Unless the XML file containing the racial traits doesn't include all the modifiers, then Productive only gives the manufacturing bonus.

Furthermore, checking against a homeworld with 10 population and 50% approval, there is no evidence for a +1 production from Productive. The expected raw production of such a world is 20.02 if there isn't a production bonus from Productive or 21.02 if there is, and the raw manufacturing/research/wealth production at 100% slider position is 20.0 (give or take; sometimes you get 19.9, sometimes you get 20, most likely due to a slider position which isn't exactly 100% but which rounds to 100%). The sum of the raw outputs with the slider in default position is 20.1 (6.7*3), which is within the margin of error for rounding to the tenths place in the manufacturing/research/wealth tool tips; besides which, at 21 base production each of those raw output values should be 7 rather than 6.7.

Therefore, I would rule out the possibility that Productive gives bonuses to raw production. You may, however, have the tech that grants +1 raw production (Enhanced Production in the Colonization tree, same specialization as Soil Enhancement and Enhanced Growth, if I recall correctly; if there are other such techs, I cannot think of them off the top of my head). There are also a few technologies that grant percentage bonuses to production, at least in the Terran tree; they're mostly in the governments section of the Influence tree, if I recall correctly.

As for how the production bonus from a starbase stacks with the production bonus from approval, I believe it is additive. I checked this on a homeworld with 6.7 population, 100% approval (+25% production), 1 economic starbase (+10% production), and Enhanced Production (+1 production). The homeworld's raw manufacturing at 100% manufacturing was 25.0; if we assume that rounding in game always rounds up on the slider values and rounds down on the raw manufacturing values, then the maximum possible production which would give us "25.0" raw manufacturing at "100%" manufacturing is 25.1 / 0.99 = 25.35. The expected value of the planet's production with the starbase bonus stacking multiplicatively with the approval bonus is (11 + 2*6.7^0.7)*1.25*1.1 = 25.54, while the expected value of the planet's production with the starbase bonus stacking additively with the approval bonus is (11 + 2*6.7^0.7)*(1 + 0.25 + 0.1) = 25.07. Setting the sliders to 33%/33%/33% gave raw production values of 8.4/8.4/8.3, which sums to 25.1, while setting the sliders to 50%/50%/0% gave raw output values of 12.5/12.5/0.0; if the production had been 25.5 these should have been roughly 8.5/8.5/8.5 and 12.8/12.8/0 respectively.

I think there's enough there to conclude that the starbase production bonus stacks additively with the approval production bonus, and since this is the case I would further presume that the starbase production bonuses stack additively with one another. This is what I'd expect regardless, as this is how all other multipliers in the game behave.

As far as getting the numbers in Bamdorf's example to work:

Bamdorf probably has +1 production globally from Enhanced Production, accounting for the +1 that Bamdorf misattributed to the Productive trait. The planet has +5 production from its capital and +1 production from the Durantium Refinery. Together, this gives +7 flat production. We see evidence of two economic starbases for +20% production, and of 100% approval for +25% production, giving a known multiplier of 1.45 (which accounts for the -1.5 production from removing the Durantium Refinery, with a little rounding). I suspect that Bamdorf has Interstellar Governance (or its equivalent, if not using the Terran tech tree), which gives a further +10% production, though this wasn't mentioned in the details of the example.

(5 + 1 + 1 + 2 * 4^0.7) * (1 + 0.25 + 2 * 0.1 + 0.1) = 12.28 * 1.55 = 19.03

Bamdorf, does this solve your bookkeeping issues? Have you researched a tech in the Influence tree that gives a +10% production bonus, or do you have a third economic starbase that you forgot about? Also be aware that there's a bit of rounding that goes on in the game; if you round the base production to 12.3, then you'll get a base production of 19.07, which would round to 19.1 when displayed in game.

Well, I find starbases are highly effective - but mostly as a way to burn off excess production on manu worlds when im not at war. Far more effective than projects IMO. See, unlike buildings, you can stack multiple constructor modules on a single ship. Once I get large hulls I can usually stack at least 6 construction modules on a single ship, and pump them out at 1/turn. This is roughly equivalent to about 1 fully upgraded factory, assuming you have researched a decent way down the manu line. But the key is 1 starbase per turn. Where a fully upgraded factory might take 5 turns to build. So, when thought of that way, its actually a highly effective way to boost your worlds. Just dont waste too much time on them until you can produce a bunch of construction modules at once. 

Also a great way to add manu to research worlds for upgrading etc. And stacking 5 or so starbases around a world is easy.

Well, I am not a math person, but I have learned a lot reading the forum and I use the hints that I understand, if they don't work me to death.

