Difference between revisions of "Formulae"

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This is an explanation page for the various formulae involved in calculating stats in game.
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This is an explanation page for the various formulae involved in calculating stats in game.  
  
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=Augmenter Calculations=
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= Augmenter Calculations =
  
−
==Augmenter Addition==
+
== Augmenter Addition ==
−
Augmenter addition is a multi-step process. First all augmenters are tweaked using the augmenter tweaking formula below.
 
  
−
Then the tweaked bonus is converted to a factor (F) using one of two formula, depending on if it is a positive augmenter or a negative augmenter. If the tweaked augmenter gives +83% then by adding 1 the tweaked bonus (B) is 1.83. In a similar fashion, if the tweaked augmenter gives -83% then B is .17.
+
Augmenter addition is a multi-step process. First all augmenters are tweaked using the augmenter tweaking formula below.
 +
 
 +
Then the tweaked bonus is converted to a factor (F) using one of two formula, depending on if it is a positive augmenter or a negative augmenter. If the tweaked augmenter gives +83% then by adding 1 the tweaked bonus (B) is 1.83. In a similar fashion, if the tweaked augmenter gives -83% then B is .17.  
  
 
<math>
 
<math>
Line 13: Line 14:
 
  B \ge 1, & B - 1 \\
 
  B \ge 1, & B - 1 \\
 
  B < 1, & \dfrac{-1}{B} + 1
 
  B < 1, & \dfrac{-1}{B} + 1
−
\end{cases}
+
\end{cases}</math>  
−
</math>
 
  
−
Now we sum all of the factors for all augmenters together:
+
Now we sum all of the factors for all augmenters together:  
  
 
<math>
 
<math>
−
F_{sum} = F_1 + F_2 + F_3 + F_4 + F_5 + F_6 + \cdots
+
F_{sum} = F_1 + F_2 + F_3 + F_4 + F_5 + F_6 + \cdots</math>  
−
</math>
 
  
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Next we convert this factor sum back to a bonus:
+
Next we convert this factor sum back to a bonus:  
  
 
<math>
 
<math>
Line 29: Line 28:
 
  F_{sum} \ge 1, & F_{sum} + 1 \\
 
  F_{sum} \ge 1, & F_{sum} + 1 \\
 
  F_{sum} < 1, & \dfrac{-1}{B - 1}
 
  F_{sum} < 1, & \dfrac{-1}{B - 1}
−
\end{cases}
+
\end{cases}</math>  
−
</math>
 
  
 +
<br> It is this B that can be used to multiply with some stat to get the augged stat. For a bonus that can be compared to augmenter stats, we just subtract 1. 1.83 corresponds to +83% and .17 corresponds to -83%. Given the above calculation, one should take note that negative augmenters provide a greater effect than positive augmenters of the same magnitude.
  
−
It is this B that can be used to multiply with some stat to get the augged stat. For a bonus that can be compared to augmenter stats, we just subtract 1. 1.83 corresponds to +83% and .17 corresponds to -83%. Given the above calculation, one should take note that negative augmenters provide a greater effect than positive augmenters of the same magnitude.
+
== Augmenter Tweaking  ==
  
−
==Augmenter Tweaking==
+
For example, a ship with one augmenter equipped to grant +56% to some statistic would receive the following bonus, as a function of the player's level of Augmenter Tweaking, labeled ''AT'', Imperial Tweaking, labeled ''IT'', and Engineer Class, labeled ''EC''.  
−
 
 
−
For example, a ship with one augmenter equipped to grant +56% to some statistic would receive the following bonus, as a function of the player's level of Augmenter Tweaking, labeled ''AT'', Imperial Tweaking, labeled ''IT'', and Engineer Class, labeled ''EC''.
 
  
 
<math>
 
<math>
−
\left(1+.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\times.56
+
\left(1+.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\times.56</math>  
−
</math>
 
  
−
<br><br>
+
<br><br>  
  
−
Similarly, if the equipped augmenter granted -56% instead, the resulting penalty is calculated as follows.
+
Similarly, if the equipped augmenter granted -56% instead, the resulting penalty is calculated as follows.  
  
 
<math>
 
<math>
−
\dfrac{1-.56}{1+\left(.56\times\left(.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\right)}
+
\dfrac{1-.56}{1+\left(.56\times\left(.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\right)}</math> <br><br>  
−
</math>
 
−
<br><br>
 
  
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=Colony Suitability=
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= Colony Suitability =
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Initial Suitability (<math>S_i</math>) is calculated by 100 multiplied by the Attributes.
 
