Encourage Planetary Growth v. Nutritional Plenitude

[Zenopath]

Lets compare.
Should you use them right away, and if so, which?

First, lets look at what they do.
Encourage Planetary Growth (costs 1000 food) +25% growth on 1 planet. (for 120 months)
Nutritional Plenitude (+25% food upkeep +5% happiness, +10% growth)

Ok, so concrete case, you have 1 planet with 28 pop eating 1 food each and no other growth bonuses, and have 1000 food saved up.

(Note; this is based on a real game. It was year 2204, I should mention that to get 1000 food that fast, I had built a 3rd farm as my first building very early on so I could use EPG as soon as possible at start of game. I did this math because I wanted to know if building that farm had been a good idea or not. To get the extra workers, I had demolished my generator district, because I was playing trade heavy, didnt need it. Most players will probably get 1000 food excess much later in game.)

Base growth over those 10 years is 3 per month, that is 1 pop per (100/3) 34 months, or (120/34) 3.53 total pop grown.

1) With EPG you pay 1000 food upfront.
you get (3x1.25) 3.75 growth per month, that is 1 pop per (100/3.75) 27 months, or (120/27) 4.44 total pop grown.

Extra pop created = (4.44-3.53) 0.91 extra pop

2) With NP you pay 600 food over time.
(note: only in this example, actual number will depend on your food consumption divided by 4 minus a refund of about 25%*, so roughly 1/5th)
I get that number by: (28x0.25) 7 food per month, then subtracting 2 because of the 5% happiness boost, which gives a refund*. Total of (120x5) 600** food. (see footnotes)
You get (3x1.1) 3.3 growth, that is 1 pop per (100/3.3) 31 months, or (120/34) 3.87 total pop grown.

Extra pop created = (3.87-3.53) 0.36 extra pop

3) With both you pay 1600 food.
You get (3x1.35) 4.05 total pop growth, which is 1 pop per 25 months, or (120/25) 4.8 total pop grown.

Extra pop created = (4.8-3.53) 1.27 extra pop

Cost per population:
On a food per extra growth ratio, numbers are
EPG = (1000/0.91) 1098 food to 1 pop ratio
NP = (600/0.36) 1667 food to 1 pop ratio
Both = (1600/1.27) 1259 food to 1 pop ratio

Return on Investment:
Working as a farmer, ignoring costs of new farms, energy upkeep, and costumer goods, will give surplus of 5 food, since he eats 1.
So to find the ROI time i will divide the ratios above by 5, and add time till first pop appears.

EPG = (1098/5) 220 + 27 = 247 months.
NP = (1667/5) 334 + 31 = 365 months.
Both = (1259/5) 251 + 25 = 276 months.

Conclusions:
None of them are great return on investment (ROI) right at start of game (they are good ROI later on), waiting till year 24, if you use it on year 4 is a long wait.

You should definately use EPG at some point. But maybe not right away. It has been argued that the break even point for NP as compared to EPG is 13.33 pop/planet by people´s replies, and that seems fair, though that number ignores happiness boost, which, I think would put that break even number closer to 17 pop/planet, as a very rough estimate.

With a 247 months ROI for EPG, you are pretty much better off investing in building a colony ship and making a new colony, which has a shorter ROI.

Making the choice between building an 3rd farm district, or an 2nd alloy plant as your first building and turning on consumer benefits for extra consumer goods (to get 200 cg for the colony ship), will decide which you will be able to do first.

So, if you want to boost growth, you will want 3rd farm and wait to get 1000 food for EPG, then if you want to use NP, you could, but you should save 1000 food first, and it might or might not be a good idea. Depends on how much food surplus you have.

For myself, my take away is that, when choosing what to build first on my planet, I think I will go with that 2nd alloy plant before the 3rd farm. In fact, why not build your 3rd farm on your 1st colony, and rush to colony ship instead of EPG? But that is just my opinion.

As always, let me know what you think, and if you spot any mistakes.





Footnotes:
* = The effect from happiness is pretty minimal, and hard to quantify, but, I can sort of give you numbers for it.
(edit: TL;DR, you could say it refunds something like 25% of its food costs with bonus productivity, roughly.)
I will start a race with same build a few times until i get a leader with +5 happiness perk and nothing else that effects happiness or economy. I will use Commonwealth of Man stock race because they have no happiness or economic modifiers other than wasteful which we will ignore.

Output, day one, ruler with ¨Champion of the People" = 4.06 energy, 23.56 minerals, 12.35 food, 9 cg, 11.14 alloy.
Output, day one, ruler without = 3.53 energy, 23.28 minerals, 11.92 food, 8.78 cg, 11.03 alloy.

