Productivity Module Math

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DaveMcW
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Productivity Module Math

Post by DaveMcW » Mon Sep 08, 2014 9:14 am

Productivity modules are hard to use correctly. They do not work in beacons, and do not work on final products. You need to compensate for their electricity, pollution, and speed penalties.

But in high-value recipes, the bonus production can be worth it.


Recipe Value

Here are the raw resources per second for various intermediate products. I assume oil is worth 0.1 raw resources after the latest fluid changes. All solid recipes are produced in an assembling machine 3.

R/sec Recipe
686 rocket part
30.0 research (60 second space tech + lab speed 6)
28.8 uranium fuel cell
27.6 research (30 second yellow tech + lab speed 5)
26.3 high tech science pack
14.5 production science pack
11.0 research (30 second purple tech + lab speed 4)
10.6 sulfuric acid
9.88 military science pack
8.86 processing unit
6.25 electronic circuit
5.56 rocket control unit
5.00 iron gear wheel
4.84 science pack 3
3.75 plastic bar
3.75 sulfur
3.13 low density structure
2.83 research (30 second blue tech + lab speed 2)
2.50 copper wire
2.50 coal liquification
2.46 flying robot frame
2.08 advanced circuit
2.00 oil processing
1.46 science pack 2
1.35 battery
1.25 lubricant
1.14 stone brick
1.00 heavy oil cracking to light oil
1.00 electric engine unit
0.75 science pack 1
0.75 uranium processing
0.75 light oil cracking to petroleum gas
0.65 stone
0.63 explosives
0.57 iron plate
0.57 copper plate
0.57 steel plate
0.56 engine unit
0.53 iron ore
0.53 copper ore
0.53 coal
0.42 rocket fuel
0.42 light oil to solid fuel

Rocket part is by far the best recipe to use with productivity modules. Late game research, late game science packs, sulfuric acid, processing unit, electronic circuit, rocket control unit, and iron gear wheel are also great.

Uranium fuel cell has high potential, but consuming it is hard. You need over 100 nuclear reactors to run a fuel cell assembler at full speed.


Return on Investment

Here are the raw resource costs of various modules.

67.5 productivity module
689 productivity module 2
3983 productivity module 3
67.5 speed module
689 speed module 2
3293 speed module 3
376 assembling machine 3
2.2 1kW of solar and accumulator power

You can divide these by the production bonus to calculate your break even point from investing in modules. The assembling machines and electricity are needed to counter the power and speed penalties.

6.25 resources/second (electronic circuit) * +4% production (productivity module) = 0.25 bonus resources/sec

( 67.5 resources (productivity module) + 84 kW power penalty * 2.2 resources/kW + 376 resources (assembling machine) ) * 1/(1 - 0.15) speed penalty - 376 resources (we start with one assembling machine) = 363.2 total investment

363.2 / 0.25 / 60 = 24.2 minutes to recoup investment


Diminishing Returns


Adding more productivity modules gives diminishing returns on investment. These numbers all are for electronic circuits in an assembling machine 3.

1x productivity module (+4%): 24.2 minutes
2x productivity module (+8%): 29.4 minutes
3x productivity module (+12%): 37.4 minutes
4x productivity module (+16%): 51.5 minutes
1x productivity module 2 (+6%): 53.4 minutes
2x productivity module 2 (+12%): 64.9 minutes
3x productivity module 2 (+18%): 82.6 minutes
4x productivity module 2 (+24%): 114 minutes
1x productivity module 3 (+10%): 138 minutes
2x productivity module 3 (+20%): 168 minutes
3x productivity module 3 (+30%): 214 minutes
4x productivity module 3 (+40%): 294 minutes

A 40% production bonus is fun, but waiting 5 hours for it to be worth something is not fun!


More Speed

You can do better by using speed modules to counter the speed penalty. This has the added benefit of using less space in your base (unless you go overboard with beacons). Again with electronic circuits.

2x productivity module, 2x speed module (+8%): 32.2 minutes
3x productivity module, 1x speed module (+12%): 34.1 minutes
3x productivity module 2, 1x speed module 2 (+18%): 68.3 minutes
3x productivity module 3, 1x speed module 3 (+30%): 141 minutes
4x productivity module 3, 2x speed module 3 in beacon (+40%): 161 minutes
4x productivity module 3, 4x speed module 3 in beacons (+40%): 123 minutes
4x productivity module 3, 6x speed module 3 in beacons (+40%): 111 minutes
4x productivity module 3, 8x speed module 3 in beacons (+40%): 101 minutes
4x productivity module 3, 10x speed module 3 in beacons (+40%): 94 minutes
4x productivity module 3, 12x speed module 3 in beacons (+40%): 89 minutes
4x productivity module 3, 14x speed module 3 in beacons (+40%): 85 minutes
4x productivity module 3, 16x speed module 3 in beacons (+40%): 83 minutes

I assume each beacon boosts 2 assembling machines.


