do resources in factorio go up or down. and at what productivity lvl they switch direction?

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at what productivity lvl the profit changes to deficit? assuming default settings map

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do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by napouser »

so lets say u start with a stadard map

u get access to some basic resources lets say 200k of iron and u start making stuff

eventually u get more mines and advance to finish game

continue to get a huge 10000 spm base wich means 100+ mines of ~10mill iron so access to 1000million iron active mines

that 1billion iron is in fact 2 billion assuming 10lvls of mining productivity and gives 10000spm but the 10000 science packs per minute are worth more than the consumptiuon of actual iron recourses

that is cauzed due to factory productivity . the initial iron becomes 120% in bars x1,40 in circuits x1.4 in reds x1.4 in blues then 1.4 in rcu then x1.4 in rockets and finally 1.2 in actual science progress in the labs

so in the end the 1 b iron becomes 2b from mines and lets say 20billions worth of research

now as u grow ur base from 100 spm to 10000 spm the rate at wich the 1b iron is depleted is increased

so lets say with 1000spm u have a declining rate of -100k/sec removed from the map

but with 10000 u get -1m/s iron

however as ur recources decline u raise ur productivity from 10 to 1000



so the 1b mines become 100b instead of 2b



i think ive heard nilaus claiming that essentially ur resources become almost infinite at some point (the rise is faster than consumtion)

i strongly disagree with that idea

however i am trying to express it in a more mathematical way with some form of function instead of just "guts feeling"



as ur productivity grows lets say from 1000 to 1001

thats 10% more base iron

witch means that the 100billion will become 100.100. 000.000 expected iron ore





so my question is this

assuming u get 100million extra from 1 research

if the cost of iron of 1 lvl of research is less than 100m then the rate at wich ur resources is increasing instead of decreasing



so that can prove that nilaus is right.

is he? maybe some times but mostly not



my argument is based on 2 issues



even if at some point 1 research gives u more than the cost (doubtfull but i need to do some calcs)

eventually the cost will surpass the benefit becauze the benefit is always a flat 10% while the cost is increasing slowly by 2500packs per reasearch so at 1000 lvls the cost is like 2.5 mill per reasearch

the question still remains that where is that turning point?



2) even if 1 is truth u still require an ideal base where u get the resources in a balanced way

thats impossible

tthe way factorio mines work is u place a bunch of drillers and the conveyors get blocked all the way to the beggining of the driller line. when that driller runs out it will stop producing so the next driller will be unblocked. so u cant mine in a uniform balanced way the mine. even if u use bots the bots will prioritize the closest driller then the farthest

and of course the trains will prioritize the closest mine and when they are done will go to further ones

so even if the whole 100million ore base grows from 100billions by 10% the 100bill is not consumed uniform but in such way that each piece that gets removed wont get benefit anymore



for example

u got a base with a mine of 10 mill and 100productivity reasearch so 100x10% = 1000% = 10x so 100mill excpected resources

it has 100 patches of ore at 1mill each (lets assume uniform distribution wich never happens)

getting from 100 lvl to 101 will give 10% on base wich is 1 mill

each patch gets 10% benefit so it goes to 1.01mill. total 100x1.01 = 101mill

after some days 30 patches are done so only 70 left

so going from 100 to 101 research will result in affecting 70x1x1.01= 7.07mill



if instead u miraculasly managed to get 30% of each patch of 1mill so u had 100 patches of 700.000 ore left then u would end up with 707 000 x100 = 7.07 mill



it looks the same but it isnt

why?



well if u get lets say 1 million ore from the mine in the time it takes to get 2 millions worth of extra ore in productivity its obviusly raising so eventually will reach infinite



but if u mining 2 millions from 4 patches is different than mining it from 100 patches

in fact the deteriorating rate is 25 times faster than a uniform mining

that means that the rate at wich u get 1 ore from a patch can never exceed the time it takes to do a research and give u more free ores



in fact 1 ore from a patch takes ussually 2-3 secs assuming some huge productivity of 500

that means if reasearch reaches 2-3 hours u will have thousands of ores depleted from that patch. that means they are gone for ever and therefore the total yeild of the mine will permanetaly go down until eventually 0.



so even if u getting researcgh upgrades every hour u will still be unable to maintain ur patches



can any1 verify this ?



