Turret mechanics: Difference between revisions

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{{Update|[[#Practical applications]] replace EFT image with PYFA image}}

'''Turret mechanics''' dictate how accurately turrets hit and how much damage is dealt. It is obvious that these two are connected since missing shots directly affects applied damage but the hit and damage mechanics are actually connected in another way too.

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''Hit Chance'' is an exponent expression that gives an accuracy percentage based on two terms: tracking and range. These two terms, and thus the hit chance value, are determined by the two ships involved and their movement relative to each other. The more the target fits within the right range and tracking parameters of the gun, the higher the hit chance is up to 1.00 probability (100%).

When a turret shot is fired, the game generates a random decimal number between 0 and 1. This number is then used in the ~~'''~~[[#Hit Math|Hit Math]]~~'''~~ and ~~'''~~[[#Damage|Damage]]~~'''~~ equations described below. This random number is used twice:

When a turret shot is fired, the game generates a random decimal number between 0 and 1. This number is then used in the [[#Hit Math|Hit Math]] and [[#Damage|Damage]] equations described below. This random number is used twice:

* First, in order for a shot to hit, by convention the random number must be ''below'' the calculated hit chance value.

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== Range ==

Every turret has two range parameters called "Optimal Range" and "Accuracy Falloff".

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The penalty for exceeding the optimal range by a small amount is reasonably low; the chance to hit a target at 33% of the falloff range in excess of the optimal range is still above 90%. Minmatar ships especially have significant falloff ranges allowing them to fight effectively beyond their optimal range. However, as the distance increases, the chance to hit decreases faster and faster.

When using turrets that fight inside falloff ranges it can be useful to know that being at optimal+(falloff / 2) results in -20% average damage and being at optimal+falloff results in -60% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below).

When using turrets that fight inside falloff ranges it can be useful to know that being at optimal + ( falloff / 2) results in -20% average damage and being at optimal + falloff results in -60% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below).

Falloff and optimal ranges are visible in the turrets info window. They are further modified by skills, ammo, modules, hull bonuses and incoming tracking disruptors. Target distance is visible on the overview.

== Tracking ==

Tracking tells how well turrets hit a moving target. If the target is stationary relative to the shooter tracking is ignored and only range effects hit chance. If the target is both inside optimal range and stationary the turrets have 100% chance to hit. As a result against stationary target the turret tracking is irrelevant and even the largest turrets can hit the smallest targets if the target is foolish enough to sit still.

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The concept of turret tracking value is simple: The smaller a turret is, the faster its tracking speed will be: small autocannon, for example, track faster than medium autocannon. Short-ranged varieties of turret have better tracking than their long-ranged counterparts -- so, for example, medium pulse lasers track faster than medium beam lasers and large blasters track faster than large railguns. There is only one value for tracking unlike the optimal and falloff for range. One way to look at it is to consider the turret to always being in "tracking falloff" with zero optimal tracking.

[[File:Angular velocity.png~~|right|256 px~~|thumb|The general case of angular velocity. Angular velocity of ship depends on ship velocity, target velocity and distance. The total velocity vector is target velocity vector-your velocity vector and the dashed vectors are parallel and perpendicular components of total velocity vector. Note the 90° angles.]]

[[File:Angular velocity.png|thumb|The general case of angular velocity. Angular velocity of ship depends on ship velocity, target velocity and distance. The total velocity vector is target velocity vector-your velocity vector and the dashed vectors are parallel and perpendicular components of total velocity vector. Note the 90° angles.]]

[[File:Orbit angular velcoity.png~~|right|256 px~~|thumb|Angular velocity while orbiting is much simpler than the general case. The angular velocity is simply the orbiting velocity divided by distance. Many situations where one ship is much faster can be approximated to to be like this.]]

[[File:Orbit angular velcoity.png|thumb|Angular velocity while orbiting is much simpler than the general case. The angular velocity is simply the orbiting velocity divided by distance. Many situations where one ship is much faster can be approximated to to be like this.]]

Instead of measuring an object's speed as m/s or miles/hour, a speed can also be measured as an angle. A good example is the suns movement across the sky, where it moves 360° in 24 hours, which makes the angular velocity 15°/hour.

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Since the tracking depends on all three: target signature radius, turret tracking and angular velocity it can be hard to intuitively see when it is possible to hit. For example a medium autocannon with 50 tracking shooting a cruiser with 150 m signature radius and an angular velocity of 0.073 rad/s has 90% chance to hit. In same situation, but when shooting at frigate with 50 m signature, the hit chance is only 39%.

