6
2 0.729739670999407 1.45947934199881
3 0.873719281884655 2.62115784565397
4 1.02780316430916 4.11121265723663
5 1.18986483073061 5.94932415365304
6 1.35858144866315 8.15148869197892
7 1.53304121311619 10.7312884918133
8 1.71257325320832 13.7005860256665
9 1.89666101652382 17.0699491487144
10 2.08489319246111 20.8489319246111
12 2.47250219542067 29.6700263450481
15 3.07815789138122 46.1723683707183
With this, when you build your eighth planet you begin to require every new planet set to influence (so ninth planet will imply a net loss of empire general output), and it becomes impossible to maintain an empire with 15 colonies. This means you should get the policy before fifth planet, but you can afford to delay it until seventh planet without much of a loss.

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#3 Post by Oberlus »

As per Vezzra's summary of last online meeting:


A. Influence upkeek for wide, connected empires

- Cost based on number of planets, but with a slower exponential rate than default upkeep (post above).
- Planets disconnected from Capital (or other special buildings) require extra upkeep.

No idea what could this policy be called.
The concept conveyed by the policy name/fluff should not be opposite to centralized or decentralized government, it should be combinable with either of those.
It's too similar to C (see below)...


B. Influence upkeep for centralized/narrow empires

- Distance based, with overall smaller influence costs than default upkeep.
- When de empire grows, it can stick to this policy if some special "centralization" buildings, acting as secondary capitals, are placed strategically. Or it can switch to influence upkeep for wide empires.

This could be the CENTRALIZATION policy, or a new policy that requires it.


C. Influence upkeep for distributed empires

- Cost based on number of planets, but with a slower exponential rate than default upkeep (post above) but slightly faster than A.
- Planets that are not supply-connected to Capital or other special buildings do not require extra upkeep.
- Overall, better than A for disconnected empires, worse than A for connected empires. Distributed empires can/should switch to A once they start rising supply and connecting their supply groups.

This could be the CONFEDERATION policy.


Maybe A should be removed.

User avatar
Krikkitone
Creative Contributor
Posts: 1541
Joined: Sat Sep 13, 2003 6:52 pm

Re: Influence Upkeep alternatives

#4 Post by Krikkitone »

What I could see for ease of understanding

cost per colony
Constant1 + Constant2*# of other colonies + Constant3*distance from capital (base distance +2? if not connected)

That seems a lot easier for understanding than fractional exponents...and easier for adjusting

“Tall” policies increase Constants 2+3 (with some other benefits)
“Wide” policies decrease Constant 2 (with some other penalties)
“Decentralized” policies decrease Constant 3 (with some other penalties)

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#5 Post by Oberlus »

Krikkitone wrote: Fri Oct 30, 2020 10:04 pm cost per colony
Constant1 + Constant2*# of other colonies + Constant3*distance from capital (base distance +2? if not connected)

That seems a lot easier for understanding than fractional exponents...and easier for adjusting
I don't think that could work. There is no exponential upkeep growth for number of colonies, so late game only distance from capital will matter (distance do have some form of exponential growth, sort of).

Total colony upkeep cost would be
N*C1 + (N-1)*C2 + N*C3*AVG_DISTANCE
= N*(C1 + C2 + C3*AVG_DISTANCE) - C2
You can't control N to reduce total colony upkeep cost (reducing N means reducing growth so defeat), and C1 and C2 are linear to N, so the main factor to reduce would be C3, along with trying to keep your empire compact/narrow.

Ophiuchus
Programmer
Posts: 1932
Joined: Tue Sep 30, 2014 10:01 am
Location: Wall IV

Re: Influence Upkeep alternatives

#6 Post by Ophiuchus »

UI/predictibility of course sucks with all these formula approaches (you need basically to know the formula).

Also a problem is the non-monotony of this - basically adding a colony can reduce your influence production. It would be better if just the benefits become smaller.
We could have something like no happiness increase if you run out of influence, this would prevent any ROI on adding new colonies.
Oberlus wrote: Fri Oct 30, 2020 11:48 am Constant + Factor (# of colonies)^Exponent.
Constant = 0.5
Factor = 0.1
Exponent = 1.2
...
With this, when you build your eighth planet you begin to require every new planet set to influence (so ninth planet will imply a net loss of empire general output), and it becomes impossible to maintain an empire with 15 colonies. This means you should get the policy before fifth planet, but you can afford to delay it until seventh planet without much of a loss.
Sounds reasonable. Think we should run with it anyway for the time being to get experience with the balance

If we want an intermediate policy we could have one which works like this: minimal influence cost on a planet if the next colony is four or more hops away. inreasing influence cost for three, two, one, zero hops. This would be good for e.g. a distributed Sly empire without extra settlements in the systems. And it would be bad for supply-connected empires in many cases. It would also be bad if you start putting extra colonies to get the benefits from gas giant generators. So by late mid game Sly usually also would like to switch.
I think such a progession of adopting different policies because of the encountered universe layout and also tech progression makes nice gameplay.
Any code or patches in anything posted here is released under the CC and GPL licences in use for the FO project.