some rough calcs can go as follow

assuming a base of 10000spm can consume 4k iron /s thats 1/4 of a million per minute

so after a minute u get 10000 sp wich is 1 upgrade of 2500 then 1 of 5000 then part of the 7500 so lets say 2.5 upgrades

on a 100mill map thats 20mill. the cost is only 250k

fast forward to 100lvls so the map is now worth 1000mill

1 upgrade gives 10 mill as always but now costs 250 000 packs so 25 minutes so 25x250k = 6 mill

so my guess is at 200lvls the map upgrade costs more than the 10mill it provides

so i guess thats the right number. obviusly thats assume that the base starts as 10000spm wich is impossible since it takes weeks to build such a monster and it assumes a stable 100 mill map wich is impossible since u start with a moderate small 50 mill worth of mines and eventually can go up to 10 billion.

i guess its dynamically more complicated than i thought

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by MEOWMI »

It's not so much that the resources increase, it's more that it's hard to tell exactly how much you can get out of an ore patch in total if you're rapidly researching productivity upgrades. It will eventually run out. The only way to prevent that would be to constantly add new mines which requires more resource patches... and this quickly becomes unwieldy as research costs rapidly grow. The result is that mines will last far far longer than normal, but they would still theoretically eventually run out.

I've not derived any formulas, however, it shouldn't be too hard to see that the resource increase provided by the upgrade cannot offset the cost required to research it.

The resource patches do start lasting much much longer, not literally infinite, but the need to refresh mines will decrease massively. At this time, you're probably close to the point where you start losing UPS...

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by mmmPI »

napouser wrote: ↑
Wed Oct 12, 2022 12:28 pm
i think ive heard nilaus claiming that essentially ur resources become almost infinite at some point (the rise is faster than consumtion)

i strongly disagree with that idea

however i am trying to express it in a more mathematical way with some form of function instead of just "guts feeling"
I think there are 3 different ways to understand "ressource become infinite at some point". rise faster than consumption, this is possible if you have a very large number of mining drill covering a large amount of ressources, it can happen for a few level that the research gives you a 10 % of the already covered ore which would represent more than the cost of the research itself. But if you continue the research eventually all ore will dry up unless you add new mining drill so it's not infinite really.

The other way to understand "infinite" is when you place a mining drill covering 10 million ore because it is very very far away from the center of the map, and you have productivity level 1000, and you output the mining drill on a belt. The mining drill will produce mostly ore from the productivity bonus, and very very few would actually be removed from the ore patch since 1 cycle of the mining drill remove 1 ore but produce 101. For 102 ore to be removed by half a blue belt, you need something like 4 or 5 second. Which means 10,000,000 ore will be removed from the mining drill in 500,000 second or so, which is 138 hours. At this point you need 2 mining drill for a full blue belt, and each mining drill last 5 days ? if the ressources patches are large enough to place a lane of 10 or 12 mining drill, you just made yourself enough reserve for amonth of 1 blue belt output. still not really infinite.

I think i've heard the same reasonnings but i think it was not strictly refering as "infinite" as is forever it will run, but rather, it will run very very long.

The third one is more philosophical : The higher the productivity lvl the longer you are free of human intervention after placing a ressource-extracting machine and research are infinite .... But it will never "switch direction", only at the end become closer and closer to 100% "free ressources" whitout ever reaching.

(Edit : there should be a "never" or " always" vote )

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by napouser »

MEOWMI wrote: ↑
Wed Oct 12, 2022 12:49 pm


I've not derived any formulas, however, it shouldn't be too hard to see that the resource increase provided by the upgrade cannot offset the cost required to research it.


yea its rather obvius to me but for others like nilaus its the opposite
i am just trying to prove it mathematically

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by Nidan »

napouser wrote: ↑
Wed Oct 12, 2022 1:10 pm
MEOWMI wrote: ↑
Wed Oct 12, 2022 12:49 pm


I've not derived any formulas, however, it shouldn't be too hard to see that the resource increase provided by the upgrade cannot offset the cost required to research it.


yea its rather obvius to me but for others like nilaus its the opposite
i am just trying to prove it mathematically
Isn't that rather simple?
Cost for mining prod research doubles each level, while it only gives a 10% base increase in ore. 1.1 < 2. qed.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by napouser »

Nidan wrote: ↑
Wed Oct 12, 2022 4:47 pm
napouser wrote: ↑
Wed Oct 12, 2022 1:10 pm
MEOWMI wrote: ↑
Wed Oct 12, 2022 12:49 pm


I've not derived any formulas, however, it shouldn't be too hard to see that the resource increase provided by the upgrade cannot offset the cost required to research it.


yea its rather obvius to me but for others like nilaus its the opposite
i am just trying to prove it mathematically
Isn't that rather simple?
Cost for mining prod research doubles each level, while it only gives a 10% base increase in ore. 1.1 < 2. qed.

