random50

Join Date 03/2006

Research, Production and Economy formulas

WARNING - contains spoilers (sort of)

Being fairly (ok, very) anal, I didn't like not knowing exactly what was going on with regards the calculations. Eg, does building two stock exchanges on a planet give you 60% bonus or 69% (30% compounded twice). 60% of what exactly? Are all types of bonuses lumped together or are they applied multiplicatively? So to resolve this I did a bit of messing about with a battle of the gods scenario. What I found is below. I can't promise it's completely correct, but it seemed pretty accurate (it predicted a few different setups I tried correctly, which was good enough for me!)

1. Bonuses (and presumably penalties, if your chosen one is not in office) from the ruling party are applied as racial bonuses. They are included in the figure on the "civilization stats" screen.

2. Bonuses obtained from the tech tree (eg +10 for Xeno Economics) are applied as racial bonuses. They are included in the figure on the "civilization stats" screen.

3. The government forms are wrongly reported. They ONLY give an economy bonus. The real rate is lower than reported as well. They apply 10/20/30% bonus respectively and are applied as racial bonuses. This is NOT included in the figure on the civilization stats screen.

Economy

The income on a planet is given by

34.5*sqrt(population)*tax rate*(sum of buildings on planet)*racial bonus

I'm not certain about the 34.5, but it's at least very close to that number (34.x). So for example, if you have a Star Democracy, a 20% inherent economy bonus, a 10% bonus from the ruling political party and a tax rate of 50% then you will have

1) A multiplier of 0.5 as tax rate.

2) A racial bonus multiplier of 1+0.2(inherent)+0.1(political party)+0.15(bonus for researching economics through to stock exchanges)+0.2(from Star Democracy)=1.65

A planet with 3 stock exchanges and an economic capital would have:

3) A buildings multiplier for the planet of 1+3(0.3)(stock exchanges)+0.5(econ capital)=2.4

So that planet would provide you with

34.5*sqrt(pop)*0.5*1.65*2.4 BC income every turn.

I'm not entirely certain about that 34.5 or the rounding (if there is any, and if so, how often the formula is rounded in its calculation) so this formula is sometimes a few BC out, but it's pretty accurate.

I have formulas calculating research and social/military production too to reasonable accuracy as well. Should I type that out too or has this already been done somewhere else and I'm wasting my time? If so, then a link would be great!

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so for clarification purposes? all bonuses for a specific bonus (ie economics, military production, ect) are an "addition" to each other rather than a "multiplication"
then this figgure is "multiplied" by your tax rate setting (the .5 for 50%)
then the figgure is "multiplied" by 34.5 (or so?) what is this figgure? a randome figgure that the math told you? ... im thinking that it could be a difficulty modifier mebey?

btw nice work, and bring on the social military calcs also

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Awesome post random50.

I have formulas calculating research and social/military production too to reasonable accuracy as well. Should I type that out too or has this already been done somewhere else and I'm wasting my time?

Post! A cursory search of the wiki didn't turn up anything for me. If it's out there, I haven't seen it. A lot of the documentation (such as it is) is outdated now, anyway.

This is for 1.1, right?

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So government types ONLY give an eco bonus? no 25/50/75 Production & research? I feel so violated, i guess increased production/research was all in my head, i never accually checked, just assumed it happened. Good job

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all bonuses for a specific bonus (ie economics, military production, ect) are an "addition" to each other rather than a "multiplication"

Yep. Sort of. Both economy and production have two separate multipliers, but within each multiplier the bonuses are additive, not multiplicative.

ie, as above, there's a buildings multiplier for economy and that category definitely contains stock exchanges and the econ capital. An econ capital plus a stock exchange combine to give a multiplier of 1.8, not 1.5*1.3. Two SE gives 1.6, not 1.3*1.3 and so on. There's a few other buildings that give econ bonuses (manufacturing capital is one, from memory). Presumably they also fall into the buildings multiplier, though I've not checked.

then the figgure is "multiplied" by 34.5 (or so?) what is this figgure? a randome figgure that the math told you? ... im thinking that it could be a difficulty modifier mebey?

Yep, it came from the math. I couldn't pin it down exactly...I suspect because of rounding issues. It gives the right values to within a percent or two though. I don't THINK it's affected by difficulty, but it DOES change by scenario. The Battle of the Gods scenario has a much lower multiple...around 25 if I remember rightly. That confused me for a while when I was working this stuff out as initially I was assuming the 34.5 I'd already worked out from the normal scenario!

This is for 1.1, right?

Yep.

Been there, did that.

