After studying and reading the economy threads many times and taking into account my experience with the game and its predecessors. I sat down and did some number crunching and some math to find out how this game really works and how to play better and more efficient.
Disclaimer 1: This is a long post.
Disclaimer 2: This is work related to what's in beta 4. I will not make any attempt to make suggestions about how to change, correct or tweak the system, nor if I like it or dislike it. I just want to come to correct conclusions in reference to what's in the current binary. I leave the rest to you and Stardock to work it out.
Disclaimer 3: I understand that in beta 5 all of this work could be void, I don't care, cause I had a lot of fun going through all of this in my head this Saturday morning (Hi from Europe!).
Intro and basic definitions:
1. Population is converted to production using: production = 2*pop^0.7, other mods that are applied to that are the morale boost and a possible future racial pick.
2. Production is divided by your allocation to manufacturing, research and wealth.
3. Each final output is calculated as: output = production*allocation * (1+ modifiers). Modifiers are: empire wide, relics, buildings, racial picks, colonization events, adjacency bonuses, events, anomalies, etc., for that resource type. They are expressed in percent and in the formula that means 1=100%, 0.35=35% etc. All modifiers of the same type are simply added together. The formula adds 1 cause with no bonuses you get what you put in (base=100%).
4. You can select how much manufacturing is sent to the sponsored shipyard and how much remains on the planet, by using a proportional slider. If you are not building anything on the planet and the shipyard, production is lost.
5. You can select to build a social project to increase resources like research and wealth with production. This project never finishes and produces resources by first dividing the current manufacturing (from pop allocation and all of your bonuses including morale) by four and then feeding that result as base production through the selected resource modifiers:
output = production* manufacturing allocation*(1+ manufacturing mods)/4 * (1+ relevant resource mods)
Remarks and conclusions as stated from people:
-You can't take advantage of your labs or wealth buildings to create more manufacturing.
-Hybrid worlds with social projects produce far more than single resource specialized worlds. They are also more flexible. If you have > 300% manufacturing bonuses you cancel out the penalty and from there on you produce far more.
A Game of.. Domes
So the economy game is about taking advantage of the free slots to build domes, buildings, improvements to produce the resources you need to whack your opponents. For this discussion we will ignore the pop to production transformation and we will also ignore adjacency bonuses and improvement levels.
To keep it simple I'll introduce the basic planetary model [BPM]. In this model each farm produces 1 production, each factory, lab and wealth improvement adds 100% to its respective resource modifiers. Also these planets don't produce any free food, and there is no colony capital to give extra bonuses or production. This model is done purely for illustration purposes, you can interpolate in your game for the missing factors.
Manufacturing force with the power of the Square (TM)
So to produce the most manufacturing given the bpm and the equation you need to maximize:
output = production * (1 + manufacturing mods)
or: output = production + production * manufacturing mods
or if you consider the mods already added to 1: output = production*mods, with allocation = 100 manufacturing.
Geometrically thinking, what's the rectangle that has the largest area and the smallest sides? A square! so optimal output is production = mods or for each 1B pop you need 100% bonus. So for our simple bpm this means farms = factories, so take planet class divide by 2 and build that number of farms and factories. This means that manufacturing is growing geometrically at the rate of the square.
Optimal build order: Allocation is always 100% Manufacturing. Since pop takes time to grow build the factories first and as you are about to reach pop limit add a farm and go back to factories. The yor could have an advantage here for 2 reasons: they have free food so no farms are needed and they can fill the planet with pop much faster. You need to micro between factories and pop though. More analysis is needed here, this might be wrong.
Empire modifiers effect: Since there are no global modifiers for food, as you get more % in manufacturing, you need to destroy factories and add farms!! That's exactly the opposite of what you would expect! More efficiency means maximizing the square and not making one side of the rectangle larger. For the game you have to take into account diminishing returns from 2*pop^0.7
Examples: Class 20 world
10 fact + 10 farms = 10*(1+10) =110 (optimal with integer buildings and slots)
1 farm + 19 fact = (1+19) = 20 (pure factories are five times worse!!! That would be 40 with the right pop formula tough)
19 farm + 1 fact = 19*(1+1) = 38 (same with farms but much better due to 1+1 i.e. base 100% and a doubling.
8 farms + 12 fact = 8*(1+12) = 104 (going down on either side produces worse results)
Creating resources with the power of the Cube (TM)
The fact that in hybrid worlds you feed all the production and all of the manufacturing output into your resource (wealth or research) bonuses is undeniably the best way to go. You set up your specific social project and set the slider to 100% manufacturing and no output to shipyards.
output = prod * (1+manufacturing mods)/4 * (1+resource mods)
Dividing by four might discourage you at first but with a bit of basic algebra:
output = prod * (1+manufacturing mods)* 1/4 * (1+resource mods)
and since multiplication is commutative you can move it anywhere!
or output = prod * (1+manufacturing mods) * (1+resource mods) *0.25
so the “ If you have > 300% manufacturing bonuses...” is not only true but it also works with any other bonuses: morale, wealth, research and in a multiplicative way between them.
