## Equations

This will be a one-stop shop for common equations needed when playing the game. Credit will be given to original wiki posters who determined equations, and to those who simplify them

## Planet Equations

### Planet Colonization Cost

Current Simplified Formula (Author - QCubed, Corrected by - FerrusManus):

N = Number of Planets Controlled

C = N^3 * 1000

Current Simplified Formula In English (Translated By - QCubed, Corrected by - FerrusManus):

(Colonization Cost) = ((Number Of Planets Controlled)^3) * 1000

### Planet Invasion Cost

Current Simplified Formula (Author - QCubed, Corrector - FerrusManus):

N = Number of Planets Controlled

I = N^3 * 2000

Current Simplified Formula In English (Translated By - QCubed, Corrector - FerrusManus):

(Invasion Cost) = ((Number Of Planets Controlled)^3) * 2000

### Planet Invasion Chance

With thanks to Darth Flagitious

InvAtt = Your Invasion Attack (Your "Normal" Attack + "normal" buffs (i.e. crux/crimson/crystal etc.)+ Invasion-specific attack (from modules) + Invasion buffs (Stryll Pathogen, Mutagenic Cartridges etc.))*Invasion %Bonus(Decimators, Kulgox)

InvDef =(Planet Attack + Planet Defense + Invasion Defense Items) * (1+(LegionBonus/100))

• LegionBonus/100 is to change from percent to decimal

Chance% = (InvAtt/(3*InvDef))*100

• 100 is to change from decimal to percent

There is a maximum success chance of 90% regardless of ship attack and planet defenses. (Unconfirmed: there is also a minimum of 10%)

### Maximum Planet Limit

Current Simplified Formula (Author - QCubed):

R = Current Rank

M = RoundDown((R / 4) + 1)

Current Simplified Formula In English (Translated By - QCubed):

(Maximum Planet Limit) = RoundDown(((Current Rank) / 4) + 1)

### Resource Availability Formula

Original Formula (Author - QCubed):

A = Availability Number*
R = (-1 + (A * 0.25))
R% = (-1 + (A * 0.25) * 100)

*Note: Availability Multiplier is a number from 0 to no known limit, which corrosponds to the named resource availability starting from No Resource being (0) and incrementing by one per resource upgrade. Hence an artifact which increases "resource availability by 2" (AKA "Two Levels) is incrementing the value of A by 2.

Quick Reference Chart of Availability Text to corresponding Availability Number:

• v = Very, e = Extremely, u=Ultra, m=Mega)
• None = 0, eSparse = 1, vSparse = 2, Sparse = 3, Average = 4, Abundant = 5, vAbundant = 6, eAbundant = 7, Rich = 8, vRich = 9, eRich = 10, uRich = 11...(For Mega Rich [mRich] Availabilities see the Note below!)1

1Mega Rich Availability has no known Maximum and Begins at "Mega Rich" (0x mRich) and Availability is calculable as follows:
1 Continued: "Nx mRich = (N + 12)" (ie. mRich = 12, 1x mRich = 13, 2x mRich = 14...etc.)

Original Formula In English (Translated By - QCubed):

(Resource Multiplier) = -1 + ((Availability Number) * 0.25)
(Resource Multiplier In Percent) = (-1 + ((Availability Number) * 0.25)) * 100)

### Planet Space to Size Formula

Original Formula (Author - QCubed):

Z = Size of Planet (Number System)
S = (Z*6)+15
Note: The Size of a Planet is a number from 1 to 11, corrosponding to vTiny = 0 and Mega Colossal = 11, incremening by 1 for each value in between.

Original Formula In English (Translated By - QCubed):

(Space Available) = ((Size Of The Planet) * 6) + 15

## Ranks/XP

### Total XP For Rank 'R' (Total)

Original Formula (Author - QCubed):

R = Rank

XP(T) = 20 * (R ^ 2)

Original Formula In English (Translated By - QCubed):

(Total XP) = 20 * ((Rank)^2)

### XP Needed to reach Next Rank (Difference Between Last Rank and Next)

Original Formula (Author - QCubed):

R = Rank

XP(R) = (40 * R) + 20

Original Formula In English (Translated By - QCubed):

(Difference in XP) = (40 * (Rank)) + 20

### Energy to Rank-up

E = Energy Needed to Rank-up
XP(R) = XP Needed to reach Next Rank

```(NOTE: For Autoranking see the above formula for XP(R))
```

XP(S) = Ratio of XP from source of XP (eg. NPC/Mission/Scanning/Whatever)
H = Human Race Multiplier (ie. If Human = 0.1, else = 0)
N = Neural Multiplier (ie. If Neural Active = 0.15, else = 0)
L = RSL Multiplier (ie. If RSL Active = 0.1, else = 0)

E = RoundUp( XP(R) / ( XP(S) * (1 + H) * (1 + N) * (1 + L) ) )

```Since this formula is a little complex I have provided an example:
```

As Human race with RSL Active, from Rank 1000 to Rank 1001, and running only the XTS-9 Refinement mission:

E = ( (40 * 1000) + 20 ) / ( 1.75 * (1 + 0.10) * (1 + 0) * (1 + 0.10) )
E = ( 40000 + 20 ) / ( 1.75 * 1.1 * 1 * 1.1 )
E = 40020 / ( 1.75 * 1.1 * 1.1 )
E = 40020 / ( 1.75 * 1.21 )
E = 40020 / 2.1175
E = 19,000

### XP/Energy Ranking Ratio Formula

A More useful formula for most intents and purposes (and far simpler) is to figure out the Energy ratio needed to rank up given the energy you have on hand.