  
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{|border="2" cellspacing="0" cellpadding="2"
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Initial Suitability (<math>S_i</math>) is calculated by 100 multiplied by the Attributes.
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!Attribute / Multiplier
+
 
−
!0.5
+
{| border="2" cellspacing="0" cellpadding="2"
−
!0.75
 
−
!1.00
 
 
|-
 
|-
−
!Gravity
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! Attribute / Multiplier
−
|Heavy
+
! 0.5
−
|Low
+
! 0.75
−
|Normal
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! 1.00
 
|-
 
|-
−
!Temperature
+
! Gravity
−
|Blistering
+
| Heavy
−
|Cold
+
| Low
−
|Temperate
+
| Normal
 
|-
 
|-
−
!Atmosphere
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! Temperature
−
|Gaseous
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| Blistering
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|Noxious
+
| Cold
−
|Terran
+
| Temperate
 +
|-
 +
! Atmosphere  
 +
| Gaseous  
 +
| Noxious  
 +
| Terran
 
|}
 
|}
  
−
So:
+
So:  
 +
 
 +
<math>
 +
S_i = {100\times\mbox{Gravity}\times\mbox{Temperature}\times\mbox{Atmosphere}}</math>
 +
 
 +
<br> Final Suitability (<math>S_f</math>) is Initial Suitability (<math>S_i</math>) times the bonus from [[Colonial Administrator]] (CA) plus the bonuses from Terraforming <math>T_{sum}</math>.
  
 
<math>
 
<math>
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S_i = {100\times\mbox{Gravity}\times\mbox{Temperature}\times\mbox{Atmosphere}}
+
S_f = \left( S_i \times \left(1 + .05 \times CA \right)\right) + T_{sum}</math>  
−
</math>
 
  
 +
''Note: All suitability calculations are '''rounded down'''''
  
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Final Suitability (<math>S_f</math>) is Initial Suitability (<math>S_i</math>) times the bonus from [[Colonial Administrator]] (CA) plus the bonuses from Terraforming <math>T_{sum}</math>.
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= Construction  =
  
−
<math>
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Build time is:
−
S_f = \left( S_i \times \left(1 + .05 \times CA \right)\right) + T_{sum}
 
−
</math>
 
  
−
''Note: All suitability calculations are '''rounded down'''''
+
<math>Time = \dfrac{M_h\times\mbox{10}}{W_f}</math>
  
−
=Construction=
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== Bulk Construction ==
  
−
Build time is:
+
Bulk material discount calculation is:  
  
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<math>Time = \dfrac{M_h\times\mbox{10}}{W_f}</math>
+
<math>Discount = {0.9\times\mbox{Log}^{B}}</math> Where B is the amount building
  
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==Bulk Construction==
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Bulk build time discount calculation is:  
−
Bulk material discount calculation is:
 
  
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<math>Discount = {0.9\times\mbox{Log}^{B}}</math>
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<math>Time Discount = {0.9\times\mbox{Log}^{B}}</math> Where B is the amount building  
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Where B is the amount building
 
  
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Bulk build time discount calculation is:
+
= Movement and Agility  =
  
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<math>Time Discount = {0.9\times\mbox{Log}^{B}}</math>
+
== Speed  ==
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Where B is the amount building
 
  
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=Movement and Agility=
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Speed is defined as distance traveled per second.
  
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==Speed==
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<math>Speed = \dfrac{Distance}{Time}</math>
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Speed is defined as distance traveled per second.
 
  
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<math>Speed = \dfrac{Distance}{Time}</math>
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== Thrust  ==
  
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==Thrust==
+
Acceleration (a) is Thust (T) divided by Weight (W). Acceleration is defined as Speed per second.  
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Acceleration (a) is Thust (T) divided by Weight (W). Acceleration is defined as Speed per second.
 
  
 
<math>
 
<math>
−
a=\dfrac{T}{W}
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a=\dfrac{T}{W}</math>  
−
</math>
 
  
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==Turning==
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== Turning ==
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Turning (T) in revolutions per second is equal to the turning stat (t) times 152 divided by Weight (W).
+
 
 +
Turning (T) in revolutions per second is equal to the turning stat (t) times 152 divided by Weight (W).  
  
 
<math>
 
<math>
−
T=\dfrac{152\times\mbox{t}}{W}
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T=\dfrac{152\times\mbox{t}}{W}</math>
−
</math>
+
 
 +
=  Slots  =
 +
 
 +
Calculations for slots systems
 +
 
 +
===  Slaves ===
 +
==== Trade Slaves ====
 +
 
 +
Trade Slave Slots (<math>TS_s</math>) is determined by the tech of the slave (<math>S_t</math>), and your skill in [[Remote Control]] (<math>RC</math>) and [[Slave Research]] (<math>SR</math>). <math>S_s</math> is the Slots per ship.
 +
<math>TS_s = RC + S_R</math> This calculation is always rounded up.<br>
 +
<math>S_s = \dfrac {S_t}{2}</math>
 +
 
 +
==== Combat Slaves ====
 +
Are the same as Trade Slaves, however, you are limited to a maximum of 9 slaves, which effectively means any ship that is Tech 4 or under takes 2 slots each.
 +
 
 +
===  Drones  ===
 +
 
 +
====  Temporary Drones  ====
 +
 
 +
Temporary Drones don't have slots as such, as a non-[[Engineer]], you get 3 Temporary Drone slots, to lay any Tech of drone. This can be increased to 6 via [[Drone Mastery]], which adds an extra slot every 10 levels.
 +
 
 +
====  Permanent Drones  ====
 +
 
 +
Permanent Drone slot system is much like the slave one. <math>S_t</math> represents total slots, <math>D_t</math> represents Drone tech, <math>S_d</math> represents slots per drone, <math>DD</math> is your [[Drone Deployment]] level, and <math>DR</math> is your [[Drone Research]] level.
  
