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I somehow think that someone did this before, but I was bored and I like doing stuff with excel. But I didn't come here only to post this, but also to ask for discussion and maybe some help as well. Please tell me if my math went wrong at some point, because that would help me a lot.

Also please request if you want a certain value added to the table and I will do so.

The sheet explained:
The sheet only includes tier 3 modules. In formulas they are called P, S and E. The sheet does not take into account beacons requiring a lot of energy - this is because beacons need a flat value, no matter what and all values in the sheet are relative.
Modules: The amount of the stated module installed OR the amount of beacons affecting the machine (with the beacon having two modules of the type). If the beacon has only one module of the type the value is 0,5.
Productivity: (1 + P * 0,1)^steps
Energy Consumption: 1 + (P *0,8 + S * 0,7 - E * 0,5)
Crafting Speed: 1 + (-P * 0,15 + S * 0,5)
Energy Efficiency: Crafting Speed * Productivity / Energy Consumption
Crafting Efficiency: Productivity * Crafting Speed


However, in pure speed this combination of modules is not superior to speed modules, despite the additionally created items. Only at 13 speed beacons (not sure you can even fit this many) the synergy between speed and productivity surpasses pure speed in crafting efficiency (= items made per second). However, even with less speed productivity gives you free items, that's why people rather use the combination than pure speed. And that's also why depleted oil pumps should only use speed modules. Of course except if you somehow manage to stack 13 beacons ontop of an oil pump, then productivity gets better.

Explanation of the chart: On the top we are using 4 productivity modules with increasing numbers of beacons. On the bottom we use 4 speed modules, that's why the numbers are 4 higher each.

Note: If we assume a machine with 2 module slots, this does not change! The breakpoint is still very close to 12. If we put it in a diagram it becomes more obvious. Blue = machine with speed modules, pink = machine with productivity modules. X axis = speed beacons, Y axis = crafting productivity (items per second compared to a normal unmodified machine) Maybe I can provide some more info on processes with more steps. For now I can say that a 4 step process (smelting, green, red, blue circuits) even becomes 113% energy efficient, because the amount of free items you get in the process just is ridiculous (329% productivity = 2,29 free items per item crafted). Of course because blue circuits are made of mostly green and red ones are made of plastic (only 2x 120% productivity) it's not as high, but it probably isn't too far off either. I left out copper cables because they make up only 60% of a green circuit and it's hard to calculate - same for plastic made from petroleum which was made cracking light oil.

Syrchalis wrote:And that's also why depleted oil pumps should only use speed modules.

But that is wrong. When using 11 or 12 speed beacons around a pumpjack, using one productivity and one speed is more productive than pure speed. See this test done ingame: http://imgur.com/a/lkIGV

Right, but that never actually happens in a realistic scenario If it's only one deposit, you aren't going to waste 20+ x3 modules, and if it's more than one deposit, you won't be able to fit more than about 8. I seem to average, like, 3 beacons per deposit in real games. I actually wonder if at a certain point it makes more sense to build beacons over some deposits.

d4rkpl4y3r wrote:

Syrchalis wrote:And that's also why depleted oil pumps should only use speed modules.

But that is wrong. When using 11 or 12 speed beacons around a pumpjack, using one productivity and one speed is more productive than pure speed. See this test done ingame: http://imgur.com/a/lkIGV

But I did say that at 12/13 beacons productivity becomes better - and additionally it is a very rare occurrence.

Syrchalis wrote:But I did say that at 12/13 beacons productivity becomes better - and additionally it is a very rare occurrence.

You didn't say 12/13, you said 13:

Syrchalis wrote:Only at 13 speed beacons (not sure you can even fit this many) the synergy between speed and productivity surpasses pure speed in crafting efficiency (= items made per second).

But the breakpoint is at 11 beacons. If you get another number you must have messed up your math. Even if you fill the pumpjack with two prod3 modules it is more beneficial at 12 beacons and not 13, so you must have made a mistake somewhere. That is all I wanted to say. You have to revisit your math if you got a breakpoint of 13 because that result is wrong.

Also about your question if you can fit that many beacons: 12 beacons is the maximum around a 3x3 machine.

d4rkpl4y3r wrote:

Syrchalis wrote:But I did say that at 12/13 beacons productivity becomes better - and additionally it is a very rare occurrence.

You didn't say 12/13, you said 13:

Syrchalis wrote:Only at 13 speed beacons (not sure you can even fit this many) the synergy between speed and productivity surpasses pure speed in crafting efficiency (= items made per second).

But the breakpoint is at 11 beacons. If you get another number you must have messed up your math. Even if you fill the pumpjack with two prod3 modules it is more beneficial at 12 beacons and not 13, so you must have made a mistake somewhere. That is all I wanted to say. You have to revisit your math if you got a breakpoint of 13 because that result is wrong.

Also about your question if you can fit that many beacons: 12 beacons is the maximum around a 3x3 machine.

I was calculating for FOUR productivity modules and that was my statement. For a single module the math is different. And I already wrote that for two it's close to 12 instead of 13, so a smart person will be able to guess that with just one prod module the breakpoint is even lower.

Generally this wasn't about accuracy as much as saying:
1. Speed is better than productivity in throughput
2. Up until a breakpoint
3. Which is very high, reachable, but so high that you either don't have the resources to waste on such a tiny optimization or you have so many resources that these few % will not matter.

I'm not saying you're wrong, because you're not - but I was simply focusing on the more practical aspect than pure theory, that's why I never used theoretical numbers (unreachable high, negative, etc.)