Look, ma... four combat bouts!

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#7 Post by Oberlus »

Ophiuchus wrote: Sat Oct 31, 2020 11:57 am I think such a progession of adopting different policies because of the encountered universe layout and also tech progression makes nice gameplay.
Agree. The same we are not expecting an empire to win a game sticking to mass drivers, or standard armor plates, or basic industry output, we do not have to expect that an early influence-upkeep policy takes you safely to end game.
Ophiuchus wrote: Sat Oct 31, 2020 11:57 am minimal influence cost on a planet if the next colony is four or more hops away. increasing influence cost for three, two, one, zero hops. This would be good for e.g. a distributed Sly empire without extra settlements in the systems. And it would be bad for supply-connected empires in many cases. It would also be bad if you start putting extra colonies to get the benefits from gas giant generators. So by late mid game Sly usually also would like to switch.
I'm not sure I like this. It would force you to go further, delaying your growth a bit if you can get other GGs closer. If that is the intended policy to make life easier to distributed supply-less empires like Sly, it could be not much better than default upkeep with supply-disconnection penalties. Plus I don't see yet a reasonable fluff or policy name for that "you get punished for having nearby other fellow planets, it doesn't matter if you are surrounded by enemy planets".

User avatar
Krikkitone
Creative Contributor
Posts: 1541
Joined: Sat Sep 13, 2003 6:52 pm

Re: Influence Upkeep alternatives

#8 Post by Krikkitone »

Oberlus wrote: Sat Oct 31, 2020 11:28 am
Krikkitone wrote: Fri Oct 30, 2020 10:04 pm cost per colony
Constant1 + Constant2*# of other colonies + Constant3*distance from capital (base distance +2? if not connected)

That seems a lot easier for understanding than fractional exponents...and easier for adjusting
I don't think that could work. There is no exponential upkeep growth for number of colonies, so late game only distance from capital will matter (distance do have some form of exponential growth, sort of).

Total colony upkeep cost would be
N*C1 + (N-1)*C2 + N*C3*AVG_DISTANCE
= N*(C1 + C2 + C3*AVG_DISTANCE) - C2
You can't control N to reduce total colony upkeep cost (reducing N means reducing growth so defeat), and C1 and C2 are linear to N, so the main factor to reduce would be C3, along with trying to keep your empire compact/narrow.

It is exponential

the total for N worlds would be

C1*N + C2*N^2 + C3 * N^~1.5
since distance is ~# of planets to the 0.5 power

Rather than changing the exponent, you change the balance of N^1 (linear) and N^2 (“exponential”) growth by changing the constants.

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#9 Post by Oberlus »

Krikkitone wrote: Sat Oct 31, 2020 11:54 pm It is exponential

the total for N worlds would be

C1*N + C2*N^2 + C3 * N^~1.5
since distance is ~# of planets to the 0.5 power

Rather than changing the exponent, you change the balance of N^1 (linear) and N^2 (“exponential”) growth by changing the constants.
Oh, right, my equation was wrong. Thank you.

Assuming 4 IP per influence-focused planet

For what could be the starting values:
C1 1
C2 0.1
C3 0.2
Population centers Total IP Upkeep Avg. IP upkeep Influence colonies Percentage
1 1.2 1.2 0 0.00%
2 2.76568542494924 1.38284271247462 0 0.00%
3 4.63923048454133 1.54641016151378 1 33.33%
4 6.8 1.7 1 25.00%
5 9.23606797749979 1.84721359549996 2 40.00%
6 11.9393876913398 1.98989794855664 2 33.33%
7 14.9040518354904 2.12915026221292 3 42.86%
8 18.1254833995939 2.26568542494924 4 50.00%
9 21.6 2.4 5 55.56%
10 25.3245553203368 2.53245553203368 6 60.00%
12 33.5138438763306 2.79282032302755 8 66.67%
15 47.6189500386223 3.17459666924148 11 73.33%
17 58.2185591271001 3.42462112512353 14 82.35%
20 75.8885438199983 3.79442719099992 18 90.00%
30 149.86335345031 4.99544511501033 37 123.33%

