I did some searching online but could not find an example with numbers, so asking here.
Let's say I'm researching Aquilo which nominally takes 3000 science packs.
If I use Biolabs, their natural bonus reduces the cost to 1500 science packs.
What happens if I add prod modules?
Specifically, let's put 4 prod3 modules in each biolab (+40% productivity).
Is this bonus added or multiplied?
If added, the productivity goes from 200% (natural) to 240% and Aquilo research will now require 3000/2.4 = 1250 science packs.
If multiplied, the productivity goes from 200% (natural) to 200 * 1.4 = 280, and Aquilo research will now require 3000/2.8 = 1072 science packs.
Which one is correct?
Biolabs with +40% from prod modules. How many packs will Aquilo require?
Re: Biolabs with +40% from prod modules. How many packs will Aquilo require?
The calculation goes like this.
Biolabs are a production machine, similar to an assembling machine or a mining drill. It has input (ingredients) and (output) products.
For a biolab, the input are science packs (the physical object), and the product isn't physical, it's research science value (this is what is used for unlocking technology).
The basic science "recipe" of that machine will produce 1 research science as output for 1 science pack as input.
Productivity always applies to the product, so it increases research science.
Science drain (or drain in general) applies to the input, so it decreases input consumption.
One research cycle will consume drain * input science packs. Since drain is 50%, one cycle will consume one half of a science pack.
The cycle will produce (1+productivity bonus) as research value. So if your productivity bonus is +40%, it's 1.4 for one cycle.
So for one lab for one cycle 0.5 science packs are being consumed and 1.4 research science is produced.
Since you can run another cycle to consume the other 0.5 science packs and produce another 1.4 research science, you get 2*1.4 = 2.8 research science per 1 science pack. The formula is:
research science = (1 + productivity bonus) / drain
with productivity bonus = 0.4 and drain = 0.5 you get (1+0.4) / 0.5 = 2.8 research per 1 science pack
So to research Aquilo (3000 research science) you need 3000 / 2.8 = 1071.4 science packs if you do research by using biolabs with 4 T3 productivity modules.
By the way, since I mentioned mining drills: the legendary big mining drill has 8% drain, so one mining cycle will consume just 0.125 ore from the resource patch or with other words it needs 8 cycles to consume 1 ore from the resource patch.
The whole calculation is similar to the biolab, so in case you have mining productivity +100% (through research), it's
ore output = (1+productivity bonus) / drain = (1+1.0) / 0.125 = 16
Result: you get 16 ore output for 1 ore consumed from the resource patch.
Biolabs are a production machine, similar to an assembling machine or a mining drill. It has input (ingredients) and (output) products.
For a biolab, the input are science packs (the physical object), and the product isn't physical, it's research science value (this is what is used for unlocking technology).
The basic science "recipe" of that machine will produce 1 research science as output for 1 science pack as input.
Productivity always applies to the product, so it increases research science.
Science drain (or drain in general) applies to the input, so it decreases input consumption.
One research cycle will consume drain * input science packs. Since drain is 50%, one cycle will consume one half of a science pack.
The cycle will produce (1+productivity bonus) as research value. So if your productivity bonus is +40%, it's 1.4 for one cycle.
So for one lab for one cycle 0.5 science packs are being consumed and 1.4 research science is produced.
Since you can run another cycle to consume the other 0.5 science packs and produce another 1.4 research science, you get 2*1.4 = 2.8 research science per 1 science pack. The formula is:
research science = (1 + productivity bonus) / drain
with productivity bonus = 0.4 and drain = 0.5 you get (1+0.4) / 0.5 = 2.8 research per 1 science pack
So to research Aquilo (3000 research science) you need 3000 / 2.8 = 1071.4 science packs if you do research by using biolabs with 4 T3 productivity modules.
By the way, since I mentioned mining drills: the legendary big mining drill has 8% drain, so one mining cycle will consume just 0.125 ore from the resource patch or with other words it needs 8 cycles to consume 1 ore from the resource patch.
The whole calculation is similar to the biolab, so in case you have mining productivity +100% (through research), it's
ore output = (1+productivity bonus) / drain = (1+1.0) / 0.125 = 16
Result: you get 16 ore output for 1 ore consumed from the resource patch.
Re: Biolabs with +40% from prod modules. How many packs will Aquilo require?
Thanks for the detailed explanation!
Re: Biolabs with +40% from prod modules. How many packs will Aquilo require?
I wish the UI explained this better.