Conclusion

The first level of productivity modules is cheap and should be used in high-value recipes like processing unit, electronic circuit, and iron gear wheel. Rocket silo and late game research labs should always get the best productivity modules available.

A 3:1 productivity/speed module ratio gives the best return on investment. 4x productivity module 3 gives the ultimate in bonus resources, but requires patience, long production lines, and/or beacon support.

Always be prepared to invest in electricity and extra buildings to counter the drawbacks of productivity modules.
Last edited by DaveMcW on Thu May 25, 2017 12:42 pm, edited 14 times in total.

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Re: Productivity Module Math

Post by zlosynus » Mon Sep 08, 2014 10:56 am

I would say this just shows one aspect of productivity modules. In most cases, resources like iron and copper are vast and you don't need to save them much. So putting productivity module into iron gear factory does not really help you, speed would be better. On the other hand, alien artifacts are for most of the game quite rare. Therefore you want to start with a lvl3 assembling machine with four productivity 2 modules. And you want to upgrade these soonish to productivity 3 modules. I also use productivity modules inside oil tech at least in the beginning. (And in oil pumps where there is high yield, later switch with speed.)

So you could improve a lot your calculation if you would add rareness of resources there.

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Re: Productivity Module Math

Post by Apotheosis » Mon Sep 08, 2014 4:33 pm

One very important thing to note is that you can always get the benefits of productivity modules in labs without worrying about pollution escalation because they don't produce any pollution in the first place. Labs also have very low base power consumption compared to other devices, so the % increase in power isn't nearly as big either.

I had a bit of trouble following your post entirely OP so forgive me if I'm just restating everything you've typed, but I noticed at the end you referenced high-value recipes. It's important to consider not only the raw material savings when using productivity modules, but the raw material savings over time.

Productivity modules provide the most savings over time in things that use up raw materials faster than they’re created or used in a machine elsewhere in production. For example, the Copper Cable recipe requires 1 copper plate/ 0.5 sec or 2 copper/sec. The Electronic Circuit recipe require 3 copper cables/0.5 sec, and 2 copper cables are made from each plate, so that's a rate of 1.5 copper plates/0.5 sec or 3 copper/sec. Thus, if you're creating both copper cables and electronic circuits continuously in the same types of assemblers, putting productivity modules in the electronic circuit assemblers is a better investment than the copper wire assemblers. Conversely, while the higher-value Advanced Circuit recipe requires a lot of copper per individual item created, the base recipe speed is so slow (requiring a total of 5 copper plates/8 sec or 0.625 copper/sec) that it's one of the least desirable things to put productivity modules in in terms of copper savings, so a lot of materials used in a recipe doesn't necessarily translate to a good rate of savings--you have to factor in time too. By considering the Assembler 2 and Assembler 3 speed factors with the recipes we can compare these to furnaces and miners as well, and it can be seen that indeed electronic circuits can save you more raw copper than either the mining step or the smelting step of the process.
Assembler 2 circuit copper use: 0.75 speed factor * 3 copper/sec = 2.25 copper/sec
Assembler 3 circuit copper use: 1.25 speed factor * 3 copper/sec = 3.75 copper/sec
Electric/steel furnace copper use: smelting speed 2 * 1 plate/3.5 sec = ~0.57 copper/sec
Electric miner copper mining rate (I don't really understand how this is calculated but I've derived it experimentally): ~0.53 copper/sec

In conclusion, productivity modules provide the best copper savings over time with electronic circuits, followed by processing units, followed by copper cables, and the best iron savings over time by far is achieved with iron gear wheels, followed by electronic circuits, followed by science pack 3s. It is difficult to quantify the savings with productivity modules in labs because different research recipes require different amounts of time and science packs to complete, but because the energy use penalty and pollution penalty (only whatever energy demand increase would create at boilers) are so low it's usually a great idea.


The bare minimum amount of alien artifacts needed to research and build the Rocket Defense is 360 (260 artifacts for 2600 alien science packs, and 100 more artifacts for making 50 productivity module 3s and 50 speed module 3s). If you use productivity modules in every step of the process, starting with productivity module 2s in converting them to science packs and in the labs when researching Productivity Module 3, then switching to productivity module 3s thereafter, you can reduce this to only about 286 total artifacts needed.

