----- Derivation -----

The manufacturing formula is this:

M = (M0 + NM * etaM) * ( M0% + NM% * etaM% )

where
M ist the total manufacturing in the end
M0 is the flat manufacturing received from none-improvement bonusses
M0% is the flat manufacturing recieved from none manufacturing bonusses
NM is the number of tiles occupied be flat bonus improvements
NM% is the nmber of tiles occupied by percent bonus improvements
etaM and etaM% are the per tile efficiencies of improvements.
N0 is the number of available tiles and must be the sum of NM and NM%

Thus we can substitute NM% = N0 - NM in M, We want to find NM such that M is at a maximum. Thus we calculate the derivative of M with respect to NM and equate it to zero:

0 = etaM * ( M0% + etaM% * ( N0 - NM ) ) - etaM% * ( M0 + etaM * NM )

solving this for NM yields the optimal NM:

NM = 0.5 * [ N0 + M0% / etaM% - M0 / etaM ]

----- EXAMPLE -----

I use the following parameters:
N0 = planet class - 1 (colony capital)
M0% = 100% (no % based bonusses from citizens, tech or starbases)
etaM% = 10% per tile (basic factory with level 2 adjacency)
M0 = 4 (3 pop and 1 production from colony capital, no asteroids)
etaM% = 1.333 per tile (3 cities and 6 farms with level 2 each providing 12 manufacturing in total)

Hence we get:

NM = .5 * [ planet class - 1 + 10 - 3 ] = 0.5 * planet class + 6

This means, if you only get to choose between farms+cities and basic factories and your planet has class 12, you should not build factories and only start doing so above class 12. This neglects the space elevator deep core mines of course, which has a tile efficiency of 2 and thus is better for manufacturing than a city.

They can be considered by raising M0 to 9 (3 form the mine level 3 and 2 from the elevator level 2) and reducing free tiles N0 by 2. Then we get:

NM = .5 * [ planet class - 3 + 10 - 6.75 ] = .5 * planet class + 0.25

Meaning for a class 12 planet you should build 6 cities and farms 3 basic factories while having space elevator, deep core mine and colony capital.

Lets have a look at the assumptions I have made here:
- neglected approval, whose production modifier is multiplicative with etaM% and can multiply it with a factor of up to 1.67 (o approval in city strategy and 100% in factory strategy). On average I would consider a factor of about 1.1-1.25 reasonable here. The effect gets reduced by governance techs (loosing 25% of 100% hurts more than losing 25% of 150%).
- neglected starbases and citizens. starbases and citizens easily let you increase M0% to 150%
- Asteroid mines will increase M0
- technology can raise the tile efficiency of factory and city-farm complexes

This does still sounds like it balances out somewhat.

But we are still neglecting, that cities also provide research and wealth. We can account for that by reducing etaM% to an effective efficiency by dividing by two (four in case of research buildings, because manufacturing has two outputs, social and ship manufacturing, while cities have all 4 outputs). Space elevator tile efficiency would ahve to be adapted by dividing by 2, too and the deep core mine by dividing by 4 since it only has 1 output.

Now lets do another example with these in mind:
N0 = planet class - 3 (colony capital, space elevator, deep core mine)
M0% = 115% ( 3 starbases providing 10% each reduced by a factor of two due to addressing only manufacturing outputs)
etaM% = 6.25% per tile (basic factory with level 2 adjacency, accounting for multiple outputs of cities and approval boosting efficiencies by a factor of 1.25 again)
M0 = 8 (3 pop and 1 production from colony capital, 5 asteroids) + 1 (level 2 space elevator) + 0.75 (level 3 deep core mine) = 10.75
etaM% = 1.333 per tile (3 cities and 6 farms with level 2 each providing 12 manufacturing in total)

NM = .5 * ( planet class - 3 + 18.4  - 8 ) = .5 * planet class + 7.4

And this is substantial. It means a class 19 planet should have 1 colony capital and 16 population improvemens (+colony, capital, space elevator and deep core mine).

----- Conclusion -----

In a balance without flat bonusses from improvements except from population (so there is no commutative addition), the tile efficiency of all manufacturing improvements has to be doubled, that of research labs has to be quadrupled. I am not up to date with wealth improvement values (treasure hunting finances my empire just fine x) ).

I hope this was understandable, feel free to point out mistakes, anyone.

edit: changed up some numbers in the examples, I wan inconsistently treating whether to use all outputs of a city or only one.

To me it would be cool if every building, component, etc. requires a specific output and factories, labs, and wealth improvements turned raw production into output.

I mean it could be as simple as a laser requires 50 Parts 1, or it could be as complicated as a Doom Ray needs 160 items but they are spread amongst four components - 30 Advanced Quantum Subspace Electronics, 30 Advanced Nano Metatube Casings, 50 Advanced Graviton Capacitors, and 50 Anti-tachyon Switches.

