Turret damage: Difference between revisions

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{{Example|This is a work in progress. Some parts need to be rewritten, things will be added and the layout is not complete.}}

EVE rely on math to determine the outcome of events, like all computer games. A player can develop a feel for the workings of the game by experience and practice over time. Such knowledge is often powerful and can be used to tip the balance in pvp encounters, either by fitting ~~a ship in a special way~~ or by piloting in a certain way. Some, but not all, of this practical knowledge stems from the intuitive understanding of the math behind it. This article will look into the math that controls how guns and turrets work, hopefully this will give the reader insights into damage dealing that could otherwise take many weeks or months of playing to develop. The information here is all about numbers and theory though. So don't think that practical experience won't be needed, a pvp:er needs more than just an understanding of the math. A pvp:er need to be able to read and predict an opponents behaviour, to have a knowledge of various ships and fittings as well as to develop the nerves to stay calm in a battle that can go either way.

EVE rely on math to determine the outcome of events, like all computer games. A player can develop a feel for the inner workings of the game by experience and practice over time. Such knowledge is often powerful and can be used to tip the balance in pvp encounters, either by fitting the right guns or by piloting in a certain way. Some, but not all, of this practical knowledge stems from the intuitive understanding of the math behind it. This article will look into the math that controls how guns and turrets work, hopefully this will give the reader insights into damage dealing that could otherwise take many weeks or months of playing to develop.

(is this text just silly?)

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[[File:TurretHitChance1.JPG]]

*Transversal speed = Movement up/down/left/right relative to an object, but not towards or away from it (that is called radial speed). Measured in m/s.

*Range to target = The range to an object. Measured in meters.

*Turret tracking = A value found on the attributes tab of a turret. Measured in rad/second.

*Turret signature resolution = High values means a harder time to hit smaller targets. Measured in meters.

*Target signature radius = The size of the target, or more precisly the radius of an imagined circle that represents the target. Measured in meters.

*max(0, x) = Takes the highest value of zero or x. Used to set all negative values to zero in this case.

*Turret optimal range = A value found on the attributes tab of a turret. Inside this range no range penalites from distance is applied. Measured in meters.

*Falloff = A value found on the attributes tab of a turret. Describes how well a turret can hit beyond its optimal range. Measured in meters.

This equation can look a bit intimidating at first, but its very central to how turrets deal damage and as such its a good idea to develop an understanding for it. Its purpose is to calculate the chance to hit with ~~turrets~~.

This equation can look a bit intimidating at first, but its very central to how turrets deal damage and as such its a good idea to develop an understanding for it. Its purpose is to calculate the chance to hit with each turret.

To paraphrase Oli Geist, this can be abstracted to:

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Chance to hit = 0.5^(tracking term) * 0.5^(range term)

From this we can see that tracking and range are ~~treated entirely separetly~~ and are then multiplied. So anything that effects range does not effect the tracking. In other words, excellent tracking can not make up for a lack in range.

From this we can see that tracking and range are calculated seperatly and are then multiplied. So anything that effects range does not effect the tracking. In other words, excellent tracking can not make up for a lack in range.

=General=

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==Tracking==

What about tracking? Well, if the transversal speed is 0, the tracking term evaluates to zero (multiply with a zero and the answer is always zero). Since 0.5^0 = 1, this means that the tracking part of the equation will ~~give you~~ a 100% hit chance, as long as the target ~~is also~~ inside the optimal range the chance to hit will remain at 100%. So getting your target to fly straight to you, or straight away from you, is great~~. Because~~ you ~~will hit every time as long as~~ the ~~target remains inside optimal range. This is what makes~~ the ~~tactic known as kiting so effective~~. If the target makes sure to keep up the transversal speed~~, the~~ best way to minimize this term is some combination of:

What about tracking? Well, if the transversal speed is 0, the tracking term evaluates to zero (multiply with a zero and the answer is always zero). Since 0.5^0 = 1, this means that the tracking part of the equation will gives a 100% hit chance, and as long as the target stays inside the optimal range the chance to hit will remain at 100%. It doesn't matter if you are in a tiny frigate and if your foe use capital ship guns, your small size means nothing if your transversal is zero. This is not how things works in real life, but it is how EVE works. So getting your target to fly straight to you, or straight away from you is great, if you are the one with the big guns. If the target instead makes sure to keep up the transversal speed it will be harder to hit. The best way to minimize this term is some combination of:

*Keep the target at '''longer''' range

*Lower the transversal speed

*Increase your turret's tracking speed

*Increase the target's signature radius

Modules that can help with these are AB's/MWD's, webs, tracking computers, and target painters. You can also choose 'keep at range' on a target to minimize the traversal -- though bear in mind that your target will be able to hit you more easily too. Note also that if the range should ever become zero, the equation makes a forbidden division with zero. This results in an error and the turrets will ~~no longer be able to hit~~.

