Coolthulhu wrote:Holy-Fire wrote:
You're stating the obvious and have completely missed the point of my comments.
I am stating the obvious only because you claimed it's not true:
Holy-Fire wrote:Coolthulhu wrote:
Productivity modules' effectiveness increases exponentially with the length of assembling machine chain involved.
This is an optical illusion. It isn't what's really going on.
Holy-Fire wrote:I'll say again: The benefits you get from each additional productivity module scale linearly.
This is simply not true. You'll even get different final cost if you move modules from 110% machine to a 120% one.
Say, machine 1 produces wood at 110% productivity (2.2 wood per 1 raw wood). Machine 2 produces chests at 110% productivity (1.1 chest per 4 wood). 20 raw wood -> 44 wood -> 12.1 chests. If scaling was linear, it would be 12 chests. It gets much worse with longer chains.
I can't easily provide a well-explained example here because the formula is huge, so I'll repost what I wrote on the wiki: lvl 3 module is [1473 c, 775 i] (+artifact) base, but [123 c, 95 i] at 160% prod per machine - if the scaling was linear, it would cost 320 copper and 168 iron (productivity 460%).
I have created a lua script just to calculate productivity of chained machines. The numbers above include all the stuff like copper wires in advanced circuits not getting productivity from electric circuits.
I have re-read your posts to make sure I am not missing any points. I am trying not to sound hostile here, but the more I read them, the less it looks like you read mine thoroughly.
I must first apologize for my prolonged absence, real life got in the way.
I can assure you that I do understand what you wrote; the thing is that I don't think the figure you are calculating is important, and unfortunately I didn't make enough effort to explain what it is I am calculating, and why.
So I'll try now and take your wood chest as an example.
If you have +x% productivity in every machine in the chain, then for every unit of input raw wood, you can get (1+0.01x)^2 times as many chests as you would have if you did not have productivity bonus. If the length of the chain is n instead of 2, that's (1+0.01x)^n. This is perfectly exponential, but also perfectly uninteresting.
What you should be looking at instead is how much better off you actually are for every additional module you place.
Let's look at a production line working at full capacity. In this case you have 2 machines doing raw wood -> wood and 1 machine doing wood -> chest. The chest machine generates 1 chest per second. Each chest is "worth" 2 raw wood (not counting assembling energy for now). The ratio 2/1 (raw materials for finished product, divided by time per product) is going to be important.
You now go and put a +5% module on the chest machine. What do you have to show for it? If before the machine generated 1 chest per second, now it's generating 1.05 chests per second, with the same input materials. That's a net gain of 0.05 chests per second. This gain does not depend on what happens anywhere else in your production chain. Since each chest is worth 2 RW, that's a total gain of 0.1 RW/s for your economy (the economic worth of each chest does depend on the rest of your economy, but hold on).
To know how good is it to put your module there, as opposed to putting it elsewhere or putting a different model, you need to compare this gain (0.1 RW per second) with the energy cost.
If instead you put that module in one of the wood machines, you'd get an extra 0.1 wood per second. Each would costs half a RW, so that's a gain of only 0.05 RW/s. The reason you get less benefit for putting the module in the wood machine is that wood has a lower ratio of cost / time. The benefit you get for placing a module in a machine is always proportional to this ratio, so if you don't have enough modules it's best to put them in the machines with the highest ratio.
(Parenthetically, the benefit you get from placing efficiency modules, in terms of energy saved per second, does not depend on this. So the higher the ratio, the more you'll want to put prod modules instead of efficiency).
Now, the crux of my argument - If you put a prod module in the chest machine, you get an extra 0.05 chest per second. If you put a module in a wood machine, you get an extra 0.1 wood per second. If you put a module in all 3, you get an extra (0.05 chest + 0.01 wood + 0.01 wood) per second. This is completely linear. Nothing exponential at all going here.
But to truly understand module scaling, we need to figure out how much all of this is worth in your entire economy. And if we do this, we'll find that it actually scales worse than linearly. It is in fact exponential, but the wrong kind of exponential.
The best way to look at it is to treat raw ores as the unit of currency in your economy, as it all boils down to mining and transporting your resources (including coal for energy) And then the question is - We want X units of a final product. How much raw resources do we need for it?
Suppose you want 1000 wooden chests. How much RW do you need? Without any modules, you'll need 500 RW.
If you put a +10% module in the chest machine, you multiply your number of chests by 1.1, so you need only 454.5 RW - you saved 45.5 RW by using the module.
If instead you put this module in one of the wood machines, then assuming you keep the other one running to finish in roughly the same time, you get 4.2 wood per 2 RW, which is a factor of 1.05 over normal - so you'll need only 476.2 RW, savings of 23.8 RW.
But if you put modules in all 3 machines, the factor is 1.21, so you'll need 413.2 RW. That's savings of 86.8 RW, which is LESS than 45.5 + 23.8 + 23.8. The more modules you put, the less each will save you in terms of how much resources you need to extract in order to generate what you need.
A more accurate calculation will factor in the "embodied energy" in each item, reflecting the energy needed to run the machine that produced it from its ingredient, and how productivity modules affect the number of machines needed to work in full capacity. The result is the same though.
Another point I was making is that many chains in Factorio are exponential. E.g., you'll need 8 machines in the first level of the chain, 4 machines in the second, 2 in the third and 1 for the final product. The cost of the final product is huge, so the benefit you get is exponential in the length of the chain, but the number of modules needed is also exponential in the length of the chain. Thus the benefit per module is not exponential. In these chains the later steps have a higher cost/time ratio, so you get the most benefit per module by putting a module in the last step.
I hope you read this, and that I have explained myself at least well enough for you to be able to comment about it.
(And I hope they didn't break beacons, I didn't play Factorio in a while either.)