It goes up by 2500 not 100%

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by Nidan »

napouser wrote: ↑
Wed Oct 12, 2022 4:54 pm
Nidan wrote: ↑
Wed Oct 12, 2022 4:47 pm
napouser wrote: ↑
Wed Oct 12, 2022 1:10 pm
MEOWMI wrote: ↑
Wed Oct 12, 2022 12:49 pm


I've not derived any formulas, however, it shouldn't be too hard to see that the resource increase provided by the upgrade cannot offset the cost required to research it.


yea its rather obvius to me but for others like nilaus its the opposite
i am just trying to prove it mathematically
Isn't that rather simple?
Cost for mining prod research doubles each level, while it only gives a 10% base increase in ore. 1.1 < 2. qed.

It goes up by 2500 not 100%
oh, my bad. Apparently I was misremembering things.

Looking up the actual formula from the wiki, it gives 10% * (level - 3) while costing 2500 * (level - 3). The ratio between them is (2500 * (level - 3) ) / (10% * (level - 3)) = 2500/10%, which is constant.
Therefore, given everything else in the factory stays the same, the relative cost of the mining productivity research doesn't change. I.e. it doesn't get cheaper, but neither does it get more expensive.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by napouser »

Nidan wrote: ↑
Wed Oct 12, 2022 5:20 pm
napouser wrote: ↑
Wed Oct 12, 2022 4:54 pm
Nidan wrote: ↑
Wed Oct 12, 2022 4:47 pm
napouser wrote: ↑
Wed Oct 12, 2022 1:10 pm
MEOWMI wrote: ↑
Wed Oct 12, 2022 12:49 pm


I've not derived any formulas, however, it shouldn't be too hard to see that the resource increase provided by the upgrade cannot offset the cost required to research it.


yea its rather obvius to me but for others like nilaus its the opposite
i am just trying to prove it mathematically
Isn't that rather simple?
Cost for mining prod research doubles each level, while it only gives a 10% base increase in ore. 1.1 < 2. qed.

It goes up by 2500 not 100%
oh, my bad. Apparently I was misremembering things.

Looking up the actual formula from the wiki, it gives 10% * (level - 3) while costing 2500 * (level - 3). The ratio between them is (2500 * (level - 3) ) / (10% * (level - 3)) = 2500/10%, which is constant.
Therefore, given everything else in the factory stays the same, the relative cost of the mining productivity research doesn't change. I.e. it doesn't get cheaper, but neither does it get more expensive.


Interesting
So assuming a specific map and unified consumption of all nodes u can probably reach a stable condition.

In other words if ur base is big enough that 10% of it can make just 2500 pots ur never going empty is that what u are saying?

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by Nidan »

No, it'll always cost resources, but the amount of resources removed from the ground is always the same. If you need to mine x iron ore for level 10, then you'll also need to mine x iron ore for level 1000.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by napouser »

Nidan wrote: ↑
Wed Oct 12, 2022 5:59 pm
No, it'll always cost resources, but the amount of resources removed from the ground is always the same. If you need to mine x iron ore for level 10, then you'll also need to mine x iron ore for level 1000.


No. U need x + 2500 + 2500 + …. for the later levels but i think i get what u saying

U end up mining the same becauze in the end the actual recourses will go down at the same rate due to higher multiplyer. So the extra % will facilitate for the extra 2500s.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by mmmPI »

Nidan wrote: ↑
Wed Oct 12, 2022 5:20 pm
Looking up the actual formula from the wiki, it gives 10% * (level - 3) while costing 2500 * (level - 3). The ratio between them is (2500 * (level - 3) ) / (10% * (level - 3)) = 2500/10%, which is constant.
Therefore, given everything else in the factory stays the same, the relative cost of the mining productivity research doesn't change. I.e. it doesn't get cheaper, but neither does it get more expensive.
That would be if the first few level were not cheaper than 2500 and the bonus given cumulative. This means at first the cost / benefit is smaller, meaning faster pay off, while overtime, it goes up to reach the 2500/10.

