Turret damage: Difference between revisions

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<math>\pagecolor{Black}\color{White}\text{Chance to Hit} = {0.5^{\left({\left({\frac{V_{angular} \times 40000m}{acc_{turret} \times sig_{target}}}\right)^{2} + \left({\frac{max(0, \Delta_{distance} - opt_{turret})}{fall_{turret}}}\right)^{2}}\right)}}</math>

...where:

* <math>\pagecolor{Black}\color{White}v_{angular}</math> : Angular velocity of target. Simply put, how many circles the target can run around you per <math>\pagecolor{Black}\color{White}\frac{1}{2\pi}</math> seconds.

* <math>\pagecolor{Black}\color{White}v_{angular}</math> Angular velocity of target. Simply put, how many circles the target can run around you per <math>\pagecolor{Black}\color{White}\frac{1}{2\pi}</math> seconds.

* <math>\pagecolor{Black}\color{White}acc_{turret}</math> : "Turret accuracy score" found on the attributes tab of a turret.

* <math>\pagecolor{Black}\color{White}acc_{turret}</math> "Turret accuracy score" found on the attributes tab of a turret.

* <math>\pagecolor{Black}\color{White}sig_{target}</math> : Target signature radius. The size of the target, or more precisely the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.

* <math>\pagecolor{Black}\color{White}sig_{target}</math> Target signature radius. The size of the target, or more precisely the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.

* <math>\pagecolor{Black}\color{White}\max({0, x, \ldots})</math> ~~: a~~ math function that takes the highest value of zero or ''x''. It is used to prevent negative values in this case; any negative numbers are replaced with zero instead.

* <math>\pagecolor{Black}\color{White}\max({0, x, \ldots})</math> A math function that takes the highest value of zero or ''x''. It is used to prevent negative values in this case; any negative numbers are replaced with zero instead.

* <math>\pagecolor{Black}\color{White}\Delta_{distance}</math> : Distance between firing ship and target.

* <math>\pagecolor{Black}\color{White}\Delta_{distance}</math> Distance between firing ship and target.

* <math>\pagecolor{Black}\color{White}opt_{turret}</math> : "Turret optimal range" found on the attributes tab of a turret. Inside this range no range penalties from distance are applied. Measured in meters.

* <math>\pagecolor{Black}\color{White}opt_{turret}</math> "Turret optimal range" found on the attributes tab of a turret. Inside this range no range penalties from distance are applied. Measured in meters.

* <math>\pagecolor{Black}\color{White}fall_{turret}</math> : "Falloff" found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.

* <math>\pagecolor{Black}\color{White}fall_{turret}</math> "Falloff" found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.

Now let's look a little closer at the equation itself, there is something to be learned from that.

To paraphrase Oli Geist, this equation can be abstracted to

~~:''chance~~ to ~~hit'' ~~= 0.5~~(''~~tracking term~~'' ~~+ ''range term~~'')~~</~~sup~~>.

<math>\pagecolor{Black}\color{White}\text{Chance to Hit} = 0.5^{\text{tracking term} + \text{range term}}</math>

Math students may recognize that something of the form ''x''(''a''+''b'') is identical to ''xaxb'', so we can rewrite the above as

~~:''chance~~ to ~~hit'' ~~= 0.5~~''~~tracking term~~'' ×~~ 0.5~~''~~range term''</~~sup~~>

<math>\pagecolor{Black}\color{White}\text{Chance to Hit} = 0.5^{\text{tracking term}} \cdot 0.5^{\text{range term}}</math>

Why is this interesting? From this we can see that tracking and range are actually calculated separately, then the results from each are multiplied. This shows that Range and Tracking are indeed two different and independent things, and both will be used to score a hit.

@@ Line 112: / Line 112: @@
 <math>\pagecolor{Black}\color{White}\text{Chance to Hit} = {0.5^{\left({\left({\frac{V_{angular} \times 40000m}{acc_{turret} \times sig_{target}}}\right)^{2} + \left({\frac{max(0, \Delta_{distance} - opt_{turret})}{fall_{turret}}}\right)^{2}}\right)}}</math>
 ...where:
-* <math>\pagecolor{Black}\color{White}v_{angular}</math> : Angular velocity of target. Simply put, how many circles the target can run around you per <math>\pagecolor{Black}\color{White}\frac{1}{2\pi}</math> seconds.
+* <math>\pagecolor{Black}\color{White}v_{angular}</math>  Angular velocity of target. Simply put, how many circles the target can run around you per <math>\pagecolor{Black}\color{White}\frac{1}{2\pi}</math> seconds.
-* <math>\pagecolor{Black}\color{White}acc_{turret}</math> : "Turret accuracy score" found on the attributes tab of a turret.
+* <math>\pagecolor{Black}\color{White}acc_{turret}</math>  "Turret accuracy score" found on the attributes tab of a turret.
-* <math>\pagecolor{Black}\color{White}sig_{target}</math> : Target signature radius. The size of the target, or more precisely the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.
+* <math>\pagecolor{Black}\color{White}sig_{target}</math>  Target signature radius. The size of the target, or more precisely the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.
-* <math>\pagecolor{Black}\color{White}\max({0, x, \ldots})</math> : a math function that takes the highest value of zero or ''x''. It is used to prevent negative values in this case; any negative numbers are replaced with zero instead.
+* <math>\pagecolor{Black}\color{White}\max({0, x, \ldots})</math> A math function that takes the highest value of zero or ''x''. It is used to prevent negative values in this case; any negative numbers are replaced with zero instead.
-* <math>\pagecolor{Black}\color{White}\Delta_{distance}</math> : Distance between firing ship and target.
+* <math>\pagecolor{Black}\color{White}\Delta_{distance}</math> Distance between firing ship and target.
-* <math>\pagecolor{Black}\color{White}opt_{turret}</math> : "Turret optimal range" found on the attributes tab of a turret. Inside this range no range penalties from distance are applied. Measured in meters.
+* <math>\pagecolor{Black}\color{White}opt_{turret}</math> "Turret optimal range" found on the attributes tab of a turret. Inside this range no range penalties from distance are applied. Measured in meters.
-* <math>\pagecolor{Black}\color{White}fall_{turret}</math> : "Falloff" found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.
+* <math>\pagecolor{Black}\color{White}fall_{turret}</math> "Falloff" found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.
 Now let's look a little closer at the equation itself, there is something to be learned from that.
 To paraphrase Oli Geist, this equation can be abstracted to
-:''chance to hit''&nbsp;= 0.5<sup>(''tracking term''&nbsp;+ ''range term'')</sup>.
+<math>\pagecolor{Black}\color{White}\text{Chance to Hit} = 0.5^{\text{tracking term} + \text{range term}}</math>
 Math students may recognize that something of the form ''x''<sup>(''a''+''b'')</sup> is identical to ''x<sup>a</sup>x<sup>b</sup>'', so we can rewrite the above as
-:''chance to hit''&nbsp;= 0.5<sup>''tracking term''</sup>&nbsp;× 0.5<sup>''range term''</sup>
+<math>\pagecolor{Black}\color{White}\text{Chance to Hit} = 0.5^{\text{tracking term}} \cdot 0.5^{\text{range term}}</math>
 Why is this interesting? From this we can see that tracking and range are actually calculated separately, then the results from each are multiplied. This shows that Range and Tracking are indeed two different and independent things, and both will be used to score a hit.