Differences = 0.53 energy, 0.28 minerals, 0.43 food, 0.22 cg, 0.11 alloy. worth collectively, about 2.12 ¨value¨ output, if we multiply cg by 2 and alloys by 4 (their market value).

I will covert all that and round it down to be 2 food and call it a refund.

If this is confusing, ignore it, that´s why its a footnote. Almost no one reads them except people trying to fact check.

** = yes, the fact that your population changes to 29 then 30 and 31 during those 10 years means that the monthly cost does go up per month, and the refund, due to higher productivity also goes up. Dont care, too complicated.

 

[Nurgle84]

Thats pretty easy. Always Plentitude, because you will produce enough for increased upkeep and all colony ships you need and still have leftover to sell on the internal market in the early game. And if you have stack hanging around because you did not watched you food, you use it for the growth descision.

 

[AlanC9]

I always use both.

 

[Zenopath]

To be clear, i do not have a strong position on this issue. In past i have used both as well, I started this post because I wanted to know, for myself, the ROI to see how it should impact my game, in terms of fastest possible start strategy. After doing the numbers, I think EPG is better, mainly because NP has this unfortunate thing where your 30th month will see 99% growth, then next month, the 31th month will bring it to 0%.

If you have some other growth bonus, you could get a more favorable number. Like, with an extra +10% race perk or xenophobe, 3.6 growth is 28 months, which is a lot better.

 

[Blurb]

You can simplify your calculations a lot if you do away with the whole "pops grown" and "months per pop" thing - instead, just deal in pop growth exclusively.
Further simplifications can be made by considering EPG as a running expense:

EPG adds 0.75 pop growth/planet/month at a cost of 8.33 food/planet/month - note that cost might be subject to edict cost and edict duration modifiers
NP adds 0.3 pop growth/planet/month at a cost of 0.25 food/pop/month - I'm not sure if the cost is affected by any modifiers at all, as it is an additive cost

This means the only thing you want to worry about is how many pops you have per planet:
At 33.32 pops/planet, both will cost 8.33 food/planet/month - although EPG and NP will add 0.75 and 0.3 pop growth/planet/month, respectively.
At 13.328 pops/planet, the two will have an equal cost per added pop growth (11.10 food/pop growth/planet/month).

When it comes to increasing pop growth rates, higher number of pops per planet makes EPG a better choice, and inversely fewer pops per planet makes NP a better choice.
Given that the break-even point is at less than 14 pops per planet, I'd consider EPG as 1st priority as only very sparsely populated empires will benefit more from NP.
In times of food shortage, maybe it's even worthwhile to activate strict rationing to afford EPG on more planets - but I don't have numbers on that.

Thats pretty easy. Always Plentitude, because you will produce enough for increased upkeep and all colony ships you need and still have leftover to sell on the internal market in the early game. And if you have stack hanging around because you did not watched you food, you use it for the growth descision.

You're making a baseless assumption that the food policy is better for pop growth.
What am I supposed to gain from reading your post?

 

[Roddo]

 

[Zenopath]

You can simplify your calculations a lot if you do away with the whole "pops grown" and "months per pop" thing - instead, just deal in pop growth exclusively.
Further simplifications can be made by considering EPG as a running expense:

I could have done that, but the fact that remainders get shaved off make (10%) 3.3 growth less valuable than (15%) 3.45 growth by a pretty wide margin.

EPG adds 0.75 pop growth/planet/month at a cost of 8.33 food/planet/month - note that cost might be subject to edict cost and edict duration modifiers
NP adds 0.3 pop growth/planet/month at a cost of 0.25 food/pop/month - I'm not sure if the cost is affected by any modifiers at all, as it is an additive cost

This means the only thing you want to worry about is how many pops you have per planet:
At 33.32 pops/planet, both will cost 8.33 food/planet/month - although EPG and NP will add 0.75 and 0.3 pop growth/planet/month, respectively.
At 13.328 pops/planet, the two will have an equal cost per added pop growth (11.10 food/pop growth/planet/month).

Good to know actually, thanks. I was mostly wondering about right at start, but with that 13.33 pop/planet number in mind i can now better decide which to use later in in game. I might redo calculation to see what the break even pop/planet number is with the happiness modifier added in as a refund of say, 25% cost reduction to NP.

When it comes to increasing pop growth rates, higher number of pops per planet makes EPG a better choice, and inversely fewer pops per planet makes NP a better choice.
Given that the break-even point is at less than 14 pops per planet, I'd consider EPG as 1st priority as only very sparsely populated empires will benefit more from NP.
In times of food shortage, maybe it's even worthwhile to activate strict rationing to afford EPG on more planets - but I don't have numbers on that.