I only realised it didn't work after seeing posts on these boards. And it wasn't until I checked yesterday I found out it wasn't even giving the econ bonus claimed. I can't for the life of me understand why they're changing the game mechanics WITHOUT changing the corresponding UI entry. I'd have thought that's a minute's work!?

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(censored) (censored) (censored) (censored) internet connection!

That's 15 minutes of life wasted. And of course the oh so helpful "server not found" error message came up the split second before I pressed Ctrl+c to save the post!

Anyway, skimping on the detail as I'm not typing it all out again right now...

For research and social/military there are again two multipliers, aside from the obvious slider ones.

1. Buildings...for research this is tech capital, omega research (which appears to be planet wide NOT civ wide as claimed). For manufacturing it's the manufacturing capital alone (I think...I may be forgetting some of the other superprojects)

2. Racial multiplier...whatever is displayed on your civ stats screen (which is inherent+political party+researched techs bonus)+(oddly) any starbase bonuses covering that planet.

Again, bonuses within each class are additive not multiplicative, so a 20% bonus and a 30% bonus gives an overall 1.5 multiplier, not 1.2*1.3.

Then the production and research on a planet, assuming NO planet focus selected, is given by

Relevant production points (ie research buildings for research, factories for military/social) provided by buildings on the planet*spendings sliders*buildings multiplier*racial multiplier

Things I haven't yet figured out or have yet to investigate:

1. What's going on with rings/moons. The 10% bonus they're supposed to provide doesn't seem to get added to either multiplier, nor does it work as an individual multiplier. As a stopgap, taking HALF the bonus and applying it to one of the multipliers (either one, but not both) will be a little more accurate than ignoring the bonus altogether. I suspect this comment will also apply to any bonuses or penalties resulting from colonization and other random events.
2. How planetary focus changes things.
3. How mining resource bonuses are applied.

LOL! Seems like I am typing most of it out again after all! This time I've Ctrl+Ced it. Of course, this time it won't crash!

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And here's the explanation of the focus buttons:

Tech is translated into military/social (and vice versa) at the rate of 1 BC of spending for every 4.

Military is shifted to social (and vice versa) at the rate of 1 BC of spending for every 2.

This translation is calculated based on the production before ANY racial or planet building bonuses are applied but AFTER any special tiles bonuses.

For example, if you have 40 potential manufacturing points and 60 potential research points on a planet (that's purely the sum of the MP and TP of the factories, labs and initial colony or civ capital) then:

If you set spending and research sliders to 100%, you'll be producing 60 research points, modified by bonuses as I described above. If you then click the "social" focus button, 15 of those research points will be transferred to social production. Those 15 points will receive bonuses from racial abilities and planetary buildings exactly as outlined above for social production. Meanwhile, the remaining 45 research points will receive bonuses from racial abilities and planetary buildings as outlined above for research production.

If you had 50/50 spending in military and research on the same planet then you'll have a base of 30 points going into research and 20 going into military. Clicking social focus now would send 10 of the military points into social and 7 (it rounds down) of the research points.

What this means is that (yet again) contrary to claims in the manual and in-game tutorials, using the focus buttons does NOT automatically result in a loss of overall production. In fact, if you have a higher overall multiplier on a planet in the area of focus than in the other areas, focusing will actually INCREASE the total production on a planet.

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Hi!
random50, good work!

I suggest you to post that on wiki. Here on forums this will get lost in two days.

BR, Iztok

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One question:
Since tax is releted to square root of population number dosn't that mean that there are diminishing returns for bigger planets.
I mean two colonies with pop of 9 will give two plantets with mutiplier of 3, while one with 18pop will just give 4.24

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Hi!
random50, good work!
I suggest you to post that on wiki. Here on forums this will get lost in two days.
BR, Iztok

I've never used WIKI so whilst I may get round to it eventually, don't hold your breath.

If somebody wants to get the ball rolling for me using this info, you're very welcome. I'll stop by and correct any errors and try to update it if/when I discover anything new.

Since tax is releted to square root of population number dosn't that mean that there are diminishing returns for bigger planets.
I mean two colonies with pop of 9 will give two plantets with mutiplier of 3, while one with 18pop will just give 4.24

Yes, you'll get more BASE income from any given population the more planets that it's spread over.

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A few more bits of info to add:

1. Mining resource bonuses are added to your racial ability and are included in the figure on the civ stats screen. They are therefore additive to the racial multiplier in the formulas.