{| class="wikitable" ~~border=0~~

{| class="wikitable"

! Hit chance from tracking || Angular velocity (rad/s) as a function of <br /> tracking (T) and signature radius (S)

|-

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|}

It is often best to use [[Third-party tools|a Third-party ~~tools~~]] to see how well your guns track moving targets. ~~Both EFT and~~ PYFA ~~are~~ able to draw damage application figures on moving targets.

It is often best to use a [[Third-party tools|Third-party tool]] to see how well your guns track moving targets. [[PYFA]] is able to draw damage application figures on moving targets.

Much of this information is most useful when theorycrafting, as there is often little time or need for complex mathematics during combat. However, pilots who are familiar with these concepts can still use them in a general sense to make decisions when in space.

{{expansion past | Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat (not that it was feasible to compare tracking numbers before unless fighting targets of same size). The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single number simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace ~~40000~~ with Turret Signature Resolution. If you encounter nonsensical tracking values anywhere they may be in this old format.

{{expansion past

| Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat (not that it was feasible to compare tracking numbers before unless fighting targets of same size). The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single number simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace 40,000 with Turret Signature Resolution. If you encounter nonsensical tracking values anywhere they may be in this old format.

To convert turret tracking speed to rad/s the following formula can be used:

<~~pre~~>turret tracking (new) = ~~Turret~~ tracking (old) * 40000 m / Optimal Signature Resolution</~~pre~~>}}

:<math> \displaystyle \text{turret tracking (new)} = \text{turret tracking (old)} \times 40,000 m / \text{Optimal Signature Resolution} </math>

}}

== Hit Math ==

A turret's chance to hit a target is calculated using the equation below. It will produce a result between 0 and 1, representing a probability between 0% and 100%. This value is then compared to a random number between 0 and 1. By convention, the random number has to be less than the calculated result to hit. If the random number is greater than the calculated chance, the turret misses.

'''Note: The entire expression contained within the outermost set of parentheses is an exponent.'''

:<math>\displaystyle\text{Chance to hit} = 0.5^{\Large \left( \left( \frac{\text{Angular} \times ~~40000~~ \text{ m}}{\text{Tracking} \times \text{Signature}} \right)^2 + \left(\frac{\max(0,\ \text{Distance} - \text{Optimal})}{\text{Falloff}} \right)^2\right)}</math>

:<math> \displaystyle \text{Chance to hit} = 0.5^{\Large \left( \left( \frac{\text{Angular} \times 40,000 \text{ m}}{\text{Tracking} \times \text{Signature}} \right)^2 + \left(\frac{\max(0,\ \text{Distance} - \text{Optimal})}{\text{Falloff}} \right)^2\right)} </math>

''Angular'' is the [[Angular Velocity|angular velocity]] (movement between the attacker and the target expressed as an angle in radians per second).

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= Damage =

The damage that a turret deals will be randomly spread around a fixed value called base damage. The base damage is calculated from the turret's Damage Multiplier attribute, the ammo's damage values, hull modifiers and skills. The base damage is the so called "paper damage" that is shown in all info windows. "Paper DPS" is simply "paper damage" divided by rate of fire.

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The damage modifier for a normal hit is calculated with the following formula. In 100% hit chance situation this leads to even distribution from 50% to 149% with extra spike at 300% damage.

:<math>x = \operatorname{rand}(0, 1)</math>

:<math> x = \operatorname{rand}(0, 1)</math>

:<math>\text{Random Damage modifier} = \begin{cases}

:<math> \text{Random Damage modifier} = \begin{cases}

x + 0.49, & \mbox{if } x \geq 0.01 \\

3, & \mbox{if } x < 0.01

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From this two equations for normalized dps can be derived

:<math>\text{Normalized DPS} = \begin{cases}

:<math> \text{Normalized DPS} = \begin{cases}

0.01 \times 3 + ( \text{Hit chance} - 0.01 ) \times ( 0.5 \times ( 0.5 + 0.49 + \text{Hit chance} ) ), & \mbox{if } \text{Hit chance} \geq 0.01 \\

3 \times \text{Hit chance}, & \mbox{if } \text{Hit chance} < 0.01

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The combat log will show the quality of a hit as follows

[[File:Turret_HitChance_and_AverageDamage.PNG~~|500px~~|thumb|~~right~~|Average applied DPS compared to hit chance.]]

[[File:Turret_HitChance_and_AverageDamage.PNG|thumb|500px|Average applied DPS compared to hit chance.]]