I am mostly an intuitive player, and it is surprising how close intuition comes to math sometimes. I have never built farms on 10 and under planets simply because there isn't room and I don't build more than 1-2 on my best colonies. Nice to know that math supports me.

By late game there are not many 10 and under colonies. They have all been upgraded to 15 or more so I will go back and build some farms on the new space that is available.

This is wrong as far as I can tell though. I just started a new game. First turn, first planet, population 10. If I look at my raw manufacturing, research, and wealth, they are 6.6 each (more after bonuses are applied. If the 2*P^0.7 was correct my total production would be 8.1. Divide that by 3 each would get 2.7 points, not the 6.6 that the game shows. What am I missing? Is there a modification that you do the production after that formula is applied? Does the game show the full breakdown somewhere?

 First, you need to keep in mind proper order of operations.  You show 2*10^.7 as being = 8.1, which can only happen if you did (2 * 10) ^ .7

Exponents always happen before multiplication, so 2*10^.7 is supposed to be calculated as (10 ^ .7) * 2 = 10.02

Now that that is covered, your production is:

((2*P^.7) + Flat bonuses) * Multiplicative bonuses

Flat bonuses could include tech, durantium factories, etc.

Multiplicative bonuses would be things like your factories, racial bonuses, starbases, approval mods, etc.  These are generally additive multipliers.

In your example

((2 * (10^.7) + 5 Colony Capital + 5 Civilization Capital) * 1.00 = 20.024

Then you have to multiply in your approval modifier, which joeball mentions in the next post.  At 48% approval you'd have a 1% penalty to production, so 20.024 * .99 = 19.82

If you split it evenly you'd see 6.6 of each.

Have you accounted for the +5 flat production from the civilization capital and the +5 flat production from the colony capital? Illauna's formula is correct for population effects, not for the full base production. A civilization capital with 10 population can be expected to have

10 + 2 * 10^0.7 ~= 20.0 flat production

This will be further modified by approval. At game start, a homeworld for a non-Patriotic non-Content faction will have 48% approval, which should give a ~1% penalty to base production, leaving you with 19.8 base production. 19.8 divided evenly across three output types gives 6.6 to each production type, which is what you have.

And no, there is not a full breakdown anywhere. Planetary production is about as hidden from the player as it is possible for something to be while the player still has access to numbers which are based off of it (or upon which it is based) in a known way.

Actually, I'm reasonably certain the game would round this up to 6.7 rather than down to 6.6. However, it was stated that this was at the beginning of the game, and a standard homeworld ahs 4.8 morale (+3 for the colony capital, +2 for being the civilization capital, -0.2 for having a 'large empire' of one "colony") and 10 population, giving an approval rate of 48% for an approval modifier of -1% or so to production.

You're right joeball, my mistake.

Hmm, if the approval bonus/penalty to production is additive with other production multipliers, that means Malevolent Thalans (or a custom using their tree) could basically ignore approval (from a production standpoint). My capital in my first real game with this combo had something like +250% or more total production due to Hive + Death Furnace + adjacency bonuses, on top of a slue of manufacturing bonuses, and as many Durantium Refineries as possible so that +1 production gets multiplied to insanity.

That game also taught me the +100% military manufacturing is nuts. There are very few sources of that bonus, so it was effectively doubling my production from my homeworld to my shipyard. I ended up giving it its own shipyard and it was still faster than a 5 sponser yard.

EDIT: Also, hi Arumba! So excited to see you participating in the community and growth of this game.

I'm just another nerd, trying to make the game(s) I love better

Thanks so much Arumba and joeball123. That makes a lot more sense. Also a bit embarrassed that I forgot to apply the exponent first. Stupid math.

I am not a min/maxer by any means, but I do like to know where the numbers come from.

Also, note that increased population makes it harder for an invasion to succeed.  Approval affects the "Resistance" modifier, but the actual invasion success is calculated against the total population in absolute terms.

Also, each "level" bonus from adjacency or tile varies in effect, based on the structure.  The way to see the effect is hover over the structure, and look at the popup stats, and in the middle of it, you will see a section headlined "Level X", and the bonus associated with that level.

For example, most 1- and 2- level buildings give a +5% per level bonus. Level 3 buildings often give a +10% per level bonus, and certain buildings don't do percentages (e.g. Food and Approval buildings give base number bonuses, not percentage bonuses).

Depends on the building, the Malevolent Intimidation Center for instance gives a percentage boost to Approval, with that boost increasing with adjacency. So much so that it and a regular approval building is usually enough for a planet and a bit of extra growth as well.