Geometrically thinking, what's the rectangular cuboid that has the largest volume and the smallest sides? A cube! So the optimal build is production = manufacturing = resource and in our bpm model: farms = factories = labs or exchanges
So it's read “the output is equal to the 'cube' of all modifiers and the result is divided by four”.
The divisor can be ignored, cause 4 is extremely low. And a cubic function grows much faster than a square function. Given the large numbers in modifiers in the mid to late game the cube blows out of the water any specialized planet with only labs or exchanges, but you can't do this trick with manufacturing.
The cube curve overtakes the square curve at: if n=4 and X^2=X^3/n, x*x = x*x*x/n : x=4 or 1+3 in modifiers: i.e. 300%
Optimal build order: Allocation is always 100% Manufacturing. Since pop takes time to grow build the factories first and as you are about to reach pop limit add a farm and go back to factories. After you are done with the factories you start building the labs or the exchanges.
The yor have an advantage here again: they have free food so no farms slots are needed and they can fill the same planet with more of the other 2 buildings maximizing the cube size better even in class 30 worlds!!
Empire modifiers effect: Since there are no global modifiers for food, as you get more % in manufacturing and in other resources, you need to destroy factories or labs or exchanges depending on what bonuses you collect and add farms!! That's exactly the opposite of what you would expect! More efficiency means maximizing the cube this time and not making one side of the cube larger.
So if you just got 300% in research relics or trade resources (in b5) go through your empire removing labs and adding a factory and a farm on each planet.
Examples: class 30 world bpm:
10 farms, 10 fact, 10 labs: 10 * (1+10)/4 * (1+10) = 302.5
compare with an all labs square approach with the same mods:
15 farms,15 labs: 15*(1+15) = 240
and that's with just 1000% bonuses and 10B pop and we're already way past the /4 penalty....
Even if pop can't grow much bigger than 50-60B, you can do the math for the late game yourself.
1. Diminishing effect from population: The hybrid cubic approach needs pop/3 compared to pop/2 for the 'square' all labs, all exchanges, all factories approach. When you need less pop you hit the diminishing returns later.
2. Compare a civ with 500% research, 0% manufacturing with a civ with 0% research and 500% manufacturing.
-Which one produces more research? They both produce the same research, one will have more factories and the other will have more labs in their hybrid worlds.
-Which one produces the most research by X turns? : Always the one with 500% manufacturing and 0% research. That civ can build the factories and the labs much sooner due to the large bonus. Population grows the same (more or less) for all civs except for the Yor: with the 500% in manufacturing the Yor will be even more ahead in research cause he will build the factories, the labs and the pop much faster!! The manufacturing civ can also build pop growth and morale buildings much faster!
Since you can only build 1 improvement per turn, you can use the slider and minimax the rest production into research or wealth each turn given the improvements that are already built.
3. So since I can't roll other bonuses in manufacturing, and since industry will always be a square growth (p*m) and not a cube growth (p*m*x), manufacturing bonuses are much more precious? : Yes, manufacturing bonuses apply to all your worlds regardless of what you're doing there if you follow the hybrid approach, and there's no other way to boost industry anyway.
4. What about the racial picks to wealth and research? :They only help in the early game just before you switch to the hybrid way and can take the 0.25 penalty. If you have to pick between them and the manufacturing bonus, always pick manufacturing since it also helps with colonization and early fleet production.
5. Starbase effects: With the hybrid approach you take advantage from 2 out of the 3 bonus types in your worlds (manufacturing + 1 other). With the all X approach you would only benefit from 1 out of 3 bonus types. So starbase effects are “doubled”. You also take advantage of the fact that you can roll 2 tier n starbase module effects into 1 resource with the hybrid, otherwise you have to research all tiers of modules to get the 'half' the effect, but you need more modules.
6. Flexibility in upgrades: The hybrid can upgrade buildings to a new tier because there's industry in them worlds! As long as you perform upgrades you don't produce said resource though, unless you play with the sliders at a great loss!
7. Emergency ship building: If you are at war and you need more ships you can instantly switch to building a few extra ships. You can also build the occasional constructor, scout, colony ship, transport in all of your systems and planets! (if you forego a few turns of resource production or play with the slider!)
8. Resource capitals: if you need super research, build both the manufacturing and the research capital on the same planet! If you have a good class planet and can also fix the adjacency bonuses as well. This is especially nice if you're going for a research victory.
9. On worlds where the adjacency bonuses are good or where the planet has a bonus to a resource, you just need less buildings for that resource.
10. If your races buildings are lacking for a particular resource, you just need more of them on the planet to have the same effect in the hybrid. You can still push for a victory of type X even if your buildings aren't up to par.
11. UI: There is no display for the sum of the modifiers, you have to divide the numbers shown to get the sum fast.
12. If your modifier sums are unbalanced, you can trade relics (or trade goods in b5) to produce more! It also makes sense if you don't need all of that approval bonuses that are lying around!
13. Brad and co, are already past the 60%/70% mark for the AI? If the AI doesn't consider the above style, it's a dead fish in the water just as GC2 AI was, with an all labs/factory approach.
Thank you in advance for your comments, corrections, opinions and Karma!