Equations
(→Planet Space to Size Formula) |
(→Energy to Rank-up) |
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=== Energy to Rank-up === | === Energy to Rank-up === | ||
| - | E = Energy Needed to Rank-up | + | E = Energy Needed to Rank-up <br> |
| - | XP(R) = XP Needed to reach Next Rank | + | XP(R) = XP Needed to reach Next Rank<br> |
| - | (NOTE: For Autoranking see the above formula for XP(R)) | + | (NOTE: For Autoranking see the above formula for XP(R))<br> |
| - | 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) | + | XP(S) = Ratio of XP from source of XP (eg. NPC/Mission/Scanning/Whatever)<br> |
| - | N = Neural Multiplier (ie. If Neural Active = 0.15, else = 0) | + | H = Human Race Multiplier (ie. If Human = 0.1, else = 0)<br> |
| - | L = RSL Multiplier (ie. If RSL Active = 0.1, else = 0) | + | N = Neural Multiplier (ie. If Neural Active = 0.15, else = 0)<br> |
| + | L = RSL Multiplier (ie. If RSL Active = 0.1, else = 0)<br> | ||
E = RoundUp( XP(R) / ( XP(S) * (1 + H) * (1 + N) * (1 + L) ) ) | E = RoundUp( XP(R) / ( XP(S) * (1 + H) * (1 + N) * (1 + L) ) ) | ||
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As Human race with RSL Active, from Rank 1000 to Rank 1001, and running only the XTS 9 mission: | As Human race with RSL Active, from Rank 1000 to Rank 1001, and running only the XTS 9 mission: | ||
| - | E = ( (40 * 1000) + 20 ) / ( 1.75 * (1 + 0.10) * (1 + 0) * (1 + 0.10) ) | + | E = ( (40 * 1000) + 20 ) / ( 1.75 * (1 + 0.10) * (1 + 0) * (1 + 0.10) )<br> |
| - | + | E = ( 40000 + 20 ) / ( 1.75 * 1.1 * 1 * 1.1 )<br> | |
| - | E = ( 40000 + 20 ) / ( 1.75 * 1.1 * 1 * 1.1 ) | + | E = 40020 / ( 1.75 * 1.1 * 1.1 )<br> |
| - | + | E = 40020 / ( 1.75 * 1.21 )<br> | |
| - | E = 40020 / ( 1.75 * 1.1 * 1.1 ) | + | E = 40020 / 2.1175<br> |
| - | + | ||
| - | E = 40020 / ( 1.75 * 1.21 ) | + | |
| - | + | ||
| - | E = 40020 / 2.1175 | + | |
| - | + | ||
E = 19,000 | E = 19,000 | ||
---- | ---- | ||
Revision as of 05:21, 19 April 2013
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
Contents |
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
Original Formula (Author - N/A):
X = Number of Planets Controlled minus one (1) p(x) = (x^3 + 3x^2 + 3x + 1) * 1000
Original Formula In English (Translated By - QCubed):
(Colonization Cost) = ((((Number Of Planets Controlled):-1)^3) + ((3 * ((Number Of Planets Controlled):-1))^2) + (3 * ((Number Of Planets Controlled):-1)) + 1) * 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
Original Formula (Author - N/A):
X = Number of Planets Controlled minus one (1) p(x) = ((x^3 + 3x^2 + 3x + 1) * 1000) * 2
Original Formula In English (Translated By - QCubed):
(Colonization Cost) = (((((Number Of Planets Controlled):-1)^3) + ((3 * ((Number Of Planets Controlled):-1))^2) + (3 * ((Number Of Planets Controlled):-1)) + 1) * 1000) * 2
Planet Invasion Chance
With thanks to Darth Flagitious
Chance% = (InvAtt/(3*InvDef))*100 <--Note: *100 is to convert from decimal to percent
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)) <--Note: LegionBonus/100 is to convert from percent to decimal
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 Collosal = 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 Next Rank (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 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 Sheild)) / (( 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
Damage per shot = tanh( attack*(random(0.6 to 1.666)) / (defense * 5) ) * damagecap
damagecap = 2.5 * npcrank ; for players, damagecap = 0.5 * decks in most cases.
The tanh() function is almost linear up to 0.40, therefore if your attack ~= npcdefense , you will do about 0.20 * 2.5 = 0.50 * npcrank (your rank in the case of matched npcs). If your attack > 2 * npcdefense , you will do about npcrank in damage.
To hit around the damagecap on npcs, you need around 10 * npcdefense (~96.4% of cap).
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 |
| Blade Harvester | ~29 |
| T.O. Troop Carrier | ~14 |
| Dark Arms Carrier | ~14 |
| Rogue LabPod | ~13/14 |
| Rogue Experimenter | ~2.5 |
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.