2. Morale is entirely additive. That is, a 50% morale building will give the same bonus whether you have no inherent racial morale bonuses at all, or whether you're loaded up with morale resource starbases and inherent racial abilities. There are several components:

Base racial ability: as displayed in the civ stats screen. This consists of inherent bonuses+political party bonuses+tech tree bonuses+morale resource bonuses

Base planet ability: simply the sum of all morale contributions from buildings on the planet

Morale is then given (approximately) by:

(base racial + base planet)/(1.025^adjusted pop)-(Adjusted population*3)+"good planet bonus"-tax rate penalty

Notice the base racial, base planet and "population size" components are all scaled by the adjusted population, which is just population (in billions) - 1. The last two components, the 10% high quality planet bonus you get for PQ 11+, and the tax rate penalty are NOT scaled. That is, they're identical whether you have 0.1B or 100B on the planet.

I went as high as 23B population to get these formulas. They may not extend much beyond that (I've heard there's cap on the "population size penalty") and they're not brilliantly accurate (not bad though). The upshot is it shouldn't be too much trouble to have populations of 15-20B with a tax rate of 79% without wasting tiles on (standard) morale buildings, provided you pay some attention to morale research and the various morale boosting trade goods in the game. But it may be tough to go beyond that without heavily upgraded morale resources or inherent/political party boosts.

3. Population growth is...odd. I suspect it's capped at 0.2B per week, BUT racial population growth ability is applied ON TOP of this cap. What's for certain is it does not simply compound. If you have 12B people on one planet, then (depending on exactly what your morale/pop growth ability is) the odds are very good your total population will grow quite a bit slower than if you had 2 planets with 6B people on. (If it was simple compounding, the pop growth would be identical in both cases).

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Sure is great how this is all well-documented by Stardock, isn't it? Otherwise we'd have to... oh, wait.

At least posts like this take us one step closer to having accurate documentation. Very nice.

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random50,
do you have the latest patch (1.1)?
Since your growth formula souns too much like pre1.1 growth formula (take look at wiki for pre1.1 and 1.1 growth formulas).

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Yes I have 1.1.

I haven't produced a growth formula, just made a couple of comments about it.

I was interested in morale so started a game as a custom race with 70% pop growth. I set tax rate to 0 (just wanted to grow population as quickly as possible) then I hit "turn" an awful lot of times. What I noticed was that I got exactly the same population growth per turn when I had 15B population as when I had 5B. Furthermore, when I'd gone as far as I was interested (20B pop), I looked at the civ stats...I was rock bottom (by a very long way) in population. This couldn't happen without a cap.

I also ran a battle of the gods scenario or two whilst I was testing this with the terrans. One I used the natural racial abilities. The other I had 70% pop growth again and immediately built aphrodisiac. As before, the pop growth was identical whether I had 5 or 15B BUT it WAS different in the two games.

So....there's a cap, but population growth ability is applied to that capped number.

I've just looked at the wiki, and it says the same thing. It also gives the size of that cap as 150. I guessed 200, but didn't work it out.

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Figured out the planet quality ability bonuses at last.

Every planet has a base quality and an enhancement potential. This enhancement potential is applied as a multiplier to the base PQ and rounded down. This then gives you the number of extra tiles available through each of soil enhancement, habitat improvement and terraforming.

Example: Earth has an enhancement potential of 17% and starts off as PQ 10. With the 10% PQ ability the bases changes to 11. 17% of 11 is 1.7, so you only get one extra tile per planetary improvement type. With the 20% PQ ability, the base becomes 12. 17% of 12 is 2.04, so you get two extra tiles per planetary improvement type.

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random50, I'd just like to say you're a legend. Great work!

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Let us know if you figure out the production bonus for moons, because I don't think it's working. Start a new game with no racial bonuses to military production, set spending to 100% and start building a ship. Do you see any bonus production? I just get the base 24.

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Yes, I noticed the same thing. However, build or buy a few factories and you'll notice you do get some bonus production. So it does work to some extent.

Just looked in my current game, and the formula works perfectly for planets without bonus production from moons and/or colonization events. When there IS some bonus production supposed to be there I do indeed see some extra production, but not as much as there's supposed to be.

Things I've now tried to calculate it:

1. Include an additional multiplier to be applied after using the formula (overestimate)
2. Apply it as a bonus to the buildings multiplier (overestimate)
3. Apply it as a bonus to the racial multiplier (overestimate)
4. Apply it just to the factories (depends how many factories, but normally an overestimate)

I'm out of ideas now.

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FYI: you can see that things like morale building or market building bonuses stack by looking on the Summary screen. If you had, say, two VRC's (+60% morale each) and a stock market (+10% morale), at the bottom of that screen, you'd see Morale: +130%.

For morale, that bonus gets applied to the base morale of the planet (which varies by population), and then (I think) the taxaxtion modifier is applied. The kicker is that the base morale drops rapidly once you hit 20B pop. (It's base 40 at 20B, and base 20 at 25B) So the morale bonuses have very small effect once you hit 25B pop. It seems far far better, income-wise, to cap your pop under 20B, and build lots of stock markets that to increase your pop past 25B and need to build tons of morale buildings.