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REPLY

Ok, so I see three things.  One is that I have the techs interstellar governance (production 10%) and enhanced production ( 1 flat).    Also, apparently the productive racial trait, whiich is listed in the manufacturing bonuses and says +1 to production AND +15% does not add to base production.   Third, all the percentage production pluses are added beefore being multiplied.    So 25% approval + 2x 10% starbase factories + 10% for interstellar governance are one factor 1 + .25 + .2 + .1 = 1.55.   Thus I get to where you got and it agrees with what the game said.   OK.

So I decided to do one more. I chose my Capital, what the heck.

Input information:  Approval 100% -> 25% bonus.   1 Starbase factory for 10%, and enhanced governance for 10%.    Flat bonuses are 5 for colony capital and 1 for enhanced production.    The total raw production was 28.7.   So I got

(5  + 1 + 2 * 8.3^.7) * (1 +.25 + .1 + .1)  = something not even close.  Aha.  It is the civilization capital which ADDS TO the colony capital (not immediately obvious!) so there is another additive 5 at the beginning.   This gives the right answer.

(5 + 5   + 1 + 2 * 8.3^.7) * (1 +.25 + .1 + .1) = 28.7

Sigh.  Yes, perhaps it was time for me to retire.

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Summary.

1.  Thanks very much for helping me sort this.  The "multiplicative" items being added before being multiplied, and a more careful look at the tech tree, were the keys.

2.  The labeling of various items in the data displays is very confusing, both as to how a bonus applies AND to how it figures into the calculation.  A study of the Defs directory isn't a lot of help.  The productive bonus being listed as production+1 .... 15% in the manufacturing table is one of the worst examples.

3.  I would comment that people who talk about "intuitive" results being pretty good have a point.   A few games, paying a little attention to your choices and varying things will give one a decent idea, or should.  I agree.   

4.  I am old school, retired scientist.   So I don't believe anything until I can calculate it spot on.   And then I can objectively confirm my intuition, and maybe able to improve my choices, or my order of choices,  because I know what their effect will be.

Thanks again.

Happy to help. It doesn't help that the symbol used for production and the symbol used for manufacturing output are either identical or so similar that I can't tell the difference, and I agree that Productive +1 (or +2) is easily one of the more deceptive traits in terms of what its name suggests it would do and what it actually does; I'd tend to prefer that they hadn't hidden the trait bonuses behind names and level numbers and instead just directly displayed the bonuses, but oh well.

It would also help if planetary production weren't almost completely hidden from the player. A number showing total planetary production and a tool tip somewhere summarizing everything contributing to your planetary production would be great, even if it was buried in the Govern Planet screen or an 'advanced planet details' screen, especially since it's such a pain to track down all the bonuses you have if you don't know exactly where to look. It doesn't help that it seems as though most or all things which refer to production and have a symbol use the same symbol used for manufacturing-related things (at any rate, the symbols appear identical to me).

I wouldn't say that missing that the colony capital bonus and the civilization capital bonus add together is necessarily evidence that it was time to retire. I missed that when I was first playing with the formulas, and I'm far from retirement age. Really annoying, too, when the formula works for every data point you take except for those from your homeworld, especially since the fact that it's off by a constant gets concealed by the approval modifier, which as a hidden modifier is easy to forget about.

Fair enough I have no actual knowledge of the formula just that ^ normally means to the power of.

The difference between Production and Manufacturing are most likely the greatest source of confusion in this whole debate and they should really be explained or rather the difference in the game should be more clear.

For example... a modifier on Production is usually much more powerful that a modifier on either Manufacturing, Research or Wealth.

So... a 100 Approval planet give you a +25% modification on a planets Production value while two basic factories next to each other add 60% bonus to the Manufacturing value. A planet that has a Production value of 20 (from population and the capitol) this value is modified to 25 with max approval. If you slide all Production into Manufacturing the 60% of those factories increase the total from 25 to 40 available Manufacturing per turn. With an approval of 50 that would be 32 Manufacturing points. In order to increase a colony with 50 approval to the same level a 100 approval colony produce in this example you would need a total of 100% Manufacturing bonus.

All bonuses on values are also additive, this holds true for Production as well... so a planet with 100 approval and an Economic base who give another 10% will increase the Production value with 35%. After this you divide the production between Manufacturing, Research and Wealth.

You make a great point. 

For some time I  figured that a durantium refinery isn't all that great a building, despite the nice +3 manufacturing adjacency bonuses.   But that +1 flat addition to base production is more than it looks like - bonuses to raw production are always 100% in use because they build up the raw production of  a colony which can contribute to Manufacturing, Research, or Wealth, as you say, and a flat increase is added in before multiplicative raw production bonuses, and the approval bonus, are applied.  (And before specific Manufacturing, Wealth, or Research multipliers are applied, it goes without saying.)   And that 0.1 multiplicative contribution to total production from the first ring of an economy starbase is similarly very useful.  Four econ Starbases early in the game will give a 0.4 additive multiplier to a colony's Raw production - that's a serious improvement.