{| class="wikitable" ~~border=0~~

{| class="wikitable"

! Hit description !! Random damage modifier

|-

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=== Average damage ===

As was mentioned earlier, your chance of dealing good, more damaging hits ('smashing' shots that deal more damage) decreases as your chance to hit decreases. This relationship is not linear, and your chance of good hits decreases quite rapidly as you move into falloff. At optimal + falloff, where your chance to hit is (as always, assuming other factors don't intervene) 50%, you can expect 40%, not 50%, of your theoretical maximum DPS.

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= Practical applications =

[[File:Eft dps figure.png|thumb|500 px|Since the hit chance can be hard to work on intuitively it is often best to use a tool for it. Analyzing these figures allows the pilot to choose best weapon system for the engagement range and the best engagement range for a weapon system. Here is an example dps figure generated with EFT that shows maelstrom with artillery (green) and autocannons (red) shooting at a maelstrom. Here you can easily see that the best range for artillery is at around 40 km and the choice between AC and artillery depends on whether fight happens at below or above 30 km. Both EFT and PYFA can create these figures.]]

[[File:Eft dps figure.png|~~right~~|500 px~~|thumb~~|Since the hit chance can be hard to work on intuitively it is often best to use a tool for it. Analyzing these figures allows the pilot to choose best weapon system for the engagement range and the best engagement range for a weapon system. Here is an example dps figure generated with EFT that shows maelstrom with artillery (green) and autocannons (red) shooting at a maelstrom. Here you can easily see that the best range for artillery is at around 40 km and the choice between AC and artillery depends on whether fight happens at below or above 30 km. Both EFT and PYFA can create these figures.]]

The hit chance and its relation to range, tracking, velocity and signature radius have many effects on combat with turret ships. Taking advantage of this knowledge allows you to control range, control velocities and choose the right modules for the job. This section gives several useful tricks and maneuvers for ships that either fight with turrets or against a turret ship.

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Obviously if you find a way to pin your enemy down at a range where you can hurt them but they can't hurt you, you'll win. On the other hand, if you find yourself fighting an enemy who outranges you and can move faster than you, and you can't ameliorate either of those problems, you should consider trying to escape.

Although you can use tools like ~~EFT~~'s DPS graphs, this knowledge comes partly with experience. It's much easier to figure out against NPC rats, which always have the same characteristics while kindly heading more or less straight for you until they close into their preferred orbit range, than it is with PvP enemies.

Although you can use tools like PYFA's DPS graphs, this knowledge comes partly with experience. It's much easier to figure out against NPC rats, which always have the same characteristics while kindly heading more or less straight for you until they close into their preferred orbit range, than it is with PvP enemies.

But range control is not the end of turret management. You must also always remember that range is directly tied to angular velocity. In practice, if you're using long-ranged turrets (artillery, railguns and beam lasers) you will find that once targets get close enough within your optimal range their angular velocity will rise so much that you can't hit them. Some ways to handle small, fast, closely-orbiting targets are discussed below. Besides dealing with them once they do get close, it's worth finding a range which is within your optimal yet far enough away that the enemy are easy to track.

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In missions with slow battleship and dumb AI you can look at the velocity vector of your target either with tactical overlay or by looking at their ship model. You can then easily attempt to match velocity vector with them by manually aligning in same direction they are going. If the speed and velocity vector are matched angular velocity drops very low and hitting is much easier.

From the point of view of a large ship struggling to hit small fast ships which are orbiting close to it, either in PvP or PvE, the solution is to reduce your target's angular velocity and/or increase their signature. If you can almost entirely reduce their angular velocity you won't need to worry about increasing their signature because (as described above) the effects of signature radius and resolution affect the tracking calculation within the chance to hit calculation, not the chance to hit calculation directly. Stasis Webifiers are a common solution. T1 webs reduce their target's speed by 50%, T2 webs by 60% ([[~~Overloading|~~overheating]] a webifier increases its range, which can help you snag a player who's dancing just beyond web range). Target Painters will help, though it is not as effective as web but it has much greater range. You can also try boosting the tracking speed of your guns with Tracking Computers and Tracking Enhancers.

From the point of view of a large ship struggling to hit small fast ships which are orbiting close to it, either in PvP or PvE, the solution is to reduce your target's angular velocity and/or increase their signature. If you can almost entirely reduce their angular velocity you won't need to worry about increasing their signature because (as described above) the effects of signature radius and resolution affect the tracking calculation within the chance to hit calculation, not the chance to hit calculation directly. Stasis Webifiers are a common solution. T1 webs reduce their target's speed by 50%, T2 webs by 60% ([[overheating]] a webifier increases its range, which can help you snag a player who's dancing just beyond web range). Target Painters will help, though it is not as effective as web but it has much greater range. You can also try boosting the tracking speed of your guns with Tracking Computers and Tracking Enhancers.