For maximum population growth (and thus income growth) under the population growth cap: the more planets, the better, since each planet has its own cap and so 10x the planets means 10x the growth. The only downside is that colony maitenance will be more than your income if population is too small. I'm not sure where the break-even line is, but seeding your colonies with higher initial pops should help keep the maintenance costs from overwhelming your income if you're a super-expander. As long as you keep your original world from dropping below the point where it stops gaining max pop per turn, there seems little reason not to spread your population out. At least, not until you need to worry about getting invaded!

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I tried your Revenue formula, from the first post, and could not get it to work for me.

Eg.

Racial bonus including Mining and Tech bonuses reports 120& on the racial stats screen.
In The second level of government which according to you yields 20%
I have one econ building on the planet(stock exchange) which give 30% bonus.
My tax rate is 80%.
Population of 7.84

So with your formula I should have:
34.5*2.8*.80*1.3*2.2*1.2
= 265.225

The problem is that the planet reports a revenue of 160
So where am I going wrong in my calculation?

I tried several planets and found the same thing for all of them.

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3. The government forms are wrongly reported. They ONLY give an economy bonus. The real rate is lower than reported as well. They apply 10/20/30% bonus respectively and are applied as racial bonuses. This is NOT included in the figure on the civilization stats screen.

Off Topic:
I guess the discriptions in this game are beyond reality in many places. I've noticed stuff like this already a couple of times, though I didn't really give it much notice and so i cant remember clearly anymore where I've observed these faulty discriptions. The only ones I can recall for sure is the tech research anomaly. It sais it lets the tech advace by 25 %, in truth its only gives about 15 %. Another thing I've observed is the planet Quality Increase-option within the ethical random events. After choosing an 40% quality increase on an class 13 planet it became a class 16 planet.
Check: 13*1.4=18.2

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Castellon: the short answer is the formula is wrong. A multiplier of 24 rather than 34 will get you much nearer the mark. That's actually the multiplier I found in Battle of the Gods. I think when I checked it in a normal scenario I must have had one of the other government forms without realising which lead to the wrong calculation.

Also, I think the government form should be added to the racial bonus multiplier, so multiply by 2.4 not 2.2*1.2. It's still 5% out though.

I've just had a look again at the numbers and they become increasingly inaccurate the further away from the "norm" you go (ie very low or high populations, very high racial bonuses). This suggests to me that a*sqrt(pop) (the assumption I've used for the form of the formula) is the major component, but there's something else in there too.

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Figured out the planet quality ability bonuses at last.

Good man, Random.

This means that the PQ bonus only affect how many extra tiles you get. Hmmm, I may need to readjust my modified Yor.

Here's what I don't get. Why is it that, given the huge number of "Planet Quality Bonus Doesn't Work" threads, why didn't someone from StarDock just tell us what it does? Why did someone else have to go and figure it out?

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Alfonse

This means that the PQ bonus only affect how many extra tiles you get.

What else were you thinking it might do?

In case I didn't make myself clear, it DOES affect how many base tiles you get when you colonize (eg if it looks like class 10 before you colonize, it'll be class 12 with 12 tiles after you colonize with the 20% pq bonus) It can also potentially tip any planet you colonize into having 3 extra tiles (on top of the base extras) after all the planetary improvements, but that won't happen very often. Don't forget there's a decent chance it'll push you over the PQ 10 barrier when you'll get that 10% morale bonus.

So overall, it's nice, but probably not worth 8 points unless you're confident of colonizing a very large portion of the map.

Castellon: any chance you could get the savefile of that game to me? It sounds like the ideal type to run calcs on (sounds like you have a few whopping econ resource starbases in there as well).

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OK, I've done a bit more tinkering...

This is a much better model for the economy:

31.5*sqrt(pop)*(sum of buildings on planet)*(racial ability bonus)*government form

As before, the government form gives 10/20/30, not the 25/50/75 reported in the UI.

This formula is very accurate (much more so than the original) for all the planets in the two different save games I have.

Castellon, can you doublecheck your figures please. I have a planet with 1 stock exhange, 7.22B population, first form of government and 65% racial bonus and THAT'S producing 160 revenue at 80% tax rate, so it seems extremely odd you're getting the same with a sligthly higher population, better government and double the racial bonus. If it really is like you say, then I'm wondering if the econ starbase bonuses are nerfed (I have no econ resources in either game)

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Happy to send it to you, you can PM me the Address at Paradox if you like or Email
forum_admin@paradoxplaza.com

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