# Perpetuum Refining Formulas Research

**Perpetuum Refining Formulas Research** by Raptine

I’ve been looking for some time to find a relatively accurate refining formula on the forum but I have not had much luck. The sites and formulas (Naruby and Warux’s ATG) I found do not tally with the actual numbers I see in-game – at least not accurately enough for my tastes! In some instances the difference is quite substantial.

TLDR – lots of maths and assumptions that are probably wrong. The purpose of this post is to get it flamed, corrected or confirmed. Have fun doing either yarr. I have a horrible suspicion I missed something important – T4 flamesuit available cool

DISCLAIMER: I am not a mathematician – jargon might be incorrect.

I am aware that we do not get to see the actual decimal places in both the in-game Factory Material Efficiency (ME) value and the Relation percentage value. I started with the numbers I could obtain from the game over 3 characters – one of which was created with the only purpose to check waste on refining with absolute 0% in both ME and Relations. Characters referred to as Indy, Control and Combat from now on.

All calculations based on obtaining 300 Titanium by refining Titan Ore at a Level 1 refinery (ICS Alpha). The 300 number is arbitrary but large enough to hopefully minimize rounding errors.

**Facts (numbers from the game)**

(Indy / Control / Combat) = Legend

Factory ME % (ingame) – 89 / 75 / 76

Extension Level – 6 / 0 / 0

Relation % (in-game) – 6 / 0 / 8

Titanium required – 300 units

Titan Ore required – 9000 units

(w/o waste = 30 ore per trit unit)

Current Ore Requirements (in-game) – 10,002 / 12,000 / 11,751 units of Titan Ore

Waste (in-game) – 1,002 / 3,000 / 2,751 units of Titan Ore

**Preliminary Calculations**

Waste % factor is [(Waste/Ore w/o waste)*100]

I get values of 11.13% / 33.33% / 30.57%. This calculation is borne out with the following formula (expanding to 6 decimal places for accuracy 0.111333 / 0.333333 / 0.30567):-

[Ore w/o waste*(1+decimal of Waste % Factor)] or for the Indy char example 9000*(1+0.111333) = 1,002 units wasted and confirmed in-game.

I also worked out the unshown decimal places in the Factory ME % by [(Ore req. w/o waste*current ore req.)*100]. Results are 89.98% / 75.00% / 76.59%

**Assumptions**

A. The control char has 33.33% waste which translates to a Level 1 refinery co-efficient (without relations and extensions) of 0.333333 which is significantly different to other numbers where I have seen 0.317 and 0.03 being used. I assume that this co-efficient will remain constant throughout.

B. Following above, the combat char with no extensions records a 76.59% Factory ME which translates to a 1.59% increase in ME with a recorded 8% relations. This might be the root of the formula on the forums where people calculate the relation coefficient decrease in waste as [relation %*0.002].

C. However, I think the relation coefficient decrease in waste should be calculated on the decrease in waste %. So Control char records a 33.33% while combat records a 30.57%. The difference attributed to 8% relation (no extensions on these 2 chars) is 2.76% or expressed in 6 decimal places as a coefficient we get 2.76/8 = 0.00345 which I rounded up to a nice number of 0.0035.

Basically, I think a 10% increase in relations will decrease your Waste % value by an absolute value of 3.5%. (assuming relations are linear).

**Extension Level Coefficient (reduction in waste)**

The formulas I have seen suggest the following formula [Extension Level*0.03]. However, this was not giving me the right numbers either. Reverse calculating back using Naruby’s formula:-

Waste % factor (in decimal) = [Level 1 Waste coefficient] – ([Extension Level Reduction Coefficient] + [Relation Reduction Coefficient])

For the Indy char whereby I know for fact the Waste % factor (decimal) is 0.111333, we get:-

0.111333 = 0.333333-([Extension Level 6 Reduction Coefficient] + (6*0.0035)]

[Extension Level 6 Reduction Coefficient] = 0.201

Therefore, one Extension level reduces the Waste % Factor by 0.201/6 = 0.0335.

Assuming a certain variance due to the unshown decimal places, other assumptions above and many reverse calculations, I settled on 0.033333 as the one Extension Level coefficient.

**The Big Question Mark**

A couple of hours and too many assumptions later I came up with this formula which fits the 3 chars I have:-

Waste % factor (in decimal) = 0.333333 – ([Extension Level*0.033333] + [Relation*0.0035])

Leading to:

Actual Titan Ore required to refine x1 unit of titanium = [30*(1+ Waste % Factor in decimal)]

The formula works for me for any other commodity atm. I do need more data from others since 3 chars are hardly a significant statistical sample.

**Annoying Relation Decimal Issue**

Obviously the numbers above have a slight variance which is due to the unshown decimal places in the relation bonus. Keeping all the assumptions above, I actually worked out the decimal places for my relation bonus which theoretically should be 6.27% for the indy char and 7.91% for the combat char. Interesting to note that if I am anywhere close to being right, the relation bonus is rounded up to 8% in game.

**Weird Stuff**

For a while, I thought the extension level +3% to ME was compounded over the initial 75% value. I tried it out but the numbers came out all wrong when I took the Level 1 refinery coefficient (control) as 0.333333. In fact the relation bonus was not resulting linear over the 3 chars. Also, the combat char disproved that notion with his 76+% ME without 1 level of extensions. Following that line of thought, 8% relations resulted in +1.59% ME while 6% relations was giving me less than 0.5% increase.

The 0.002 value for the relation bonus was even weirder when I was using Naruby’s formula and comparing to my in game numbers – in some instances the 8% bonus was resulting to be less beneficial than the 6% indy relation bonus. This was using the fixed 0.333333 Level 1 refinery ME coefficient value. When I reversed the situation, I was getting different values for the refinery coefficient. I though this was improbable and hence started on a new track.

Edit: hopefully amended all tritanium references to titanium – thanks Annihilator

Edit2: Amended last sentence in Assumptions section – should refer to a decrease in waste not increase in ME.

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