Difference between revisions of "Formulae"

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This is an explanation page for the various formulae involved in calculation stats in game.
+
This is an explanation page for the various formulae involved in calculating stats in game.  
  
−
===Augmenter Tweaking===
+
= Augmenter Calculations  =
  
−
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''.   
+
== 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.
 +
 
 +
<math>
 +
F =
 +
\begin{cases}
 +
B \ge 1, & B - 1 \\
 +
B < 1, & \dfrac{-1}{B} + 1
 +
\end{cases}</math>
 +
 
 +
Now we sum all of the factors for all augmenters together:
 +
 
 +
<math>
 +
F_{sum} = F_1 + F_2 + F_3 + F_4 + F_5 + F_6 + \cdots</math>
 +
 
 +
Next we convert this factor sum back to a bonus:
 +
 
 +
<math>
 +
B_{sum} =
 +
\begin{cases}
 +
F_{sum} \ge 0, & F_{sum} + 1 \\
 +
F_{sum} < 0, & \dfrac{-1}{F_{sum} - 1}
 +
\end{cases}</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.
 +
 
 +
== 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''.  
 +
 
 +
<math>
 +
\left(1+.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\times.56</math>
 +
 
 +
<br><br>
 +
 
 +
Similarly, if the equipped augmenter granted -56% instead, the resulting penalty is calculated as follows.
 +
 
 +
<math>
 +
\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>
 +
 
 +
 
 +
for another explanation and more examples, read this forum post.
 +
http://www.starsonata.com/forum/viewtopic.php?f=17&t=42444
 +
 
 +
= Colony Suitability  =
 +
 
 +
Initial Suitability (<math>S_i</math>) is the product of the attribute multipliers for Gravity, Temperature, and Atmosphere.
 +
 
 +
{| border="2" cellspacing="0" cellpadding="2"
 +
|-
 +
! Attribute / Multiplier
 +
! 0.5
 +
! 0.75
 +
! 1.00
 +
|-
 +
! Gravity
 +
| Heavy
 +
| Low
 +
| Normal
 +
|-
 +
! Temperature
 +
| Blistering
 +
| Cold
 +
| Temperate
 +
|-
 +
! Atmosphere
 +
| Gaseous
 +
| Noxious
 +
| Terran
 +
|}
 +
 
 +
So:
 +
 
 +
<math>
 +
S_i = \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>
 +
S_f = \left( S_i \times \left(1 + .05 \times CA \right)\right) + T_{sum}</math>
 +
 
 +
''Note: All suitability calculations are '''rounded down'''''
 +
 
 +
= Construction  =
 +
 
 +
== Bulk Construction  ==
 +
 
 +
Where B is the amount building, M is the amount of material/manhours needed for 1 build, and N is the total amount needed for the multibuild.
 +
 
 +
<math>N = M \times B \times 0.9^{log\left(B\right)}</math>
 +
 
 +
<sup>*Note: log() is in base 10</sup>
 +
 
 +
== Build Time ==
 +
Build Time (T) in seconds is 10 times Manhours (M) divided by Workforce (W). Workforce is the lesser between Max Workforce and available workers on a base.
 +
 
 +
<math>T = \dfrac{M\times\mbox{10}}{W}</math>
 +
 
 +
= Movement and Agility  =
 +
 
 +
== Speed  ==
 +
 
 +
Speed is defined as distance traveled per second.
 +
 
 +
<math>Speed = \dfrac{Distance}{Time}</math>
 +
 
 +
== Thrust  ==
 +
 
 +
Acceleration (a) is Thrust (T) divided by Weight (W). Acceleration is defined as change of speed per unit time (seconds in this case). The number on the ship screen is this multiplied by 10,000.
 +
 
 +
<math>
 +
a=\dfrac{T}{W}</math>
 +
 
 +
== Turning ==
 +
 
 +
Turning (T) in revolutions per second is equal to the turning stat (t) times 152 divided by Weight (W).
  