With all three factors very low:
C1 0.3
C2 0.02
C3 0.02
Population centers Total IP Upkeep Avg. IP upkeep Influence colonies Percentage
1 0.32 0.32 0 0.00%
2 0.696568542494924 0.348284271247462 0 0.00%
3 1.12392304845413 0.374641016151378 0 0.00%
4 1.6 0.4 0 0.00%
5 2.12360679774998 0.424721359549996 0 0.00%
6 2.69393876913398 0.448989794855664 0 0.00%
7 3.31040518354904 0.472915026221292 0 0.00%
8 3.97254833995939 0.496568542494924 0 0.00%
9 4.68 0.52 1 11.11%
10 5.43245553203368 0.543245553203368 1 10.00%
12 7.07138438763306 0.589282032302755 1 8.33%
15 9.86189500386223 0.657459666924148 2 13.33%
17 11.94185591271 0.702462112512353 2 11.76%
20 15.3888543819998 0.769442719099992 3 15.00%
30 29.686335345031 0.989544511501033 7 23.33%
40 48.2596442562694 1.20649110640674 12 30.00%
50 71.0710678118655 1.42142135623731 17 34.00%
70 129.313240371477 1.84733200530681 32 45.71%
100 248 2.48 61 61.00%
150 528.742346141748 3.52494897427832 132 88.00%
200 912.568542494924 4.56284271247462 228 114.00%



With no N²
C1 1
C2 0
C3 0.1
Population centers Total IP Upkeep Avg. IP upkeep Influence colonies Percentage
1 1.1 1.1 0 0.00%
2 2.28284271247462 1.14142135623731 0 0.00%
3 3.51961524227066 1.17320508075689 0 0.00%
4 4.8 1.2 1 25.00%
5 6.1180339887499 1.22360679774998 1 20.00%
6 7.46969384566991 1.24494897427832 1 16.67%
7 8.85202591774521 1.26457513110646 2 28.57%
8 10.262741699797 1.28284271247462 2 25.00%
9 11.7 1.3 2 22.22%
10 13.1622776601684 1.31622776601684 3 30.00%
12 16.1569219381653 1.34641016151378 4 33.33%
15 20.8094750193111 1.38729833462074 5 33.33%
17 24.00927956355 1.41231056256177 6 35.29%
20 28.9442719099992 1.44721359549996 7 35.00%
30 46.431676725155 1.54772255750517 11 36.67%
40 65.298221281347 1.63245553203368 16 40.00%
50 85.3553390593274 1.70710678118655 21 42.00%
70 128.566201857385 1.83666002653408 32 45.71%
100 200 2 49 49.00%
150 333.711730708738 2.22474487139159 83 55.33%
200 482.842712474619 2.41421356237309 120 60.00%
500 1618.0339887499 3.23606797749979 404 80.80%


In the long run, the only viable influence upkeep for sustainable empire expansion is zeroing C2 and letting distance to capital be the only limiting factor.

User avatar
Krikkitone
Creative Contributor
Posts: 1541
Joined: Sat Sep 13, 2003 6:52 pm

Re: Influence Upkeep alternatives

#10 Post by Krikkitone »

0.02 would not be low for C2, it would be high.

I’d say for c2
starting/early tall~0.05
early wide/late tall 0.01
late wide 0.001

(also # of influence worlds needed would change with influence producing techs)

If you want infinite expansion then any exponent >1 (including distance) must be 0. But since these are in a finite galaxy.... a small non 0 number is fine.

the optimum # of worlds is
((Influence output/world) - C1 -C3*avg dist )/ 2*C2
(maximum is 2x that)

User avatar
Vezzra
Release Manager, Design
Posts: 5491
Joined: Wed Nov 16, 2011 12:56 pm
Location: Sol III

Re: Influence Upkeep alternatives

#11 Post by Vezzra »

Oberlus wrote: Sat Oct 31, 2020 12:48 pmThe same we are not expecting an empire to win a game sticking to mass drivers, or standard armor plates, or basic industry output, we do not have to expect that an early influence-upkeep policy takes you safely to end game.
Exactly. Hence, seconded. :D
I'm not sure I like this. It would force you to go further, delaying your growth a bit if you can get other GGs closer. If that is the intended policy to make life easier to distributed supply-less empires like Sly, it could be not much better than default upkeep with supply-disconnection penalties.
If that were the only distributed-supply-disconnected-empire-friendly policy, I would agree. However, as an alternative to another policy aimed at such empires, it can be interesting.