Modules that can help with these are AB's/MWD's, webs, tracking computers, and target painters. You can also choose 'keep at range' on a target to minimize the traversal -- though bear in mind that your target will be able to hit you more easily too. Note also that if the range should ever become zero, the equation makes a forbidden division with zero. This results in an error and the turrets will automatically miss.

=Turret damage ~~dealing~~=

=Turret damage output=

==Random damage distribution==

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***Damage dealt = RAW DAMAGE * (Sum of Resistance modified damages) / (Sum of Ammo Damages)

The quality of the hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage) for regular hits and there may also perfect hits and misses. On the normal hits this number is multiplied with the turrets ~~average~~ damage. By looking carefully at the damage generation above, it becomes clear that the Hit Chance not only means that a turret can miss but also places a cap on the maximum damage number on the non-perfect hits, the next section looks into how this effects the turrets DPS.

The quality of the hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage) for regular hits and there may also perfect hits and misses. On the normal hits this number is multiplied with the turrets base damage. By looking carefully at the damage generation above, it becomes clear that the Hit Chance not only means that a turret can miss but also places a cap on the maximum damage number on the non-perfect hits, the next section looks into how this effects the turrets DPS.

{| class="wikitable" border=0

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A turret fires on target. The chance to hit is 0.8981, the EVE server rolls a random number between 0 and 1, and gets 0.6573, its less than the chance to hit so the target is struck. At this point 0.49 is added to the random number which then becomes 1.1473. The turret had a damage multiplier of x2.1 and the ammo does 4 EM and 2 Thermal, so the base damage is 2.1 multiplied with 6 (4+2), which is 12.6. After multiplying this with the random number we get the raw damage, which is 1.1473 x 12.6 = 14.456. In this damage the raw EM part is 1.1473 x 2.1 x 4 = 9.6373 and the raw Thermal part is 4.8187. Assuming the targets shield was hit, and that only the normal 20% resistance to Thermal is in effect, the final damage then becomes 9.6373 + (4.8187*0.8) = 13.492 points, in the log the hit will be described as a well aimed one and be rounded off to one decimal place.

==Damage reduction due to a decreased hit chance==

==Damage and DPS reduction due to a decreased hit chance==

When a turret has less than 100% chance to hit the turrets damage dealing capabilites are reduced in two different ways. The first and obvious one is that it sometimes misses, the other is that the max damage on normal hits (e.g. not perfect ones) are reduced as well. Both of these effects will decrease the DPS output. If you read the previous section, you may remember that the a random number between 0 and 1 is generated to see if a turret hits. If this value is lower than the chance to hit, the turret hits, this number is then used further by adding 0.49, this sum is then multiplied with the turrets base damage to obtain the raw damage done (damage before resistances). What this all means is that targets that are tricky to hit also take less damage since high and juicy rolls now are discarded as misses. This can be seen in the damage log as well, a hard to hit target never recieves excellent or well aimed hits, sometimes barely scratching is the highest (perfect hits still happen). The practical effect is that the DPS decreases more than the chance to hit does.

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The table below shows how DPS goes down as a target becomes harder to hit. Do note that the reason for the hit chance reduction doesn't matter, be it because of falloff or just tracking issues, the DPS goes down identically. The table can be used to see both how the damage declines as one goes deeper into falloff, and how the damage declines as a result of a lowered hit chance due to tracking reasons. If you wish to combine the effects of tracking and falloff, you can do this by first picking the hit chance from falloff and then the hit chance from tracking, multiply the values to get the combined hit chance, look in the hit chance column until you find a hit chance that is closest to the product you got, and read your relative DPS from that line.

Comment: The relative DPS ~~above~~ is over 1 at the start, this is not an error. Its because its relative to the base damage of the turret. What puts it above 1 are the perfect hits since they do extra high damage.

Comment: The relative DPS below is over 1 at the start, this is not an error. Its because its relative to the base damage of the turret. What puts it above 1 are the perfect hits since they do extra high damage.

