Calculations and Formulas

*This page is a **work in progress**.*

## Multiplicative Formulas

Most things (close to 90%) are calculated multiplicatively, meaning that it grows exponentially, as opposed to linearly for additive formulas.

The general multiplicative formula is calculated like so:

# c

a
b

{\displaystyle c = a ^ b}

Where:

* c - final bonus (to multiply the value in question by)
* a - 1 + (increment of cost/bonus per *value*)
* b - total of *value*

### Note about *a*

Notice that *a* is **increased** by 1 on top of the increment, rather than the just the increment itself. When turning the increment from **percentage to number**, we divide by 100. This results in the increment itself being less than 1 which would cause the above formula to **decrease** exponentially rather than increase. Adding 1 to the number fixes this issue.

### Example

Any loop modification that does not explicitly mention **(additive)** is multiplicative by default. Say we buy/upgrade *MK1 Venture Module*, which increases Mod Points gained by 1.5% (and 8% for MK1 output). If the mod is level 3, the bonus comes out to be:

# 1. c

1.015
3

{\displaystyle c = 1.015 ^ 3}

\*
# 2. c
1.015
∗
1.015
∗
1.015

{\displaystyle c = 1.015 \* 1.015 \* 1.015}
# 3. c
1.045

{\displaystyle c = 1.045}

Since the final bonus **multiplies** Mod Points, it should be written as **x1.045** (this will appear as **x1.05** in-game, as it rounds to 2 decimal places).

*\*(recall that 1.5% would be 1.015 if calculating exponentially, not 0.015. See the note about a above if it is unclear to you)*

## Additive Formulas

A few bonuses in the game are **additive**, meaning that it grows linearly, as opposed to exponentially for multiplicative formula.

The general additive formula is calculated like so:

# c
1
(
a
∗
b
)

{\displaystyle c = 1 + (a \* b)}

Where:

* c - final bonus to multiply Mod Points by
* a - increment of bonus per *value*
* b - total of *value*

### Example

The loop modification *MK1 Connection Module* increases Mod Points gained (at level 1) by **0.01%** per manual MK1 generator bought.

Assume we have **900 manually-bought** MK1 generators. Substituing the variables above for the real values, we get:

# 1. c
1
(
0.0001
∗
900
)

{\displaystyle c = 1 + (0.0001 \* 900)}

\*
# 2. c
1
0.09

{\displaystyle c = 1 + 0.09}
# 3. c
1.09

{\displaystyle c = 1.09}

Since the final bonus **multiplies** Mod Points, it should be written as **x1.09** (this is how it will appear in-game).

Assume we will have 100 Mod Points, **before** calculating the bonus, gained on the next loop filled. With the above bonus, we will **actually** get

100
∗
# 1.09
109

{\displaystyle 100 \* 1.09 = 109}

 Mod Points.

*\*(recall that percentages must be always be divided by 100. Hence 0.01 / 100 = 0.0001)*

## Unfinished Work

*Everything beyond this point must be re-evaluated for better formatting and correction checking.*

Here is where people can find Calculations and Formulas created for use in Guides and Sheets.

### Generator Cost Formulas

* Mk1 3\*(1.065+0.004x)^(x\*(1+max(x-999,0)/1000))
* Mk2 2e3\*(2.9+0.3x)^(x\*(1+max(x-199,0)/500))
* Mk3 1e8\*(20+10x)^(x\*(1+max(x-99,0)/(1000/3)))
* Mk4 4e18\*(50+30x)^(x\*(1+max(x-74,0)/200))
* Mk5 5e46\*(220+80x)^(x(1+max(x-49,0)/200))
* Mk6 6e200\*(6e5+6e5\*x)^(x\*(1+x/(500/3)))
* Mk7 7e500\*(7e7+7e7\*x)^(x\*(1+x/50))
* Mk8 -