In the complicated versions Factories could turn raw production into one of like 10 different components, that advances over time. So for electronics maybe they start with Basic Silicon-Carbon Electronics, which any level one factory could build and it advances from there. 

treborblue,

One good thing about your idea is that it seems like it would be both fairly easy to balance and would allow for specialization. 

While I agree there needs to limits as to what is acceptable in terms of output, not everyone who plays the game is a mathematician. Adding hard caps or limiting free play is going to upset someone. (usually the vocal ones)
I play to have fun, most players do. I don't want to have to get my calculator out every time I colonise a planet.

Balance is key. I assume that when I research an upgrade for a building it will benefit me more. 

Special buildings and special weapons should require special resources, but why does building a city require a special galactic resource, just to cap output. It doesn't feel right.

The problem is exponential growth.

For example, the latest update changed a City to 3 Population +10% Population Cap per Level. This instantly broke Cities. With 3 Cities and a Colonial Hospital, my planet has 24 max population [(3+3+3+3)*2.00]. Before this update, I would only have had 17 max population (3+4.5+4.5+5).

If you want to prevent players form breaking 100N, then reduce exponential growth as much as possible. This means you either have to reduce the  amount of +% bonuses players have access to. For example, Factories with +% bonuses. or Economic Starbases with +% bonuses. It should be fine to have Uniques and Achievements with +% bonuses, because they're difficult to stack.

Keep in mind though, that 3N is an impractical limit for planetary production considering the rising costs of improvements and especially ships by the late game.

Also, the Promethium cost on Cities is not limiting me at all whatsoever.  Instead of trying to limit cities, you could try nerfing them instead. 

One more thing. Why aren't you fixing Factories? They're  awful.

In the real world its like 40n.

There's a lot of PopulationtoProductionExponent between the current 1.0 and the earlier 0.5.

Why not nerf it back down, but not so cripplingly far, so that there is a production falloff with ever increasing populations.

This value was nerfed because there was a problem- farms were king.

Then you add cities, and the crippling effect of this parameter set at 0.5 made them hardly worth the trouble.

If the game mechanics have crashed, then treat them like you would your computer.  Restore it to the last stable state and make different choices.

Hi,

This does seem rather an extraordinary aim given the much higher population and high level buildings available later on and, as has already been pointed out, self defeating  in terms of the game's popularity since a significant component of the enjoyment is building up massive planets.

Also, I'm not quite clear exactly what N refers to. Obviously, if you start with 0.5 population or indeed (if you scandalously modify a constructor) zero then the production with be hugely less than when you get to the initial population limit (and would be even if you were still using square roots). 

So does N refer to the maximum possible output when the then population limit has been reached or something else? 

Cheers,

Jon

[...]

And before exponent .5 we used linear in vanilla, which was engaging. The problem is, that by now so many other variables changed, that reproducing the vanilla equivalent of linear pop to production is not trivial anymore. Now we have to do math.

Why not using a simpler system? Like that (surely more than 3N, but the difference between a just colonized planet with one low tech building and a fully settled planet with a lot of high tier buildings may well be 100N in my opinion):

- Every tier 1 building produces 1 point of output flat (factories 1 point of production, research labs 1 point of research, markets 1 point of wealth)

- Specialization occurs through adjacencies. Every building gives 1 point of adjacency bonus. So a single factory gives only 1 point of production. Two clustered together give each other 1 point of adjacency bonus, so total output is 4. Three factories custered together then gives a total output of 9, four give 16, and so on (it's not quadratic after that, since not every factory can give adjacency bonuses to every other, but only to adjacent ones).

- You need 1 population to operate 1 building. If you have less population then all your people have to work too much which decreases overall efficiency (produced output) by a factor of (pop present / pop needed) ^ 2. If you have too much pop then there is unemployment which decreases efficiency also by a factor of (pop needed / pop present) ^2. Other morale effects like rebellion could happen also more easily.

- Research unlocks higher tier buildings which give 2, 3, 4 points of flat output each. Adjacency bonuses stay at 1 point per adjacent building of the correct type. Research may also increase general productivity, giving an overall % bonus to output.

- Higher tier buildings may need more pop to operate effectively.

- Hub buildings may give higher adjacency bonuses.

- Tile bonuses still exist, but only for the tile itself, not for adjacent tiles (since I find it kind of frustrating nearly never to be able to use tile bonuses efficiently because placing buildings because of tile ajdacency bonuses usually throws away building type adjacencies).

- Special buildings may give more than one kind of output (like research + wealth).

- Population is housed in the colony capital and cities. Cities have no adjacency bonuses as such, but if built on a tile with a bonus spreads this exact bonus to all adjacent tiles (example: building a city on a +2 production tile gives all production buildings around the city a +2 production adjacency bonus).

- Special resources like Snuggler Colony and the like are classified according to their adjacency bonus. You mine them by putting a building of the correct type on the tile with the resource, what also produces its normal output. So no tiles are lost due to resources being present on a planet, but you need double pop to operate such a tile effectively (that's 2 pop instead of 1 for a tier 1 building). Higher tier buildings multiply the special resource output by their tier.