There are rigs and modules that improve tracking directly. However, since bigger targets are easier to track, a Target Painter will also make someone easier to track. A Target Painter is an active module and will require more micromanagement of its pilot, but the good thing is that the victim is easier to track for everyone.

There are rigs and modules that improve tracking directly. However, since bigger targets are easier to track, a [[Target Painter]] will also make someone easier to track. A Target Painter is an active module and will require more micromanagement of its pilot, but the good thing is that the victim is easier to track for everyone.

Shield extenders increases the signature resolution (size) of a ship, which makes them easier to track with turrets. Armor plates increases mass (slower turn speed) and reduces the top speed with afterburners and microwarp drives, which makes them easier to track too.

== Controlling battle ==

The conclusion from all the information about tracking speed and signature radius is: when you want to avoid damage, you want your angular velocity to be as high as possible and your signature radius to be low. But if you want to hit should probably try to fight within your guns' optimal range, but be prepared to fight within your optimal + falloff range (also called 'first falloff') if you must. One of the simplest yet important rules to remember is that two ships always have the same range and angular velocity towards each-other. The pilot who can control these two values, can control how much damage turrets will be able to do.

The conclusion from all the information about tracking speed and signature radius is: when you want to avoid damage, you want your angular velocity to be as high as possible and your signature radius to be low. But if you want to hit should probably try to fight within your guns' optimal range, but be prepared to fight within your optimal + falloff range (also called 'first falloff') if you must. One of the simplest yet important rules to remember is that two ships always have the same range and angular velocity towards ~~eachother~~. The pilot who can control these two values, can control how much damage turrets will be able to do.

If the size and speed difference between you and your target is not so great, you may be able to reduce their angular velocity simply by maneuvering.

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If you have a PvP fleet of large ships that are struggling to hit a swarm of smaller targets you may find it helpful to spread out, and order each ship to target the enemies furthest away from it. Even if your enemies are flying under your guns individually, you can use the low angular velocity provided by greater range to kill the small ships attacking your fleetmates, who can do the same to the small ships attacking you. (By the same token, large ships are most vulnerable to smaller enemies when they're on their own.)

However, if you're in a ship that is very much larger and slower than your target, you're unlikely to be able to win through good manual piloting. Sometimes, however, the solutions to this problem aren't directly related to gunnery. battleship fits usually outsource frigate problems to [[drones]]. In PvP larger ships can use drones, large energy neutralizers, smartbombs or the help of smaller support ships to drive small, fast targets off or kill them.

However, if you're in a ship that is very much larger and slower than your target, you're unlikely to be able to win through good manual piloting. Sometimes, however, the solutions to this problem aren't directly related to gunnery. battleship fits usually outsource frigate problems to [[drones]]. In PvP larger ships can use drones, large energy neutralizers, [[smartbombs]] or the help of smaller support ships to drive small, fast targets off or kill them.

For new pilots who are likely to be flying small fast ships one of the key ideas that follows from this is the tactic of 'flying under the guns' of an enemy ship: orbiting them at high speed and short range so it's very hard for their guns to track your small-signature ship. (Sometimes referred to as a form of 'speed tanking' or 'sig tanking'.) Assuming you're fast and small enough to survive under the enemy's guns, the main trick is getting there in the first place: if you burn straight towards the enemy, they will probably hit you (especially if you have an active MWD). If you approach a distant target straight on, there is no angular velocity, and the hit chance from the tracking term will be 100%. A battleship can easily hit a frigate for full damage if there is no need to track it.

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# This should make you spiral around them, moving ever closer until you can orbit (hopefully safely).