 
<math>
 
<math>
−
\left(1+.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\times.56
+
T=\dfrac{152\times\mbox{t}}{W}</math>
−
</math>
+
 
 +
=  Slots  =
 +
 
 +
Calculations for slots systems
 +
 
 +
===  Bots ===
 +
A Bots ship takes a number of slots (S) equal to half its tech (T), rounded up with a minimum number of slots of 1.
 +
 
 +
<math>S = \dfrac{T}{2}</math>
 +
==== Trade Bots ====
  
−
<br><br>
+
The number of available Trade Bot slots <math>S_T</math> is equal to your level in [[Remote Control]] (<math>R_C</math>) plus your level in [[Bot Research]] (<math>S_R</math>)
  
−
Similarly, if the equipped augmenter granted -56% instead, the resulting penalty is calculated as follows.
+
<math>S_T = R_C + S_R</math>
 +
 
 +
==== Combat Bots ====
 +
Combot Bots slots use the same formula as Trade bot slots with the additional restriction that the total number (T) of activated botscannot exceed half the value of your total slots.
  
 
<math>
 
<math>
−
\dfrac{1-.56}{1+\left(.56\times\left(.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\right)}
+
\begin{cases}
−
</math>
+
R_C = 1, & T \le 1 + \dfrac{S_R}{2} \\
−
<br><br>
+
  \\
 +
R_C = \mbox{2 or 3}, & T \le 2 + \dfrac{S_R}{2} \\
 +
  \\
 +
R_C \ge 4, & T \le \dfrac{R_C +S_R}{2}
 +
\end{cases}</math>
 +
 
 +
===  Drones  ===
 +
 
 +
====  Temporary Drones  ====
 +
 
 +
Temporary Drones don't have slots as such, players start off with the ability to lay 3 temporary drones, this can be increased by training [[Drone Mastery]], one of the tertiary skills of the [[Engineer]] class. This adds the ability to drop an extra drone at levels 1, 10 and 20 making a grand total of 6.
 +
 
 +
====  Permanent Drones  ====
 +
 
 +
Permanent Drone slot system is much like the bot 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]] [[Category:Gameplay]] [[Category: Colonies]]

Latest revision as of 18:10, 22 September 2024

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 0, & F_{sum} + 1 \\ F_{sum} < 0, & \dfrac{-1}{F_{sum} - 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)}


for another explanation and more examples, read this forum post. http://www.starsonata.com/forum/viewtopic.php?f=17&t=42444

Colony Suitability

Initial Suitability (S_i) is the product of the attribute multipliers for Gravity, Temperature, and Atmosphere.

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

So:

S_i = \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

Bulk Construction

Where B is the amount building, M is the amount of material/manhours needed for 1 build, and N is the total amount needed for the multibuild.

N = M \times B \times 0.9^{log\left(B\right)}

*Note: log() is in base 10

Build Time

Build Time (T) in seconds is 10 times Manhours (M) divided by Workforce (W). Workforce is the lesser between Max Workforce and available workers on a base.

T = \dfrac{M\times\mbox{10}}{W}

Movement and Agility

Speed

Speed is defined as distance traveled per second.

Speed = \dfrac{Distance}{Time}

Thrust

Acceleration (a) is Thrust (T) divided by Weight (W). Acceleration is defined as change of speed per unit time (seconds in this case). The number on the ship screen is this multiplied by 10,000.

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

Bots

A Bots ship takes a number of slots (S) equal to half its tech (T), rounded up with a minimum number of slots of 1.

S = \dfrac{T}{2}

Trade Bots

The number of available Trade Bot slots S_T is equal to your level in Remote Control (R_C) plus your level in Bot Research (S_R)

S_T = R_C + S_R

Combat Bots

Combot Bots slots use the same formula as Trade bot slots with the additional restriction that the total number (T) of activated botscannot exceed half the value of your total slots.

\begin{cases} R_C = 1, & T \le 1 + \dfrac{S_R}{2} \\ \\ R_C = \mbox{2 or 3}, & T \le 2 + \dfrac{S_R}{2} \\ \\ R_C \ge 4, & T \le \dfrac{R_C +S_R}{2} \end{cases}

Drones

Temporary Drones

Temporary Drones don't have slots as such, players start off with the ability to lay 3 temporary drones, this can be increased by training Drone Mastery, one of the tertiary skills of the Engineer class. This adds the ability to drop an extra drone at levels 1, 10 and 20 making a grand total of 6.

Permanent Drones

Permanent Drone slot system is much like the bot 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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