It is to note however than the "benefit" being 10% of less and less ore in a real game if you do not move your mining drill. This quantity is the one covered by mining drill, which deplete slower and slower the more you have researched since then the more ore is coming from the productivity bonus but it will never stop depleting.

Considering you dont have an infinite number of mining drill, you start with a quantity of ore covered that is "X", each next research cost you ((Y+(2500 * k)) and gives you 10% from (X-(Y+(2500*k))) where Y is cost of the current level of tech, and k the number of ore required to create the sciences packs.


Edit: also my graph is simplified, it is even more advantageous to do the first level of research, as this is considering the "cost" as 1 science pack of each type but the first few level require less pack that would be a lower K and not 2500 but the number of actual pack to accomodate previous equations.
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costbenefitprodminingtable.jpg
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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by mmmPI »

I realized my previous post is too simplistic as it doesn't reflect the fact that the "cost" is becoming lower and lower in terms of real ore the map, for the same amount of science pack due to the cumulative productivity gain.

This problem is more complex than at first glance haha

I found that you can use 1/(1+(A/10)) to transform the mining level A into the % of ore coming from the map compared to the ore coming from the prod bonus.

Such as, with level 10, you get 1/(1+(10/10))= 0.5 because at level 10 you get 100% productivity and it means 1/2 of total output comes from the map.
With level 20, you get 1/(1+(20/10)) = 1/3 because at level 20 you get 200% productivity and it means 1/3 of the total output comes from the map.
With level 3 you get 1/(1+(3/10)) = 1/1.3 ~ 0.77, because at level 3 you get 30% productivity and it means 77% of the ore comes from the map.

I'm not sure i can continue this further but maybe this could help mathing the thing i forgot earlier.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by mrvn »

Nidan wrote: ↑
Wed Oct 12, 2022 5:20 pm
oh, my bad. Apparently I was misremembering things.

Looking up the actual formula from the wiki, it gives 10% * (level - 3) while costing 2500 * (level - 3). The ratio between them is (2500 * (level - 3) ) / (10% * (level - 3)) = 2500/10%, which is constant.
Therefore, given everything else in the factory stays the same, the relative cost of the mining productivity research doesn't change. I.e. it doesn't get cheaper, but neither does it get more expensive.
I think you are still misreading things. The combined gain is 10% * (level - 3). Each level gives a 10% increase. The cost of the next level is 2500 * (level - 3) and grows for each level for the same 10% increase.

With the same number of miners each level will take longer and longer to pay off and take longer and longer to research.

I bet you can balance it such that the 10% increase for each level matches exactly the cost for the research of the level and resources will remain exactly even. If you have fewer miners then resources go down because you use up too much for research and if you have more miners the resources go up because you aren't using all the extra ore for research.

But beware that each level of research will take longer. The assumption in the above is a constant research speed and constant number of miners.

PS: By resources I mean the ore that is mined and remains for use other than the research.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by Nidan »

mrvn wrote: ↑
Wed Oct 12, 2022 7:49 pm
Nidan wrote: ↑
Wed Oct 12, 2022 5:20 pm
oh, my bad. Apparently I was misremembering things.

Looking up the actual formula from the wiki, it gives 10% * (level - 3) while costing 2500 * (level - 3). The ratio between them is (2500 * (level - 3) ) / (10% * (level - 3)) = 2500/10%, which is constant.
Therefore, given everything else in the factory stays the same, the relative cost of the mining productivity research doesn't change. I.e. it doesn't get cheaper, but neither does it get more expensive.
I think you are still misreading things. The combined gain is 10% * (level - 3). Each level gives a 10% increase. The cost of the next level is 2500 * (level - 3) and grows for each level for the same 10% increase.
Both increase at a linear rate, so the relative cost doesn't change. But I ignored the first 3 levels which offsets things and the above only applies when viewed under lim_{level -> infinity}.
I bet you can balance it such that the 10% increase for each level matches exactly the cost increase for the research of the level and resources will remain exactly even.
By doing nothing. Note the word added. In other words, if you dedicate a fixed amount of miners to mine the resources needed for mining productivity, you'll never have to adjust that amount. (But they'll be increasingly more idle since mining productivity makes them mine faster, while research takes longer.)
Again, the first three levels and any prod modules in the miners shift things a bit, making this only true when approaching level infinite. See the plot in mmmPI's post or play with e.g. wolfram alpha. One of the alternate forms clearly shows that it approaches a constant: cost / productivity = 25000 - 325000 / (level + 10)
Adding prod modules makes it 25000 - 400000 / (level + 13) (substitute x = level - 3)

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by mmmPI »

I think i found the way to modelize how much ore is left in an ore patch after a research based on the total quantity of ore covered by mining drill assuming not changing them.