# There is no six. (It burned straight towards the enemy with its MWD on and was one-shotted.)

# It might be a good idea to ~~practise~~ this on large NPC belt rats before trying it in PvP combat.

# It might be a good idea to practice this on large NPC belt rats before trying it in PvP combat.

Similarly it's good not to just burn straight away from a larger enemy if you're trying to escape, though by that point in a battle you may find you're too busy to take account of your relationship to enemy tracking. To do this spiral out:

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+{{Update|[[#Practical applications]] replace EFT image with PYFA image}}
 {{Weapon Systems Links}}
 '''Turret mechanics''' dictate how accurately turrets hit and how much damage is dealt. It is obvious that these two are connected since missing shots directly affects applied damage but the hit and damage mechanics are actually connected in another way too.
@@ Line 8: / Line 9: @@
 ''Hit Chance'' is an exponent expression that gives an accuracy percentage based on two terms: tracking and range. These two terms, and thus the hit chance value, are determined by the two ships involved and their movement relative to each other. The more the target fits within the right range and tracking parameters of the gun, the higher the hit chance is up to 1.00 probability (100%).
-When a turret shot is fired, the game generates a random decimal number between 0 and 1. This number is then used in the '''[[#Hit Math|Hit Math]]''' and '''[[#Damage|Damage]]''' equations described below. This random number is used twice:
+When a turret shot is fired, the game generates a random decimal number between 0 and 1. This number is then used in the [[#Hit Math|Hit Math]] and [[#Damage|Damage]] equations described below. This random number is used twice:
 * First, in order for a shot to hit, by convention the random number must be ''below'' the calculated hit chance value.
@@ Line 23: / Line 24: @@
 == Range ==
 Every turret has two range parameters called "Optimal Range" and "Accuracy Falloff".
@@ Line 34: / Line 34: @@
 The penalty for exceeding the optimal range by a small amount is reasonably low; the chance to hit a target at 33% of the falloff range in excess of the optimal range is still above 90%. Minmatar ships especially have significant falloff ranges allowing them to fight effectively beyond their optimal range. However, as the distance increases, the chance to hit decreases faster and faster.
-When using turrets that fight inside falloff ranges it can be useful to know that being at optimal+(falloff / 2) results in -20% average damage and being at optimal+falloff results in -60% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below).
+When using turrets that fight inside falloff ranges it can be useful to know that being at optimal + ( falloff / 2) results in -20% average damage and being at optimal + falloff results in -60% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below).
 Falloff and optimal ranges are visible in the turrets info window. They are further modified by skills, ammo, modules, hull bonuses and incoming tracking disruptors. Target distance is visible on the overview.
 == Tracking ==
 Tracking tells how well turrets hit a moving target. If the target is stationary relative to the shooter tracking is ignored and only range effects hit chance. If the target is both inside optimal range and stationary the turrets have 100% chance to hit. As a result against stationary target the turret tracking is irrelevant and even the largest turrets can hit the smallest targets if the target is foolish enough to sit still.
@@ Line 48: / Line 47: @@
 The concept of turret tracking value is simple: The smaller a turret is, the faster its tracking speed will be: small autocannon, for example, track faster than medium autocannon. Short-ranged varieties of turret have better tracking than their long-ranged counterparts -- so, for example, medium pulse lasers track faster than medium beam lasers and large blasters track faster than large railguns. There is only one value for tracking unlike the optimal and falloff for range. One way to look at it is to consider the turret to always being in "tracking falloff" with zero optimal tracking.
-[[File:Angular velocity.png|right|256 px|thumb|The general case of angular velocity. Angular velocity of ship depends on ship velocity, target velocity and distance. The total velocity vector is target velocity vector-your velocity vector and the dashed vectors are parallel and perpendicular components of total velocity vector. Note the 90° angles.]]
+[[File:Angular velocity.png|thumb|The general case of angular velocity. Angular velocity of ship depends on ship velocity, target velocity and distance. The total velocity vector is target velocity vector-your velocity vector and the dashed vectors are parallel and perpendicular components of total velocity vector. Note the 90° angles.]]
-[[File:Orbit angular velcoity.png|right|256 px|thumb|Angular velocity while orbiting is much simpler than the general case. The angular velocity is simply the orbiting velocity divided by distance. Many situations where one ship is much faster can be approximated to to be like this.]]
+[[File:Orbit angular velcoity.png|thumb|Angular velocity while orbiting is much simpler than the general case. The angular velocity is simply the orbiting velocity divided by distance. Many situations where one ship is much faster can be approximated to to be like this.]]
 Instead of measuring an object's speed as m/s or miles/hour, a speed can also be measured as an angle. A good example is the suns movement across the sky, where it moves 360° in 24 hours, which makes the angular velocity 15°/hour.