XP(E) = Energy Ratio needed to rank up. E = Energy on Hand. XP(R) = XP Needed to rank up (In the case of AutoRanking we use the XP(R) formula above)

XR(E) = E / XP(R)

In the Case of Autoranking: XR(E) = E / ( (40 * R) + 20)

the resulting Ratio can be compared to the missions and NPCs you have available to you, to choose which combination of actions you wish to take to maximize the actions you perform before you rank up (better utilize your energy if you have a lot) or minimize the time to rank up.

## NPC Formulas

### Max Damage Inflicted Against an NPC in a Single Shot

Original Formula (Author - QCubed):

M = N * 2.5

Original Formula In English (Translated By - QCubed):

(Max Damage in a Single Shot) = (NPC Rank) * 2.5

### Minimum Hits Needed to Kill an NPC

Original Formula (Author - QCubed):

K = (H + S) / ( N * 2.5)

Original Formula In English (Translated By - QCubed):

(Minimum Hits Needed to Kill an NPC) = ((NPC Hull) + (NPC Shield)) / (( NPC Rank) * 2.5)

### Best XP to Energy Ratio for Killing an NPC

Simplified Formula (Author - QCubed):

XP/E = (B / (K * 5)) + 2

Simplified Formula In English (Translated By - QCubed):

(XP to Energy Ratio) =  ((XP Earned on Kill) / ((Minimum Shots) * 5)) + 2

Original Formula (Author - QCubed):

XP/E = ((10 * K) + (B)) / (K * 5)

Original Formula In English (Translated By - QCubed):

(XP to Energy Ratio) =  (((Minimum Shots)*10)+(Bonus XP Earned on Kill))/((Minimum Shots)*5)

### Combat Formula Approximation

With thanks to BinaryMan and FerrusManus

Updated January 2014. The 'random factor' is random(0.6, 1.0), then a coin toss to multiply or divide the raw attack by this number. The output range is still 0.6 to 1.666. The average output is at or very close to 1.00-1.05.

Damage per shot = tanh( attack*(random(0.6 to 1.666)) / (defense * 5) ) * damagecap

This translates into a min, max, and average damage in terms of % of enemy damage cap. Take your attack and divide by the enemy defense. This is the 'attack factor'. Then divide by 5, this is the adjusted attack factor.

The average damage result will be TANH(adjusted attack factor). The minimum damage will be TANH(adjusted attack factor * 0.6) The maximum damage will be TANH(adjusted attack factor * 1.666)

For example to reach an average of 50% damcap per shot, you need 2.75 attack factor. So if you know the enemy health total and defense and rank, you can estimate what attack you need to kill it, on average, in N shots.

## NPCs

damagecap = 2.5 * npcrank

## players

damagecap = maximum( decks/2, (rank+19)/2 ).

The "attack randomization" is not linear, but a large data sample indicates the lower multiplier is 0.6 and the upper is the inverse, 1/0.6 = 1.666, and most of that range is linear. The shape of the randomization appears to be a truncated arctanh() function. The average effective attack multiplier is about 1.10.

### NPC Spawn Weight Approximation

NPC weights are relative; the exact spawn % depends on the pool of eligible NPCs, which is based on rank, scan (for cloaked npcs), and active missions (for mission npcs). The following is the approximate weighting:

Name Weight
Dark Runner + Sha'din Raptor + Sha'din Charger + Chron Shift Carrier + Drannik Replicator + Drannik Archivist + Crimson (Flame)Hawk + Ionic Battleship + All Zolazin Spawns (7 types, all spawn individually so together they are like weight 7000, the rank 10 has 2 subtypes which account for weight 2000 of that) ~1000
Rogue Tech Collector 840-850
Rogue Data Analyzer 700
Dark Trafficker + The Fornyis ~133
Stryll Trapper ~127
Sha'din Penetrator ~57
RSL Siege Cannon ~41
Sha'din Shockfighter ~39
Lazuli Harrower ~36
Mylarai Extractor ~31
Sabre Gunship ~30
T.O. Troop Carrier ~14
Dark Arms Carrier ~14
Rogue LabPod ~13/14
Rogue Experimenter ~2.5

## Base Raid Success Calculation

The exact formula is disclosed in this forum post by DF:

raid chance = 100 * (1 - [(DR - 1) / (BL - 1) / 10]) * 1.07^PARM * 1.09^PARS * 1.2^AVAR * 1.3^RP

where:
DR = damage rank
BL = base level
PARM = number of protean armouries
PARS = number of protean arsenals
AVAR = 1 if systematic avarice UST effect is active (during Scruuge seasonal event), otherwise 0
RP = 1 if raider profession, otherwise 0

## Artifacts from Artifact Points

The chance of getting a specific artifact on a single pull from your artifact points is quite simply 1/n, where n = the number of artifacts that have AP values less than or equal to the AP you currently have. (See Common Artifacts to find how many points a specific artifact costs.)

To maximize your chance at getting a specific type of artifact, find the number of points required for that artifact and then follow these 3 easy steps:

• Step 1: Wait till the first moment your accumulated artifact points are higher than the value at which the desired artifact requires.
• Step 2: Pull artifacts from your artifact points, stopping the moment your points drop below the value the desired artifact requires.
• Step 3: Goto Step 1.

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