Equations
(→NPC Spawn Weight Approximation) |
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| + | == Artifacts from Artifact Points == | ||
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| + | 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.) | ||
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| + | 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. | ||
Revision as of 04:15, 10 January 2012
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):
N = Number of Planets Controlled C = (N-1)^3 * 1000
Current Simplified Formula In English (Translated By - QCubed):
(Colonization Cost) = (((Number Of Planets Controlled):-1)^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):
N = Number of Planets Controlled I = (N-1)^3 * 2000
Current Simplified Formula In English (Translated By - QCubed):
(Invasion Cost) = (((Number Of Planets Controlled):-1)^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
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 Chart of Availability to corresponding 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, mRich = 12, 1xm Rich = 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 Level (Difference Between Last Rank and Next)
Original Formula (Author - QCubed):
R = Rank XP(D) = (40 * R) + 20
Original Formula In English (Translated By - QCubed):
(Difference in XP) = (40 * (Rank)) + 20
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
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 artanh() 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.