@@ Line 81: / Line 80: @@
 Since the tracking depends on all three: target signature radius, turret tracking and angular velocity it can be hard to intuitively see when it is possible to hit. For example a medium autocannon with 50 tracking shooting a cruiser with 150 m signature radius and an angular velocity of 0.073 rad/s has 90% chance to hit. In same situation, but when shooting at frigate with 50 m signature, the hit chance is only 39%.
-{| class="wikitable" border=0
+{| class="wikitable"
 ! Hit chance from tracking || Angular velocity (rad/s) as a function of <br /> tracking (T) and signature radius (S)
 |-
@@ Line 97: / Line 96: @@
 |}
-It is often best to use [[Third-party tools|a Third-party tools]] to see how well your guns track moving targets. Both EFT and PYFA are able to draw damage application figures on moving targets.
+It is often best to use a [[Third-party tools|Third-party tool]] to see how well your guns track moving targets. [[PYFA]] is able to draw damage application figures on moving targets.
 Much of this information is most useful when theorycrafting, as there is often little time or need for complex mathematics during combat. However, pilots who are familiar with these concepts can still use them in a general sense to make decisions when in space.
-{{expansion past | Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat (not that it was feasible to compare tracking numbers before unless fighting targets of same size). The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single number simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace 40000 with Turret Signature Resolution. If you encounter nonsensical tracking values anywhere they may be in this old format.
+{{expansion past
+| Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat (not that it was feasible to compare tracking numbers before unless fighting targets of same size). The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single number simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace 40,000 with Turret Signature Resolution. If you encounter nonsensical tracking values anywhere they may be in this old format.
 To convert turret tracking speed to rad/s the following formula can be used:
-<pre>turret tracking (new) = Turret tracking (old) * 40000 m / Optimal Signature Resolution</pre>}}
+:<math> \displaystyle \text{turret tracking (new)} = \text{turret tracking (old)} \times 40,000 m / \text{Optimal Signature Resolution} </math>
+}}
 == Hit Math ==
 A turret's chance to hit a target is calculated using the equation below. It will produce a result between 0 and 1, representing a probability between 0% and 100%. This value is then compared to a random number between 0 and 1. By convention, the random number has to be less than the calculated result to hit. If the random number is greater than the calculated chance, the turret misses.
 '''Note: The entire expression contained within the outermost set of parentheses is an exponent.'''
-:<math>\displaystyle\text{Chance to hit} = 0.5^{\Large \left( \left( \frac{\text{Angular} \times 40000 \text{ m}}{\text{Tracking} \times \text{Signature}} \right)^2 + \left(\frac{\max(0,\ \text{Distance} - \text{Optimal})}{\text{Falloff}} \right)^2\right)}</math>
+:<math> \displaystyle \text{Chance to hit} = 0.5^{\Large \left( \left( \frac{\text{Angular} \times 40,000 \text{ m}}{\text{Tracking} \times \text{Signature}} \right)^2 + \left(\frac{\max(0,\ \text{Distance} - \text{Optimal})}{\text{Falloff}} \right)^2\right)} </math>
 ''Angular'' is the [[Angular Velocity|angular velocity]] (movement between the attacker and the target expressed as an angle in radians per second).
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 = Damage =
 The damage that a turret deals will be randomly spread around a fixed value called base damage. The base damage is calculated from the turret's Damage Multiplier attribute, the ammo's damage values, hull modifiers and skills. The base damage is the so called "paper damage" that is shown in all info windows. "Paper DPS" is simply "paper damage" divided by rate of fire.
@@ Line 142: / Line 141: @@
 The damage modifier for a normal hit is calculated with the following formula. In 100% hit chance situation this leads to even distribution from 50% to 149% with extra spike at 300% damage.
-:<math>x = \operatorname{rand}(0, 1)</math>
+:<math> x = \operatorname{rand}(0, 1)</math>
-:<math>\text{Random Damage modifier} = \begin{cases}
+:<math> \text{Random Damage modifier} = \begin{cases}
    x + 0.49, & \mbox{if } x \geq 0.01 \\
 ,  & \mbox{if } x < 0.01
@@ Line 151: / Line 150: @@
 From this two equations for normalized dps can be derived
-:<math>\text{Normalized DPS} = \begin{cases}
+:<math> \text{Normalized DPS} = \begin{cases}
 .01 \times 3 + (  \text{Hit chance} - 0.01 ) \times ( 0.5 \times ( 0.5 + 0.49 + \text{Hit chance} ) ), & \mbox{if } \text{Hit chance} \geq 0.01 \\
 \times \text{Hit chance},  & \mbox{if } \text{Hit chance} < 0.01
@@ Line 163: / Line 162: @@
 The combat log will show the quality of a hit as follows
-[[File:Turret_HitChance_and_AverageDamage.PNG|500px|thumb|right|Average applied DPS compared to hit chance.]]
+[[File:Turret_HitChance_and_AverageDamage.PNG|thumb|500px|Average applied DPS compared to hit chance.]]
-{| class="wikitable" border=0
+{| class="wikitable"
 ! Hit description !! Random damage modifier
 |-
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 === Average damage ===