 +
Your total Drone Slots is 4 times that of your Drone Deployment, with DR added on afterwards.
 +
Each drone takes the same number of slots as its tech, so:
 +
<math>S_t = DD\times\mbox{4}+DR</math><br>
 +
<math>S_d = D_t</math><br>
  
−
[[Category:Guides]]
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[[Category:Guides]] [[Category:Gameplay]]
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[[Category:Gameplay]]
 

Revision as of 17:10, 18 September 2010

This is an explanation page for the various formulae involved in calculating stats in game.

Augmenter Calculations

Augmenter Addition

Augmenter addition is a multi-step process. First all augmenters are tweaked using the augmenter tweaking formula below.

Then the tweaked bonus is converted to a factor (F) using one of two formula, depending on if it is a positive augmenter or a negative augmenter. If the tweaked augmenter gives +83% then by adding 1 the tweaked bonus (B) is 1.83. In a similar fashion, if the tweaked augmenter gives -83% then B is .17.

F = \begin{cases} B \ge 1, & B - 1 \\ B < 1, & \dfrac{-1}{B} + 1 \end{cases}

Now we sum all of the factors for all augmenters together:

F_{sum} = F_1 + F_2 + F_3 + F_4 + F_5 + F_6 + \cdots

Next we convert this factor sum back to a bonus:

B_{sum} = \begin{cases} F_{sum} \ge 1, & F_{sum} + 1 \\ F_{sum} < 1, & \dfrac{-1}{B - 1} \end{cases}


It is this B that can be used to multiply with some stat to get the augged stat. For a bonus that can be compared to augmenter stats, we just subtract 1. 1.83 corresponds to +83% and .17 corresponds to -83%. Given the above calculation, one should take note that negative augmenters provide a greater effect than positive augmenters of the same magnitude.

Augmenter Tweaking

For example, a ship with one augmenter equipped to grant +56% to some statistic would receive the following bonus, as a function of the player's level of Augmenter Tweaking, labeled AT, Imperial Tweaking, labeled IT, and Engineer Class, labeled EC.

\left(1+.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\times.56



Similarly, if the equipped augmenter granted -56% instead, the resulting penalty is calculated as follows.

\dfrac{1-.56}{1+\left(.56\times\left(.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\right)}

Colony Suitability

Initial Suitability (S_i) is calculated by 100 multiplied by the Attributes.

Attribute / Multiplier 0.5 0.75 1.00
Gravity Heavy Low Normal
Temperature Blistering Cold Temperate
Atmosphere Gaseous Noxious Terran

So:

S_i = {100\times\mbox{Gravity}\times\mbox{Temperature}\times\mbox{Atmosphere}}


Final Suitability (S_f) is Initial Suitability (S_i) times the bonus from Colonial Administrator (CA) plus the bonuses from Terraforming T_{sum}.

S_f = \left( S_i \times \left(1 + .05 \times CA \right)\right) + T_{sum}

Note: All suitability calculations are rounded down

Construction

Build time is:

Time = \dfrac{M_h\times\mbox{10}}{W_f}

Bulk Construction

Bulk material discount calculation is:

Discount = {0.9\times\mbox{Log}^{B}} Where B is the amount building

Bulk build time discount calculation is:

Time Discount = {0.9\times\mbox{Log}^{B}} Where B is the amount building

Movement and Agility

Speed

Speed is defined as distance traveled per second.

Speed = \dfrac{Distance}{Time}

Thrust

Acceleration (a) is Thust (T) divided by Weight (W). Acceleration is defined as Speed per second.

a=\dfrac{T}{W}

Turning

Turning (T) in revolutions per second is equal to the turning stat (t) times 152 divided by Weight (W).

T=\dfrac{152\times\mbox{t}}{W}

Slots

Calculations for slots systems

Slaves

Trade Slaves

Trade Slave Slots (TS_s) is determined by the tech of the slave (S_t), and your skill in Remote Control (RC) and Slave Research (SR). S_s is the Slots per ship. TS_s = RC + S_R This calculation is always rounded up.
S_s = \dfrac {S_t}{2}

Combat Slaves

Are the same as Trade Slaves, however, you are limited to a maximum of 9 slaves, which effectively means any ship that is Tech 4 or under takes 2 slots each.

Drones

Temporary Drones

Temporary Drones don't have slots as such, as a non-Engineer, you get 3 Temporary Drone slots, to lay any Tech of drone. This can be increased to 6 via Drone Mastery, which adds an extra slot every 10 levels.

Permanent Drones

Permanent Drone slot system is much like the slave one. S_t represents total slots, D_t represents Drone tech, S_d represents slots per drone, DD is your Drone Deployment level, and DR is your Drone Research level.

Your total Drone Slots is 4 times that of your Drone Deployment, with DR added on afterwards. Each drone takes the same number of slots as its tech, so: S_t = DD\times\mbox{4}+DR
S_d = D_t

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