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Re: Productivity Module Math

Post by SHiRKiT » Mon Sep 08, 2014 8:53 pm

On my maths I always ignore the cost of producing modules because I mass produce them all the time , non-stop.

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Re: Productivity Module Math

Post by DaveMcW » Mon Sep 08, 2014 11:01 pm

I have been thinking about beacons some more.

A speed module 3 in a beacon gives +25% to every assembling machine in range.

25% of an assembling machine with 4 productivity module 3's is one productivity module 3. So the speed module is essentially free! Surrounding one assembling machine with 12 beacons is strictly better than building 12 assembling machines. Up to a point. Eventually the assembling machine will producing so fast that inserters can't keep up.

Chemical plants and electric furnaces are trickier. A beacon needs to cover at least two of them to reach the magic number of 4 productivity modules.

Of course the optimal setup will balance beacons and assembling machines so they multiply as high as possible.

Here is a layout for smelting that has 8 beacons per furnace, and 4 furnaces per beacon. It inputs 20.3 ore/sec and outputs 24.4 plates/sec.
18-beacons.jpg
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Initial cost is:
18 beacon * 325 = 5850
16 productivity module 3 * 3983 = 63728
36 speed module 3 * 3293 = 118548
18504 kW * 2.2 = 40709
Total = 228835

228835 / 4.1 / 60 / 60 = 15.6 hours to recoup investment

Despite the very low value of the smelting recipe, with heavy beacon use it's possible it will pay off in a long game.

The time to recoup investment for a furnace with two productivity module 3's and no beacons is 33 hours.

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Re: Productivity Module Math

Post by ssilk » Tue Sep 09, 2014 12:32 am

Anybody thought about, that producing modules is much cheaper, if you use productivity modules?

I think we all will tap around in dark, until we do some real benchmarks; I mean, using the game to compute the real differences between using mods and not using.
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Re: Productivity Module Math

Post by DaveMcW » Tue Sep 09, 2014 12:39 am

If you prefer watching modules build for 20 hours instead of checking my math, go ahead. :P

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Re: Productivity Module Math

Post by FatMcK » Tue Sep 09, 2014 10:12 pm

Interesting thread. But I think there are some wrong values in the raw resource values. At least I think so.

For example copper cables. Their value is shown as 2.5. Shouldn't it be 1.25 as there are 2 cables produced per process?

How are oil based products calculated down to crude oil? I think it depends a lot if you use standard or advanced oil processing and also if you crack light/heavy oil or not.

But a major flaw in calculating this values in my opinion is anything that needs water in its process while it seems it is calculated as 1 unit of water = 1 raw resource. As water is actually an unlimited resource its value is practical 0. Some things that use water use lots of it, changing their values drastic.

For example 2 Sulfur demands 3 petroleum and 3 water, so the factor of water here is at least 50% (think about water used before in advanced oil processing and cracking). 5 sulfur acid demands 1 iron, 5 sulfur and 10 (!!) water. So sulfur acid and its products are basicly overrated by a lot.

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Re: Productivity Module Math

Post by DaveMcW » Tue Sep 09, 2014 10:32 pm

1. Copper wire is worth 0.5, an assembling machine 3 consumes 2.5 copper plates/sec and produces 5 copper wire/sec.

2. Crude oil and petroleum gas are both worth 1.

3. Water is worth 0.

4. Sulfur is worth 1.5, a chemical plant consumes 3.75 petroleum gas/sec and produces 2.5 sulfur/sec. Sulfuric acid is worth 1.7, a chemical plant consumes 6.25 sulfur/sec and produces 6.25 sulfuric acid/sec.

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Re: Productivity Module Math

Post by FatMcK » Wed Sep 10, 2014 7:50 am

Thank you for your detailed answer. It helped a lot by seeing where I was wrong. :)

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Re: Productivity Module Math

Post by Khyron » Mon Dec 29, 2014 2:50 pm

First of all, brilliant work, DaveMcW.

Why am I necro'ing this thread?
In my most recent play around I decided I was using (or misusing) modules way differently to most people. In most screenshots and LPs people end up with huge, intense pollution overlays. That hasn't been the case for me and the reason is that I basically use efficiency 1 modules in everything. That delivers some benefits - reduced pollution, fewer resources sunk in to solar & accus, smaller solar field and so on. Without having contemplated and calculated the worth of different modules and configurations I was just going off intuition. The extra power demands of speed and productivity modules seemed too much to bother. Worse with the upgraded versions. So I wanted to see what people's current opinion on modules was - do they need rebalancing, etc.

This thread has some amazing original research and should inform any discussion on re-balancing. It seems pretty clear to me that the ROI blowout is a problem given speed runs place the game length at about 10 hours. If you start producing tier 3 modules at the half way mark you'll be lucky to break even. That is, the player is not advised to pursue higher tier modules as a way of making gains (versus just building more production in parallel). Instead, higher tier modules are a time and resource sink toward achieving the end game condition. Aka: grind. So while I came to the forum with my suspicions that the modules weren't well balanced, the maths here really back that up.

A small clarification on the maths
I went through it in detail and was particularly impressed that you've included the resource cost of expanding the solar/accu to meet increased power demands. I actually didn't notice that on my first read and went off to calculate it independently, eventually arriving at the same figure as you.. haha

Where I would have calculated it in a different way is where you come to the inclusion of assembly plants. If I understand correctly, your argument is to offset the speed penalty you need additional assembly plants. When I got to this part in your maths I was surprised because I was expecting you to simply reduce the productivity module's bonus yield per second by the speed loss. Your way isn't wrong, it's just answering a different question. Both questions relate to ROI so I guess it's a matter of interpretation.

Example:
Productivity module 1 on electronic circuits: produces 4% extra, 15% slower
Yield: 0.25 Resource Units per second * .85 (adjusted for speed penalty) = 0.2125 RU/s
Module cost: 67.5
Expanded solar/accu cost: 184.8
Total RU = 252.3
ROI = 252.3 / .2125 = 19m46s

In the same ballpark as your results but a bit more in the player's favour. I'd be curious to know whether you prefer this method or if you already considered it and ruled it out.

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Re: Productivity Module Math

Post by DaveMcW » Mon Dec 29, 2014 4:11 pm

If you don't offset the speed penalties, electronic circuits become a bottleneck and slow down your entire factory.

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Re: Productivity Module Math

Post by Khyron » Tue Dec 30, 2014 7:19 am

DaveMcW wrote:If you don't offset the speed penalties, electronic circuits become a bottleneck and slow down your entire factory.
Fair enough. But if you do it that way, shouldn't you include the productivity bonus in the speed reduction calculations? The effective slow down is less than 15%...
DaveMcW wrote:( 67.5 resources (productivity module) + 84 kW power penalty * 2.2 resources/kW + 376 resources (assembling machine) ) * 1/(1 - 0.15) speed penalty - 376 resources (we start with one assembling machine) = 363.2 total investment.
Should be 376*1/(1.04-.15)...

Actually the maths is wrong there anyway. 67.5+84*2.2+376/.85-376 = 67.5+184.8+442.4-376 = 318.7 total investment.
And with the productivity correction it's 67.5+184.8+422.5-376 = 298.8 total investment.

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Re: Productivity Module Math

Post by BlakeMW » Fri Jul 29, 2016 7:25 am

This thread is still one of the best resources for Productivity Modules, despite being a couple of years old. But it is missing the numbers for rocket production (added in 0.12). Here they are:

Rocket Part: 60.2
Rocket control unit: 5.85
Low density structure: 3.125
Rocket Fuel: 0.42

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Re: Productivity Module Math

Post by DaveMcW » Fri Jul 29, 2016 11:36 am

Thanks, updated first post.

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Re: Productivity Module Math

Post by siggboy » Thu Aug 04, 2016 9:55 am

In my opinion this thread should be stickied. It's really an important part of the encyclopedia.
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Re: Productivity Module Math

Post by BlakeMW » Thu Aug 04, 2016 11:03 am

It should probably be in Cheatsheets / Calculators / Viewers. It's now more a reference than a discussion.

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Re: Productivity Module Math

Post by Koub » Thu Aug 04, 2016 11:26 am

That's exactly what I was saying to myself. That's why :
[Koub] Moved to Cheatsheets / Calculators / Viewers and stickied
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Re: Productivity Module Math

Post by Azzinoth » Sat May 06, 2017 8:07 pm

I recalculated some of this values for the new and changed recipes for Factorio 0.15.9. The calculations are for one assembler mk3 with 3 productivity modules mk3 and one speed module mk3 (except plastic which is 2 prod 1 speed). Since coal liquefaction gives 5 oil products per coal, i have assumed that 5 petroleum is worth 1 raw resources. For uranium fuel cells, i compared their energy value to coal. The amortization times are calculated including the initial costs for building the required power in form of solar. However, using nuclear energy should not change much, because the power cost was alwas the smaller part of the initial investment cost in my calculations. Keep in mind that these values are assuming that the machines are always running for that time. Anything not on this list gives even less returns, if i didnt forget something.
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Re: Productivity Module Math

Post by DaveMcW » Sun May 07, 2017 1:48 am

Updated for 0.15.9 using my own calculations.

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