 As was mentioned earlier, your chance of dealing good, more damaging hits ('smashing' shots that deal more damage) decreases as your chance to hit decreases. This relationship is not linear, and your chance of good hits decreases quite rapidly as you move into falloff. At optimal + falloff, where your chance to hit is (as always, assuming other factors don't intervene) 50%, you can expect 40%, not 50%, of your theoretical maximum DPS.
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 = Practical applications =
+[[File:Eft dps figure.png|thumb|500 px|Since the hit chance can be hard to work on intuitively it is often best to use a tool for it. Analyzing these figures allows the pilot to choose best weapon system for the engagement range and the best engagement range for a weapon system. Here is an example dps figure generated with EFT that shows maelstrom with artillery (green) and autocannons (red) shooting at a maelstrom. Here you can easily see that the best range for artillery is at around 40 km and the choice between AC and artillery depends on whether fight happens at below or above 30 km. Both EFT and PYFA can create these figures.]]
-[[File:Eft dps figure.png|right|500 px|thumb|Since the hit chance can be hard to work on intuitively it is often best to use a tool for it. Analyzing these figures allows the pilot to choose best weapon system for the engagement range and the best engagement range for a weapon system. Here is an example dps figure generated with EFT that shows maelstrom with artillery (green) and autocannons (red) shooting at a maelstrom. Here you can easily see that the best range for artillery is at around 40 km and the choice between AC and artillery depends on whether fight happens at below or above 30 km. Both EFT and PYFA can create these figures.]]
 The hit chance and its relation to range, tracking, velocity and signature radius have many effects on combat with turret ships. Taking advantage of this knowledge allows you to control range, control velocities and choose the right modules for the job. This section gives several useful tricks and maneuvers for ships that either fight with turrets or against a turret ship.
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 Obviously if you find a way to pin your enemy down at a range where you can hurt them but they can't hurt you, you'll win. On the other hand, if you find yourself fighting an enemy who outranges you and can move faster than you, and you can't ameliorate either of those problems, you should consider trying to escape.
-Although you can use tools like EFT's DPS graphs, this knowledge comes partly with experience. It's much easier to figure out against NPC rats, which always have the same characteristics while kindly heading more or less straight for you until they close into their preferred orbit range, than it is with PvP enemies.
+Although you can use tools like PYFA's DPS graphs, this knowledge comes partly with experience. It's much easier to figure out against NPC rats, which always have the same characteristics while kindly heading more or less straight for you until they close into their preferred orbit range, than it is with PvP enemies.
 But range control is not the end of turret management. You must also always remember that range is directly tied to angular velocity. In practice, if you're using long-ranged turrets (artillery, railguns and beam lasers) you will find that once targets get close enough within your optimal range their angular velocity will rise so much that you can't hit them. Some ways to handle small, fast, closely-orbiting targets are discussed below. Besides dealing with them once they do get close, it's worth finding a range which is within your optimal yet far enough away that the enemy are easy to track.
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 In missions with slow battleship and dumb AI you can look at the velocity vector of your target either with tactical overlay or by looking at their ship model. You can then easily attempt to match velocity vector with them by manually aligning in same direction they are going. If the speed and velocity vector are matched angular velocity drops very low and hitting is much easier.
-From the point of view of a large ship struggling to hit small fast ships which are orbiting close to it, either in PvP or PvE, the solution is to reduce your target's angular velocity and/or increase their signature. If you can almost entirely reduce their angular velocity you won't need to worry about increasing their signature because (as described above) the effects of signature radius and resolution affect the tracking calculation within the chance to hit calculation, not the chance to hit calculation directly. Stasis Webifiers are a common solution. T1 webs reduce their target's speed by 50%, T2 webs by 60% ([[Overloading|overheating]] a webifier increases its range, which can help you snag a player who's dancing just beyond web range). Target Painters will help, though it is not as effective as web but it has much greater range. You can also try boosting the tracking speed of your guns with Tracking Computers and Tracking Enhancers.
+From the point of view of a large ship struggling to hit small fast ships which are orbiting close to it, either in PvP or PvE, the solution is to reduce your target's angular velocity and/or increase their signature. If you can almost entirely reduce their angular velocity you won't need to worry about increasing their signature because (as described above) the effects of signature radius and resolution affect the tracking calculation within the chance to hit calculation, not the chance to hit calculation directly. Stasis Webifiers are a common solution. T1 webs reduce their target's speed by 50%, T2 webs by 60% ([[overheating]] a webifier increases its range, which can help you snag a player who's dancing just beyond web range). Target Painters will help, though it is not as effective as web but it has much greater range. You can also try boosting the tracking speed of your guns with Tracking Computers and Tracking Enhancers.
