I got math the other day and took a shot at this question/issue. I just focused on Nutritional Plentitude (NP).
Start conditions change the math, so for this example I used a corp start, at 28 bio pop, because it is the worst case of the normal starts (cause more bio pop is higher cost per turn ....). I used a start that has no leader, governor, or agenda bonuses that matter. The only racial/ethic/civic trait that is used that pulls this example out of the "norm" is thrifty (+25% trade from jobs) because if your playing corp and your are not using it ...
I use U to make comparisons. U assumes that energy = minerals = food = 1/2 consumer goods = 1/4 alloy = 2 research = 2.3 unity. Research and unity get weird, so that is based on the assumption that specialists input vs output in buildings are all basically equal in value .... which is wonky yet useful.
It is necessary to look at AP during specific periods of the start timeline. There are 3:
1. From start to 1st colony finishing development (which should be about turn 90)
2. From 1st colony to 2nd colony (which varies but should be 18-24 turns, with medium RNG)
3. Thereafter etc (and the short answer here is probably)
So .....
"Is it worth it to go AP turn 1 rather then on about turn 90?"
... is our question, because the answer to that basically shows us the other answers and no one is paying me to do this so... Here goes:
Abundant Food does 3 things and have to be looked at as a net effect over the above period.
1. +10% Pop Growth
The value of "growth" is weird because it is contingent on the value of what that pop can do when you get it. To keep it relatively simple, and stay a bit in theme, let's assume use as a farmer (best early game return) and the faction/start doesn't have any traits or bonuses that effect farming or anything that changes upkeep including starting leaders or agenda etc...
Farmer
Output
6 Food (base) + 6% from stability +2% from L1 governor = 6.24 F (or 6.24U, because F is worth 1 U)
Input
1 Food + .25 CG + .5 Energy (can't forget the upkeep of the district...) = 2U (cause CG is worth 2 U)
(we will skip addressing the sprawl from the district or the cost to build the district and issues like a district not being fully occupied etc because ... no one is paying me to do this)
Net Value = 4.24 U per tick
Growth bonuses are additive, so the more of them you have the less impact additional bonuses have. Partially because of the way the "100 effect" thing works, 20% is really the first big diminishing return point. The math on that is long, but this means the value of that +10% isn't a constant. For instance, if you took slow breeder as a racial trait, going from 90% to 100% is more valuable the going from 150% to 160% as an inward perfection and fast breeder species.
This gets messy, but keeping to a simple example, if you have no other growth bonuses and start using it first turn on our hypothetical nothing funny faction/start what it means is that you get your first pop 3 turns earlier, your next 6 turns early, etc.
To be specific, that means you get 1st pop on turn 32 rather then turn 35 and your 2nd at 63 rather then 71. Net, this means that in the first 90 turns you get 9 worker ticks (assuming you had a job ready for them and some other stuff but ... moving on).
9 x 4.24U = ~38U is a concrete return
... and you have slightly more of your next pop developed then you would otherwise ...
90 x .30 growth per turn = ~25/100 (cause you lost some to the "100 effect"...)
2. +25% Food Upkeep
28 (bio pop) x .25 = 7U upkeep for the first 31 turns (217)
29 (bio pop) x .25 = 7.25U for the next 31 turns (224.75)
30 (bio pop) x .25 = 7.5U for the last 27 turns (202.5)
~ 644U Upkeep (tick 1 - tick 90)
3. +5% Happy
Happy is really worth it's effect on stability, which ends up being a +x% to jobs/trade.
That effect is actually +1.8%. This is hard to see (it looks like 1%) because if you mouse over the stability indicator for your planet it displays +x% to jobs in as whole numbers and rounds funny. If you want to see it more accurately, look at the trade tool tip before and after turning it on or off, because for some reason trade shows stability bonuses with a decimal. The decimal really does effect other production (tested) and results are tracked to two decimal places. Just .... for some reason the stability tooltip .... its some kinda a of Paradox ..... ahem.
Next question is +1.8% of what?
The effect is +1.8% to the base job production (so % from other sources like traits or ethics do not actually matter here) AND total trade, because as you can see in the trade tooltip, the % is applied to all trade, including trade from pop and even megachurch (tested). That number is ~145U per tick using our example.
145U x .018 = ~2.6U per tick of additional income
2.6 x 31 = 80.6
2.7 x 31 = 83.7
2.8 x 28 = 78.4
~ 243U Benefit (tick 1 - tick 90)
Net Effect:
~363U cost for .25 pop
Do you think that is worth it?
To answer that, you have to look at what else you could have done instead. Without going "too" crazy here are some points of comparison:
100U is a mining station (ROI ~37 turns on a 3 energy or ROI 104 on a 2 mineral)
300U for 1 pop if you remove the "Sprawling Ruins"
300U and an ROI of ~33 ticks if you replace a city district with a farm district
300U and an ROI of ~37 ticks if you replace a generator district with a farm district
400U is the alloys to annex a sector
600U is a science vessel and scientist
1400U is a normal colony ship
800U is a pop if you transfer them home immediately using the above ship (~60 ticks and assumes you got the tradition timing right)
325U is a private colony ship if your leader has the right trait
260U is a pop if you transfer them home immediately using that one
500U is a private colony ship if not (or a slave on the market assuming your empire swings that way)
350U is a pop if you transfer them home immediately using that one
270U is ~ the cost if you take one clerk and make him unemployed for the above period because you feel like it
603U is ~ the cost for the same with a farmer
Im out.