It would favor a playstyle where you only pick the most valuable planets, and therefore need to spread really wide, so that most of your colonies will end up quite far from each other.
Plus I don't see yet a reasonable fluff or policy name for that "you get punished for having nearby other fellow planets, it doesn't matter if you are surrounded by enemy planets".
Well, it would be: "The enemy planets can't see me and don't know that we're here, so they don't bother us. But our fellow [Sly, XYZ, whatever] can, and though we like them, some minimum distance is good for good relations. If you want to get along well with your relatives, don't live in the same house..." ;)

Maybe a fluff explanation along these lines? An empire where the colonies are organized very independently, like a bunch of very loosely federated planets which appreciate a certain independence from each other?

Ophiuchus
Programmer
Posts: 1932
Joined: Tue Sep 30, 2014 10:01 am
Location: Wall IV

Re: Influence Upkeep alternatives

#12 Post by Ophiuchus »

Vezzra wrote: Sun Nov 01, 2020 1:33 pm
Oberlus wrote: Sat Oct 31, 2020 12:48 pmPlus I don't see yet a reasonable fluff or policy name for that "you get punished for having nearby other fellow planets, it doesn't matter if you are surrounded by enemy planets".
Well, it would be: "The enemy planets can't see me and don't know that we're here, so they don't bother us. But our fellow [Sly, XYZ, whatever] can, and though we like them, some minimum distance is good for good relations. If you want to get along well with your relatives, don't live in the same house..." ;)

Maybe a fluff explanation along these lines? An empire where the colonies are organized very independently, like a bunch of very loosely federated planets which appreciate a certain independence from each other?
"Internal Competition" - Our empire thrives on the competition between the planets. the closer the colonies are to each other, the more influence is spent on keeping politic frictions under control

"Imperial Enterprise" - The empire gets structure like a single big company/beaurocracy. The individuals are in perpetual power-struggle against their biggest enemies - their colleagues.

Remote supply-difference would be fluffier/explain commercial competition better than planet hops, but gamewise the mostly fixed metric of a planet distance is better.
Any code or patches in anything posted here is released under the CC and GPL licences in use for the FO project.

Look, ma... four combat bouts!

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#13 Post by Oberlus »

Thanks for all the insights, Krikkitone

This:
Krikkitone wrote: Sun Nov 01, 2020 12:09 pm the optimum # of worlds is
((Influence output/world) - C1 -C3*avg dist )/ 2*C2
(maximum is 2x that)
So total-output-optimum #worlds is always equal to half of maximum-sustainable #worlds?

User avatar
Oberlus
Cosmic Dragon
Posts: 3385
Joined: Mon Apr 10, 2017 4:25 pm

Re: Influence Upkeep alternatives

#14 Post by Oberlus »

Ophiuchus wrote: Sun Nov 01, 2020 6:20 pm
Vezzra wrote: Sun Nov 01, 2020 1:33 pm it would be: "The enemy planets can't see me and don't know that we're here, so they don't bother us. But our fellow [Sly, XYZ, whatever] can, and though we like them, some minimum distance is good for good relations. If you want to get along well with your relatives, don't live in the same house..." ;
"Internal Competition" - Our empire thrives on the competition between the planets. the closer the colonies are to each other, the more influence is spent on keeping politic frictions under control

"Imperial Enterprise" - The empire gets structure like a single big company/beaurocracy. The individuals are in perpetual power-struggle against their biggest enemies - their colleagues.

Remote supply-difference would be fluffier/explain commercial competition better than planet hops, but gamewise the mostly fixed metric of a planet distance is better.
Good, I like those!

User avatar
Krikkitone
Creative Contributor
Posts: 1541
Joined: Sat Sep 13, 2003 6:52 pm

Re: Influence Upkeep alternatives

#15 Post by Krikkitone »

Oberlus wrote: Mon Nov 02, 2020 11:55 am Thanks for all the insights, Krikkitone

This:
Krikkitone wrote: Sun Nov 01, 2020 12:09 pm the optimum # of worlds is
((Influence output/world) - C1 -C3*avg dist )/ 2*C2
(maximum is 2x that)
So total-output-optimum #worlds is always equal to half of maximum-sustainable #worlds?

Well the “avg distance” part messes that up a bit, as does the “average output”.....a 100 world empire will probably have lower average distance and higher average output than a 200 world empire (given worlds are different quality)

But...with an N^2 term, optimum would be 1/2 max yes.

Post Reply