You're making a baseless assumption that the food policy is better for pop growth.
What am I supposed to gain from reading your post?

I dont know how you got that assumption. All i did was wonder what the return on investment was for using one or the other right at start. My conclusion, which mirrors your own, is that EPG is better than NP in the situation where you have 28 pops on 1 planet. (edit) But concluded that the ROI time was so long in either case, that it might not be worth it till later in game.

But say i had 25 people on capital, and a colony of 10 (deporting some homeworlders to build admin center), at that point i would have 12.5 pop per planet and NG would, by your math be better than EPG 2 worlds.

(Edit) you were replying to someone on last 2 sentences, sorry missed that.

 

[Blurb]

I could have done that, but the fact that remainders get shaved off make (10%) 3.3 growth less valuable than (15%) 3.45 growth by a pretty wide margin.

Yeah, I considered mentioning that as a caveat.
As I see it, accounting for that "shave-off" requires checking for pre-existing growth speed modifiers, which further complicates calculations.
I went with simpler calculations over pixel-perfect accuracy, as the early game can be especially messy with growth speed modifiers - and that's even without accounting for migration, which can further complicate things.

But say i had 25 people on capital, and a colony of 10 (deporting some homeworlders to build admin center), at that point i would have 12.5 pop per planet and NG would, by your math be better than EPG 2 worlds.

I count 35 pops total, meaning 17.5 pops per planet. Disregarding that and working with 12.5 pop per planet:
We're now moving away from idealized math and into strategy territory. Sure, NP should be a good choice then, but you'll soon be getting new pops, bringing you out of the "NP-zone".
However, you'll be locked in that policy for 10 years, and it'll only become more expensive as time passes and you get more pops. In that situation you'll probably have to do some napkin math and estimate if your empire can even sustain NP for a decade, then ask your guts how they feel about the value of NP.

 

[Zenopath]

Yeah, I considered mentioning that as a caveat.
As I see it, accounting for that "shave-off" requires checking for pre-existing growth speed modifiers, which further complicates calculations.
I went with simpler calculations over pixel-perfect accuracy, as the early game can be especially messy with growth speed modifiers - and that's even without accounting for migration, which can further complicate things.


I count 35 pops total, meaning 17.5 pops per planet. Disregarding that and working with 12.5 pop per planet:
We're now moving away from idealized math and into strategy territory. Sure, NP should be a good choice then, but you'll soon be getting new pops, bringing you out of the "NP-zone".
However, you'll be locked in that policy for 10 years, and it'll only become more expensive as time passes and you get more pops. In that situation you'll probably have to do some napkin math and estimate if your empire can even sustain NP for a decade, then ask your guts how they feel about the value of NP.

Lol, yeah when i get tired my mental math gets sloppy.

Still though, there probably is a sweet spot somewhere, a 10 year period where you have like 2-4 colonies and not many pops where NG outperforms EPG

 

[Secret Master]

I see that “why not both” has been covered.

I’d like to add that as long as your empire isn’t huge, it’s not onerous to run both.

10 planets in an empire is only 10,000 food a decade for the decision.

 

[Zenopath]

I see that “why not both” has been covered.

I’d like to add that as long as your empire isn’t huge, it’s not onerous to run both.

10 planets in an empire is only 10,000 food a decade for the decision.

True, which is kinda why i was sort of more thinking about early game. A 20 year Return on Investment is painful right at start of game, but not so much like around year 50

 

[trojan1234]

Why do you make arbitrary 28 pop into calculation? Here is my math.

1.Encourage planetary growth : 1000 food for 120 months, 25% pop growth.
Cost per planet = 8.33 per month : this is 1.3-1.4 farmer(7 per pop) in eary game - 0.7 farmer(12 per pop) in late game (it depends, but roughly)
Effect : 0.75 growth for 120 months = 90 growth total in 120 months.
Regarding growth overflow discarded, 90 growth is at most 0.9 pop.

2.Nutritional Plenitude : 25% food upkeep, 10% growth and hapiness
Let's say there are N pop in planet A
Cost for planet A = 0.25*N per month
Effect : 0.3 growth for at least 10 years = 36 growth in 120 months (which is 40% of EPG)

3. Comparison

When your empire have X planets and N pop, if N/X is greater than 13.33, then EPG is cheaper in terms of unit growth per food, otherwise NP is cheaper.

Is this worth to invest? it is hard to calculate because farmer's production changes over time.
For simplicity, I assume 7 food production per farmer in early game.
EPG : Cost = 1.19 farmer pop for 10 years, Return at most 0.9 pop.
So using EPG once will make even at least 13.2 years passed.

This can be converted into NP :
NP will make even at least (You population per planet / 13.33 * 13.2 ) years pass.

I know this is very rough calculation but it will help you decide to use EPG or NP
Edit : I forgot hives. they have different number so have higher N/X to EPG and NP worth equal.

 

[Zenopath]

Why do you make arbitrary 28 pop into calculation? Here is my math.

I may not have made it clear, but I was testing the ROI of eiher decision based on a concrete example because I was litterally on year 2-3 sitting on a pile of 1000 food and 28 pops on my capital thinking. ¨Huh, wonder how long this EPG will take to pay itself of.¨ (ROI)

See it has sort of become a habit of mine, to save 1000 food, do EPG, then turn on NP at the start of my games. I dont turn on NP right away because it makes it harder to save 1000.

I was actually running the math to check to see if the above strategy was the right call, shared my math with you all just because I am that nice.

20 years Return on Investment with EPG is actually a bit longer than I thought, but not unreasonable, overall. My opinion was that if you built a second alloy factory before a 3rd farm, you would be able to get a colonyship a little sooner but would end up not being able to EPG till a little later, but that decision would be worth it, given EPG´s long ROI.

But it could be argued either way.

1.Encourage planetary growth : 1000 food for 120 months, 25% pop growth.
Cost per planet = 8.33 per month : this is 1.3-1.4 farmer(7 per pop) in eary game - 0.7 farmer(12 per pop) in late game (it depends, but roughly)
Effect : 0.75 growth for 120 months = 90 growth total in 120 months.
Regarding growth overflow discarded, 90 growth is at most 0.9 pop.

that was what my math came up with too. I just compared it to actual baseline growth over 10 years, to get that number.

2.Nutritional Plenitude : 25% food upkeep, 10% growth and hapiness
Let's say there are N pop in planet A
Cost for planet A = 0.25*N per month
Effect : 0.3 growth for at least 10 years = 36 growth in 120 months (which is 40% of EPG)

3. Comparison

When your empire have X planets and N pop, if N/X is greater than 13.33, then EPG is cheaper in terms of unit growth per food, otherwise NP is cheaper.

Yeah that number sounds about right, someone else gave me that exact figure. But i actually worked out how much of an effect 5% happiness has on day 1, if you look at my footnotes, calling it a 2 food refund in extremely rough terms. So the actual break even pop/planet point is actually a bit higher, because you should consider +5% happiness something like a 25% cost refund, if that pattern holds true on all worlds.

Is this worth to invest? it is hard to calculate because farmer's production changes over time.
For simplicity, I assume 7 food production per farmer in early game.
EPG : Cost = 1.19 farmer pop for 10 years, Return at most 0.9 pop.
So using EPG once will make even at least 13.2 years passed.

7 food production per farmer is generous, but I guess you are assuming some farming tech. With no tech bonus, no race bonus, I calculated it at 5 food per month, since he eats 1 of his own 6 food output. Which gave me a Return on investment of closer to 20 years.

 

[Zenopath]

I edited my conclusion to give you guys a better idea of what I think is best plan of action, and color coded and made minor changes to the layout of the main body to make it easier to read.

 

[Theter]

Not sure its easier to read.

All I see now is pop pop pop pop pop pop pop...

 

[Zenopath]

Not sure its easier to read.

All I see now is pop pop pop pop pop pop pop...

eh fine I will tone it down

 

[Zenopath]

Not sure its easier to read.

All I see now is pop pop pop pop pop pop pop...

Better?

 

[Theter]

Swear its messing with my brain but its better obviously <3

 

[Currywurst44]

I think you forgot to consider one of the most important sources of food consumption in the first years of the game: Colony Ships. With each one costing 200 Food it gets much harder to save up for the up front cost of EPG. You have to produce more like 1600-1800 to start using the policy on you home planet. Additionally you will have many colonies with just one or two pops after a few years which greatly reduces the average amount of pops per planet.
The only question remaining is if you should use NP in the early game at all or if you can produce something more valueable than food with your planets.

 

[Zenopath]

I think you forgot to consider one of the most important sources of food consumption in the first years of the game: Colony Ships. With each one costing 200 Food it gets much harder to save up for the up front cost of EPG. You have to produce more like 1600-1800 to start using the policy on you home planet. Additionally you will have many colonies with just one or two pops after a few years which greatly reduces the average amount of pops per planet.
The only question remaining is if you should use NP in the early game at all or if you can produce something more valueable than food with your planets.

That is a good point, and I added a note to OP better explaining my situation, which is that I had built an extra farm pretty early in the game, so I had 1000 food, I had built that farm because I wanted to use EPG as fast as possible. I then wanted to know if that had been right move.