Clearly, building stuff or researching tech that increases Raw production should have a high priority.  But it's rather important to clearly understand what you are getting!   I think there needs to be a fix put in;  not a big fix, since it is just relabeling stuff I should think.  Just a wee bit of care applied, por favor.

(None of this discussion has gotten to the business of project contributions....arrgh!)

i think the system is quite viable as it is. population, approval and modifiers to both the raw production and the final yield are all useful. there's room for improvement, though. the initial economy starbase ring is by far the most powerful ring - so much so that it's plain an simple a bad idea to upgrade the star bases when there is still room for another baseline economy base. i think that's somewhat counter intuitive. my first impulse would normally be to build about one base per system and upgrade that over time- but that strategy is really weak compared to building 3-4 (or more) bases with no further upgrades after the economy ring. 

the upgrades of the yield modifier buildings (xeno factory etc.) also have a fairly strange curve. the initial building for a mere 30 prod gives a 25% bonus, the first upgrade costs 45 prod and only adds another +5% - that's another trap for new players right there. you strangle your own early game if you leave that "auto upgrade" button checked and let the planets waste their valuable early game production on overpriced upgrades rather than using it for expansion (scouts/colony ships/constructors on mfg heavy planets, plain old 100% research slider on science worlds rather than 80% mfg/20% research to improve the labs to xeno labs etc.)

later upgrades are somewhat better (xeno to mege factory is +10% for 67 prod, mega to mfg center is another 15% for  101 prod, and mfg center to ind. sector is 151 for another +20%) and probably also more easily affordable since by the time you unlock them, your planets already have a solid production base and you'll probably also unlock a few passive boni along the way that improve base performance (like the government techs)

don't really know how useful the "projects" are at the moment. on specialized planets, they are very weak - my average research colony has maybe 3 factories and a power plant, a farm and the rest of the tiles is full of res buildings. i'd expect such a planet to perform best if the slider is set to some ratio that roughly reflects the ratio of mfg to res buildings, but the best research output is usually at 99% res/1% mfg (with the research project). the difference to simply putting it to 100% res is usually just 1-2 points, so i'd say that project is somewhat underperforming right now. imo it would be better if a hybrid prod/res planet works best at something like 30:70 ratio - in that case you could just set it to auto upgrade, and put the research project in the queue and leave it in "full auto" mode for most of the game. right now, you sort of have to micro amane every building upgrade- visit every planet, set slider to enough production so they upgrade their buildings at 1 turn each, and when the upgrade is done, set it back to 100% research. 

Im not sure how you arrive at the "building econ starbases sucks" theory. Level 1 is amazing - i try and get that asap. 

But even further levels are really good, provided you can build multiple constructors on a single ship. Sure, the first few upgrades suck, but since you can build 4+ constructors early on in a cargo ship (after a few techs), the total bonus to your planet can be +50% or more off a single turn worth of production from a manu world. Better yet, it gives your manu worlds something productive to do in peacetime - and they can support research/wealth worlds in a really productive and efficient way. 

Finally, getting the bonus manu from starbases means you need to invest in less factories to upgrade your res/wealth worlds - another bonus. 

Then there's the +approval upgrades, and the +research if you play ancient with a few relics can be huge. 3-4 relics can easily be worth 15 base research, amplified by research tech, relics and starbases can be 300+ on a world with no labs!

Improvement upgrades are in a much more dire spot than starbase - since they require an entire turn each and require you to sacrifice research/wealth to get them.

where exactly did i say anything like "building econ star bases sucks" ? actually i said pretty much exactly the opposite of that...

my criticism is that the upgrades are lackluster, which they are. sure, i'll also spam constructors to add modules to the existing bases if i have nothing better to do with my manufacturing worlds, but that's somewhat besides the point. the point is that it's counter intuitive that the first ring is by far the best. if you send out a colony ship and send some constructors along to help kickstart the new system, the best thing you can do is to build as many t1 econ bases around that planet as you can and only use the remaining moduls for upgrades when you run out of room for more t1 bases.

I was able to figure a way for 5 bases near a star, but in general I think 3 is the most practical.

That's only considering the base range of 5 though right? I haven't had a long enough game for the range increase modules, but you can increase it to 7 and then 9 eventually. I'm sure you can fit more in for a single planet with that, but I don't have the time right now to check just how many is possible.

Yes, that's only considering the base range of 5. At the maximum range of 9, you can make at least 12 starbases cover a central region, with 9 spaced evenly around the outer ring and three in the center in the pattern indicated in Arumba's diagram by the pink tiles. There might be a 'better' configuration at a 9 tile range, though I'm not aware of it.