-There are rigs and modules that improve tracking directly. However, since bigger targets are easier to track, a Target Painter will also make someone easier to track. A Target Painter is an active module and will require more micromanagement of its pilot, but the good thing is that the victim is easier to track for everyone.
+There are rigs and modules that improve tracking directly. However, since bigger targets are easier to track, a [[Target Painter]] will also make someone easier to track. A Target Painter is an active module and will require more micromanagement of its pilot, but the good thing is that the victim is easier to track for everyone.
 Shield extenders increases the signature resolution (size) of a ship, which makes them easier to track with turrets. Armor plates increases mass (slower turn speed) and reduces the top speed with afterburners and microwarp drives, which makes them easier to track too.
 == Controlling battle ==
+The conclusion from all the information about tracking speed and signature radius is: when you want to avoid damage, you want your angular velocity to be as high as possible and your signature radius to be low. But if you want to hit should probably try to fight within your guns' optimal range, but be prepared to fight within your optimal + falloff range (also called 'first falloff') if you must. One of the simplest yet important rules to remember is that two ships always have the same range and angular velocity towards each-other. The pilot who can control these two values, can control how much damage turrets will be able to do.
-The conclusion from all the information about tracking speed and signature radius is: when you want to avoid damage, you want your angular velocity to be as high as possible and your signature radius to be low. But if you want to hit should probably try to fight within your guns' optimal range, but be prepared to fight within your optimal + falloff range (also called 'first falloff') if you must. One of the simplest yet important rules to remember is that two ships always have the same range and angular velocity towards eachother. The pilot who can control these two values, can control how much damage turrets will be able to do.
 If the size and speed difference between you and your target is not so great, you may be able to reduce their angular velocity simply by maneuvering.
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 If you have a PvP fleet of large ships that are struggling to hit a swarm of smaller targets you may find it helpful to spread out, and order each ship to target the enemies furthest away from it. Even if your enemies are flying under your guns individually, you can use the low angular velocity provided by greater range to kill the small ships attacking your fleetmates, who can do the same to the small ships attacking you. (By the same token, large ships are most vulnerable to smaller enemies when they're on their own.)
-However, if you're in a ship that is very much larger and slower than your target, you're unlikely to be able to win through good manual piloting. Sometimes, however, the solutions to this problem aren't directly related to gunnery. battleship fits usually outsource frigate problems to [[drones]]. In PvP larger ships can use drones, large energy neutralizers, smartbombs or the help of smaller support ships to drive small, fast targets off or kill them.
+However, if you're in a ship that is very much larger and slower than your target, you're unlikely to be able to win through good manual piloting. Sometimes, however, the solutions to this problem aren't directly related to gunnery. battleship fits usually outsource frigate problems to [[drones]]. In PvP larger ships can use drones, large energy neutralizers, [[smartbombs]] or the help of smaller support ships to drive small, fast targets off or kill them.
 For new pilots who are likely to be flying small fast ships one of the key ideas that follows from this is the tactic of 'flying under the guns' of an enemy ship: orbiting them at high speed and short range so it's very hard for their guns to track your small-signature ship. (Sometimes referred to as a form of 'speed tanking' or 'sig tanking'.) Assuming you're fast and small enough to survive under the enemy's guns, the main trick is getting there in the first place: if you burn straight towards the enemy, they will probably hit you (especially if you have an active MWD). If you approach a distant target straight on, there is no angular velocity, and the hit chance from the tracking term will be 100%. A battleship can easily hit a frigate for full damage if there is no need to track it.
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 # This should make you spiral around them, moving ever closer until you can orbit (hopefully safely).
 # There is no six. (It burned straight towards the enemy with its MWD on and was one-shotted.)
-# It might be a good idea to practise this on large NPC belt rats before trying it in PvP combat.
+# It might be a good idea to practice this on large NPC belt rats before trying it in PvP combat.
 Similarly it's good not to just burn straight away from a larger enemy if you're trying to escape, though by that point in a battle you may find you're too busy to take account of your relationship to enemy tracking. To do this spiral out: