Speed vs Productivity modules: The 12 bacon suprise

[Belter]

I own this game for a long, playing again and of course planning a megabase.

Did a simple calculation and surprise: Speed module only setup makes no sense!

The context:
- assembly machines, L3 only
- late game, so power usage ignored, only SM3 (Speed Module 3) and PM3 (Productivity Module 3) are considered
- all bacons have 2xSM3 of course
- checked 6 Bacon (when you do a row) and 12 Bacon (max # of bacons) setups
- so 5 configs: 4xSM3 & 0xPM3 ... 0xSM3 & 4xPM3,
- calculated "Effective speed" by simple using Speed * ( 1 + Efficiency Bonus).
-- E.g. If shown speed is 8/sec with 40% efficiency -> Getting 11.2/ sec long-term considering the extra items.

Result visualized:
- 4xPM3 setups at the top, 4xSM3 setups at the bottom

EffSpeedVsResNeed.png (25.18 KiB) Viewed 4576 times

The calculation table:

EffSppedvsResNeed-TablePic.png (52.98 KiB) Viewed 4576 times

My conclusion:
- use PM3s for both 6 and 12 bacon setups (depending on your bottlenecks of course)
- 4xSM3 config in 12 bacon setup simple does not make any sense: 2.7% slower and takes more resources than 2+2

[ickputzdirwech]

Interesting calculations! You have to keep in mind, that using more productivity modules means that you need fewer resources, which means that you need fewer machines producing the ingredients. The total machines needed to produce a certain amount of items per minute is therefore in most cases lower if you use 4 productivity modules, compared to just 2.

Green circuits for example: Imagine we want to produce 100000 Green circuits per minute. Let's ignore furnaces and mining drills and focus solely on assembling machines.
If we use 2 speed and 2 productivity modules we need about 164 machines producing green circuits and copper wire. (FactorioLab)
If we use 4 productivity modules we only need about 155 machines (FactorioLab)

The more intermediate steps there are, the bigger the difference get's. Your calculation is only true for the "lowest" production step. Using 3 speed modules for them lowers the total number of assembling machines even further. (FactorioLab)
Notice however that this increases the number of furnaces needed!

[eradicator]

Not really a suprise. Calculated that myself years ago (I'm sure the thread is still somewhere around. Or use "/sudo help get_power_per_cycle" (see my signature)). The key point is: SM+SM but PM*SM. Productivity is multiplicative on the speed bonus. 4PM also has better power cost per item. Even in Megabases you don't want to be wasting massive amounts of power.

[Belter]

TY for the comments!

Yes, the smaller resource need cascades, this kind of makes this whole quesiton to not a quesiton...

My surprise was the round curve for the 16 bacon setup (was focusing on creating a fully saturated 8 belt factory...) so was a bit narrow minded...

I always knew I'm just at the beginning of this fantastic game!

[MEOWMI]

It's not entirely unlike the physical damage bonus in gun turrets, which scales so well thanks to 2 bonuses multiplying each other. Whether that helps clarify it at all or not. The main difference is that productivity modules alone incur speed penalty which veils the numerical relationship and its true benefits.

[astroshak]

Input/second : reduced by using PM3’s in machine, SM3’s in beacons around machine.
Output/second : maximized by using SM3’s in machine, SM3’s in beacons around machine.

One Beacon is 50% speed boost. One SM3 in machine is a 50% speed boost. One PM3 is a 10% productivity boost and a 15% Speed reduction.

100% base speed (1.25 for AM3). Add 50% per SM3 in machine, and per Beacon. Subtract 15% per PM3. Multiply this by the base machine speed. 100% machine output. Add 10% per PM3. Multiply this by machine speed to determine output per second. (Assumes a 1 second cycle time on the recipe; divide by the recipe craft time to see the output per second of the recipe in question)

12 Beacons, 4 PM3? 100% + 600% - 60% = 640% = 6.4 … 6.4 X 1.25 = 8 … 100% + 40% = 140% = 1.4 … 8 * 1.4 = 11.2
12 Beacons, 4 SM3? 100% + 600% + 200% = 900% = 9 … 9 X 1.25 = 11.25

The second setup, the SM3 in machine, has the higher output rate.

So, the question becomes, is there a point where the PM3 setup matches (or exceeds) the SM3 setup?

(100% + B - 60%) X 1.25 X 1.4 = (100% + B + 200%) X 1.25
(B+40%) X 1.4 = B + 300%
1.4B + (1.4X40%) = B + 300%
1.4B + 50% = B + 300%
1.4B = B + 250%
0.4B = 250%
B = 625%

At 50% per Beacon, that comes to 13 Beacons, one of which only has one SM3 in it. So, if you could fit 13 Beacons around the machine, PM3 setups have a higher output for machines taking 4 modules. What about things that only take 3, such as Refineries?
(100% + B - 45%) X 1 X 1.3 = (100% + B + 150%) X 1
(B + 55%) X 1.3 = B + 250%
1.3B + 71.5% = B + 250%
1.3B = B + 178.5%
.3B = 178.5%
B = 595%

At 50% per Beacon, you are looking at 12 Beacons to exceed a SM3 setup’s output/second; 11.5 won’t meet it, but 12 will slightly exceed it.

Plan your beaconized setups accordingly.

[Krazykrl]

It's not entirely unlike the physical damage bonus in gun turrets, which scales so well thanks to 2 bonuses multiplying each other. Whether that helps clarify it at all or not. The main difference is that productivity modules alone incur speed penalty which veils the numerical relationship and its true benefits.

Well, the (negative) speed bonus from prod modules is additive with other speed effects. Prod modules are multiplicative with speeds, but the main benefit of prod modules is that each prod module effectively multiplies all resources consumed in that assembler.

Even with only 2 production steps using 4x prod3s each; you're outputting 1.96x unit of items per 1x unit of raw resources. And this ratio curves more vertically as you add more layers with prod modules. If you add even 1 more layer of 4xprod3, you take 1.96*1.4... and you end up with 2.744x the products you would make with pure(or no) speed modules.

Megabases will always hit an UPS limit before any sort of resource exploitation cap; so reducing active entities is always a good move. You need substantially fewer production/UPS entities as you drive that multiplicative prod module curve into the sky.

Take blue science as an example.
1.000 blue belts of iron plate with all prod3s can produce 543 chem science per minute. (And require 245.9(basic) 96.2(advanced) crude/sec)
2.414 blue belts of iron plate without any prods would produce the same 543 chem SPM. (And require 754.2(basic) 348.1(advanced) crude/sec)