If you consider "X" such quantity

Then after a research you are left with X1 = X -(2500(a-2))c)/(1+(a/10))

with "a" the initial level of mining tech stricly superior to 3
and "c" the number of ore required for 1 science pack of each type

To explain better you take the total quantity X, and you remove the cost of the research multiplied by the 1/(1+(a/10)) formula which tells you how much ore consumed came from the ore patch. The factor "c" depend on how much ore you need to make 1 of each science pack when you look only after the mining drill.

If you have level 10 of mining prod, then the cost of the research in science pack is (2500* (10-2)) or 20000 science pack, which multiplied by "c" means it requires 20000c ores.

Then multiplied by the formula (1/(1+(10/10))) you get "10000*c " ore that is removed from the ore patch. That's 50% off because at level 10 you get 100% bonus meaning only 1/2 ore is coming from the patch and the other one coming from the prod bonus.

I'm not sure what is the best factor "c" possible , given this link it seem around 250 : https://kirkmcdonald.github.io/calc.htm ... IXqREu8gE=

So going from tech 10 to tech 11 means you remove 250 x 10 000 ore from your original X quantity. 2.5M, while the reseach cost 5M "raw ore" only half of it is removed from the patch.

The research then gives you 10% extra ore on what is left, which may or may not be more than 2 500 000 ore depending on your X original quantity

I show an example where you start with 1 billion ore, and you can research around up to mining productivity 198 199 or so before the ore is depleted on the attached doc:
miningore2.png
miningore2.png (90.44 KiB) Viewed 683 times
1billion.ods
(207.88 KiB) Downloaded 8 times
With a pic in case you don't trust my .ods and want to re-implement the only tricky formula yourself.

Edit : updated pic and .ods with more very important statistic, and 1 less off-by-1 error.
Last edited by mmmPI on Thu Oct 13, 2022 12:43 am, edited 1 time in total.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by Khagan »

Nidan wrote: ↑
Wed Oct 12, 2022 9:18 pm
In other words, if you dedicate a fixed amount of miners to mine the resources needed for mining productivity, you'll never have to adjust that amount. (But they'll be increasingly more idle since mining productivity makes them mine faster, while research takes longer.)
Alternatively, you can increase your research rate linearly to match the increased production.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by JimBarracus »

Well there are theoretically infinite resources on the map.
You can increase them by 10% with every research.

What it actually saves you is the need to find new ore patches sooner and gives you free ores.
The ore ouput from an ore field is increased. You can fill a train faster.

Cost also becomes irrelevant at some point. You use the free ores to get even more free ores.

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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by aka13 »

But the map is finite, so are the ores.
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Re: do resources in factorio go up or down. and at what productivity lvl they switch direction?

Post by quyxkh »

There's simply no way anyone will ever exploit the entire map. You'll run out of rig long, *long* before you run out of resources. I forget how far out you have to go to get 1G patches, but there's vastly more of those than there are 100M patches, vastly more of those than 10M patches, and that's not counting mining prod.

The map would cover a large fraction of Australia. It's 2'000kmΓ—2'000km. It would take you eight hours driving a nuc-fueled train just to get from one side of the map to another, then you'd have to do that about another thousand times just to *expose* the entire map. And that's if you've already done it once, much slower, so you could lay the track. Short of that I think the fastest transport is full-exo PA2? Less than half as fast, so 16,000 hours.

edit: going on some very quick p.teleport{1e5,0} and p.teleport{1e6-100,0} checks, it's ~1G patches at 100km and ~10G patches at 1000km,

Further edit: that was with an old map, newer ones seem to yield ~3G patches 1000km out, ~300M 100km out. One mining-prod research unit (2500 of each non-mil science pack) costs about 118K copper, 148K iron, negligible coal and stone.

Call it 250K resource per mining prod unit 'cause exact numbers aren't going to change this result, like, at all: a 10% mining prod boost makes your patches yield 10% extra, out of 100M resources that's 10M more resources, so level43 mining prod breaks even on just one reasonable patch. level83, *two* patches. So count up how many resource patches there are >50km out from the start point, divide that by forty, that's the mining prod level you can hit before you start having to worry about the research not carrying its freight.

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