Turret damage: Difference between revisions

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==The To-Hit-Equation==

This equation is used every single time someone fires a turret weapon in the game. The purpose of it is to determine the odds the turret has to hit its target. The value will always be between 0 and 1, or 0% and 100% if you will. The computer then generates a random number to see if a hit is scored or not.

<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>

<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, Distance - opt_{turret})}{fall_{turret}}}\right)^{2}}\right)}}</math>

...where:

* <math>\pagecolor{Black}\color{White}v_{angular}</math> Angular velocity of target in radians/second. Simply put, how many circles the target can run around you per <math>\pagecolor{Black}\color{White}{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. For the purposes of keeping track of (and canceling) measurement units, this may be treated as radians/second.

* <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 in meters. 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}~~\Delta_{distance}~~</math> Distance between firing ship and target.

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

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There is also one more thing we can find out by just looking at the equation. This is, however, a little trickier to follow, but the conclusion is easy. The aim is to compare the tracking term and the range term for similarities in how they behave. Do they have anything in common? To do this, we will freeze all values in those respective terms except for one variable in each, that will be 'turret tracking' and 'falloff' respectively. Then we can look at how that single variable effects the outcome in each case and see if there is any similarities between them.

The tracking part: All turrets measure tracking speed as ''~~angular velocity,~~'' ~~equal to dividing ''transversal speed'' by ''range to~~ target~~.'' This~~ is ~~all inside~~ the ~~tracking term, and basically just means how fast something moves around something else~~. Let's freeze the angular velocity, meaning the ships are orbiting each other at a constant speed. In the tracking term we also have ''~~turret signature resolution~~'' ~~divided by~~ ''target signature radius;'' ~~for easy comparison later on we will assume~~ that ~~these~~ are ~~equal (so dividing equals 1, resulting in no effect in the formula~~) ~~and freeze them as well~~. The result: a fixed number divided by ''turret tracking''.

The tracking part: All turrets measure tracking speed as a ''Turret Accuracy Score'', which describes how well a turret can cope with targets moving around the turret in circles (or how well the turret can cope with its own ship moving around the target in circles; as far as the equation is concerned, these are the same situation). Let's freeze the ''angular velocity'', meaning the ships are orbiting each other at a constant speed. In the tracking term we also have a ''40000 meters'' term (a true constant) and ''target signature radius'' (which is usually constant except when any effects that affect [[signature radius]] are applied or removed). The result: a fixed number divided by ''turret tracking''.

The range part: Being inside optimal never incurs a hit penalty, so we must move out into falloff ranges to see any changes in the to-hit equation's output values. Lets freeze everything apart from ''falloff.'' The result: a fixed number divided by ''falloff.''

Did you see what they ~~had~~ in common? In the tracking term, we now have ''something''/''Turret tracking'', in the range term we have ''something''/''falloff''. In both cases there is a value that is divided by the variable we were interested in. There is an important insight here: tracking and falloff behave identically. ~~And~~ they are not fixed limits, they become ratios that describes how quickly you lose hit chance as you start to push range and orbiting speeds, ~~and~~ the hit chance loss is gradual.

Did you see what they have in common? In the tracking term, we now have ''something''/''Turret tracking'', in the range term we have ''something''/''falloff''. In both cases there is a value that is divided by the variable we were interested in. There is an important insight here: tracking and falloff behave identically. Also, they are not fixed limits, they become ratios that describes how quickly you lose hit chance as you start to push range and orbiting speeds. Also, the hit chance loss is gradual.

==Base damage==

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 ==The To-Hit-Equation==
 This equation is used every single time someone fires a turret weapon in the game. The purpose of it is to determine the odds the turret has to hit its target. The value will always be between 0 and 1, or 0% and 100% if you will. The computer then generates a random number to see if a hit is scored or not.
-<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>
+<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, Distance - opt_{turret})}{fall_{turret}}}\right)^{2}}\right)}}</math>
 ...where:
 * <math>\pagecolor{Black}\color{White}v_{angular}</math>  Angular velocity of target in radians/second. Simply put, how many circles the target can run around you per <math>\pagecolor{Black}\color{White}{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.  For the purposes of keeping track of (and canceling) measurement units, this may be treated as radians/second.
-* <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 in meters. 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}\Delta_{distance}</math> Distance between firing ship and target.
+* <math>\pagecolor{Black}\color{White}Distance</math> Distance between firing ship and target 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.
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 There is also one more thing we can find out by just looking at the equation. This is, however, a little trickier to follow, but the conclusion is easy. The aim is to compare the tracking term and the range term for similarities in how they behave. Do they have anything in common? To do this, we will freeze all values in those respective terms except for one variable in each, that will be 'turret tracking' and 'falloff' respectively. Then we can look at how that single variable effects the outcome in each case and see if there is any similarities between them.
-The tracking part: All turrets measure tracking speed as ''angular velocity,'' equal to dividing ''transversal speed'' by ''range to target.'' This is all inside the tracking term, and basically just means how fast something moves around something else. Let's freeze the angular velocity, meaning the ships are orbiting each other at a constant speed. In the tracking term we also have ''turret signature resolution'' divided by ''target signature radius;'' for easy comparison later on we will assume that these are equal (so dividing equals 1, resulting in no effect in the formula) and freeze them as well. The result: a fixed number divided by ''turret tracking''.
+The tracking part: All turrets measure tracking speed as a ''Turret Accuracy Score'', which describes how well a turret can cope with targets moving around the turret in circles (or how well the turret can cope with its own ship moving around the target in circles; as far as the equation is concerned, these are the same situation). Let's freeze the ''angular velocity'', meaning the ships are orbiting each other at a constant speed. In the tracking term we also have a ''40000 meters'' term (a true constant) and ''target signature radius'' (which is usually constant except when any effects that affect [[signature radius]] are applied or removed). The result: a fixed number divided by ''turret tracking''.
 The range part: Being inside optimal never incurs a hit penalty, so we must move out into falloff ranges to see any changes in the to-hit equation's output values. Lets freeze everything apart from ''falloff.'' The result: a fixed number divided by ''falloff.''
-Did you see what they had in common? In the tracking term, we now have ''something''/''Turret tracking'', in the range term we have ''something''/''falloff''. In both cases there is a value that is divided by the variable we were interested in. There is an important insight here: tracking and falloff behave identically. And they are not fixed limits, they become ratios that describes how quickly you lose hit chance as you start to push range and orbiting speeds, and the hit chance loss is gradual.
+Did you see what they have in common? In the tracking term, we now have ''something''/''Turret tracking'', in the range term we have ''something''/''falloff''. In both cases there is a value that is divided by the variable we were interested in. There is an important insight here: tracking and falloff behave identically. Also, they are not fixed limits, they become ratios that describes how quickly you lose hit chance as you start to push range and orbiting speeds. Also, the hit chance loss is gradual.
 ==Base damage==