- There is no distinction between social and military production buildings. Instead bring back a slider per planet that determines how much of the overall production of a planet goes into social (building things on the planet and paying for projects) and military (building ships in a sponsored shipyard) production. If there is no sponsored shipyard everything goes into social production.

Has anyone else looked at the Crusade tech tree and thought "This looks stupid"? It just seems so arbitrary and inconsistent, especially when compared to the base game tech tree.

It would be nice if the Crusade tech tree were a bit more sensible.

deleted due to formatting issues.

I can buy this, even though I'm not 100% on board with solely using pop to allow for improvement constructions. However, pop requirement should ONLY be for the "base" improvement types (Production/Research/Wealth and maybe Influence), and never for anything like specialty buildings or Tourism/Food/Approval or the like.

Also, a big NO to requiring more pop for higher tier buildings. They already require more tech, so that's the cost for them. In addition, it makes neither logical sense nor game sense - increasing tech means better productivity (in all senses) for the same amount of population, and requiring more pop for a better improvement virtually nullifies the whole point of researching the higher tech.

Low tier Research, Production, Approval, Food, and Influence buildings should have low maintenance (say 0.5), and each tier should double this. This makes more sense than increasing population requirements, as high tech is expensive, but not pop-intensive.  Wealth and Tourism improvements should NOT charge maintenance, for what should be obvious reasons.

Approval still needs to matter significantly. I'd not do a linear one (e.g. NOT Approval/Pop), but maybe a step function, like every full 10% below 100% knocks off 10% of total production. This is easier to understand - full production should be at 100% approval, and being less happy should lower production, rather than the bifurcated "about 50% gives bonus, below gives penalty" current model. It's far easier to balance my way.

Certainly, though I'd be careful about what the base value and per-level bonus of the hub building it. Hub buildings' PRIMARY benefit should be through adjacencies, and they themselves should provide low-level bonuses even when surrounded by 6 other improvements. For example, something like a Power Plant should maybe give +3 adjacency, but itself only give +1 Production as a base, NO per-level bonus.  More powerful versions of this improvement should up the adjacency bonus, but not the bonuses on the building itself.

I'd also never charge maintenance for either Hub or one-per-planet/civ/galaxy buildings.

Absolutely not. This would remove one of the key fun things of the game, and the fact that it's not easy to make it work well is one of the major challenges. You have to accept that you can't always optimize the layout, but when you do, it can be VERY beneficial.  If you remove this feature, then why should any improvement give adjacency bonuses to more than one type?  It's the same concept.

Of course. I would also add that one-per-civ/one-per galaxy improvements are the things that give % bonuses, rather than flat ones. One-per-planet buildings tend to be Hubs, and thus should be treated as above - if they're not Hubs, then the % rule applies.  But the others should be the thing to really ramp up a single planet's value, so they're the things that absolutely should affect the planet as a whole. Base bonuses in the +50-200% range, and per/level bonuses themselves in the +10-25%/level range. They should themselves give fairly small adjacency (+1 typically or even none), since their value is to the planet as a whole, rather than as a Hub.

Sorta.  Cities absolutely should have adjacency bonuses, but only for fewer things than they do now. They should retain Population as their type, and receive modest per-level bonuses from both adjacent pop and tiles (say +0.25/level or less).  Honestly, Approval absolutely should be one of the big things they give adjacency to, and it should be a MINIMUM of +2.  Tourism as well (bare minimum of +1, and I'd even vote for up to +3).  No bonus for wealth, research, production, food, or influence though.  Cities themselves should give a small influence bonus (say +0.5).

And, of course, we should have a series of City-like improvements, in the same way we have series of Factory, et al. ones.  City, Metropolis, Megopolis, mostly with higher pop cap, but few, if any, other improved bonuses. And cities should NEVER cost maintenance, if we're balancing with the new paradigm - their function is to provide a resource (pop), and charging for that resource seems hideously unfair.

I don't see the need for this - the current model works better, and a resource is treated similar to a Hub building - it provides some base bonus (the resource in this case), no per/level bonus, and it's other benefit is via improved adjacency. In this case, we're not charging pop, since it's a resource (and we shouldn't be charging pop for a planet-bound resource if we don't for asteroid-based ones, and I don't think either are a good idea).  Improvements to the resource mine continue with improved tech, and we stick to the current model. Of all the things here, this is the thing NOT currently broken.

You don't "lose" a tile for the resource, any more than you "lose" a tile for the Capital or any other improvement. You get the resource, and it's a Hub.

Absolutely not. That brings back micromanaging in a REALLY bad way. The current method of using Missions (for Shipyards) and Projects for Social production is both far more flexible, and far less micro, not to mention that it's easy to see on the Colony summary page what a planet is set to be doing. The slider should remain in the graveyard where it belongs.  If you're not sponsoring a shipyard, then that's "wasted" (really, just unused) production. I have no problem with that, and it's far easier to balance (and less micro) than something like a slider.