{| class="wikitable" border=0

@@ Line 2: / Line 2: @@
 {{Example|This is a work in progress. Some parts need to be rewritten, things will be added and the layout is not complete.}}
-EVE rely on math to determine the outcome of events, like all computer games. A player can develop a feel for the workings of the game by experience and practice over time. Such knowledge is often powerful and can be used to tip the balance in pvp encounters, either by fitting a ship in a special way or by piloting in a certain way. Some, but not all, of this practical knowledge stems from the intuitive understanding of the math behind it. This article will look into the math that controls how guns and turrets work, hopefully this will give the reader insights into damage dealing that could otherwise take many weeks or months of playing to develop. The information here is all about numbers and theory though. So don't think that practical experience won't be needed, a pvp:er needs more than just an understanding of the math. A pvp:er need to be able to read and predict an opponents behaviour, to have a knowledge of various ships and fittings as well as to develop the nerves to stay calm in a battle that can go either way.
+EVE rely on math to determine the outcome of events, like all computer games. A player can develop a feel for the inner workings of the game by experience and practice over time. Such knowledge is often powerful and can be used to tip the balance in pvp encounters, either by fitting the right guns or by piloting in a certain way. Some, but not all, of this practical knowledge stems from the intuitive understanding of the math behind it. This article will look into the math that controls how guns and turrets work, hopefully this will give the reader insights into damage dealing that could otherwise take many weeks or months of playing to develop.
 (is this text just silly?)
@@ Line 9: / Line 9: @@
 [[File:TurretHitChance1.JPG]]
+*Transversal speed = Movement up/down/left/right relative to an object, but not towards or away from it (that is called radial speed). Measured in m/s.
+*Range to target = The range to an object. Measured in meters.
+*Turret tracking = A value found on the attributes tab of a turret. Measured in rad/second.
+*Turret signature resolution = High values means a harder time to hit smaller targets. Measured in meters.
+*Target signature radius = The size of the target, or more precisly the radius of an imagined circle that represents the target. Measured in meters.
+*max(0, x) = Takes the highest value of zero or x. Used to set all negative values to zero in this case.
+*Turret optimal range = A value found on the attributes tab of a turret. Inside this range no range penalites from distance is applied. Measured in meters.
+*Falloff = A value found on the attributes tab of a turret. Describes how well a turret can hit beyond its optimal range. Measured in meters.
-This equation can look a bit intimidating at first, but its very central to how turrets deal damage and as such its a good idea to develop an understanding for it. Its purpose is to calculate the chance to hit with turrets.
+This equation can look a bit intimidating at first, but its very central to how turrets deal damage and as such its a good idea to develop an understanding for it. Its purpose is to calculate the chance to hit with each turret.
 To paraphrase Oli Geist, this can be abstracted to:
@@ Line 21: / Line 29: @@
 Chance to hit = 0.5^(tracking term) * 0.5^(range term)
-From this we can see that tracking and range are treated entirely separetly and are then multiplied. So anything that effects range does not effect the tracking. In other words, excellent tracking can not make up for a lack in range.
+From this we can see that tracking and range are calculated seperatly and are then multiplied. So anything that effects range does not effect the tracking. In other words, excellent tracking can not make up for a lack in range.
 =General=
@@ Line 31: / Line 39: @@
 ==Tracking==
-What about tracking?  Well, if the transversal speed is 0, the tracking term evaluates to zero (multiply with a zero and the answer is always zero). Since 0.5^0 = 1, this means that the tracking part of the equation will give you a 100% hit chance, as long as the target is also inside the optimal range the chance to hit will remain at 100%. So getting your target to fly straight to you, or straight away from you, is great. Because you will hit every time as long as the target remains inside optimal range. This is what makes the tactic known as kiting so effective. If the target makes sure to keep up the transversal speed, the best way to minimize this term is some combination of:
+What about tracking?  Well, if the transversal speed is 0, the tracking term evaluates to zero (multiply with a zero and the answer is always zero). Since 0.5^0 = 1, this means that the tracking part of the equation will gives a 100% hit chance, and as long as the target stays inside the optimal range the chance to hit will remain at 100%. It doesn't matter if you are in a tiny frigate and if your foe use capital ship guns, your small size means nothing if your transversal is zero. This is not how things works in real life, but it is how EVE works. So getting your target to fly straight to you, or straight away from you is great, if you are the one with the big guns. If the target instead makes sure to keep up the transversal speed it will be harder to hit. The best way to minimize this term is some combination of:
 *Keep the target at '''longer''' range
 *Lower the transversal speed
 *Increase your turret's tracking speed
 *Increase the target's signature radius
-Modules that can help with these are AB's/MWD's, webs, tracking computers, and target painters.  You can also choose 'keep at range' on a target to minimize the traversal -- though bear in mind that your target will be able to hit you more easily too. Note also that if the range should ever become zero, the equation makes a forbidden division with zero. This results in an error and the turrets will no longer be able to hit.
+Modules that can help with these are AB's/MWD's, webs, tracking computers, and target painters.  You can also choose 'keep at range' on a target to minimize the traversal -- though bear in mind that your target will be able to hit you more easily too. Note also that if the range should ever become zero, the equation makes a forbidden division with zero. This results in an error and the turrets will automatically miss.
-=Turret damage dealing=
+=Turret damage output=
 ==Random damage distribution==
@@ Line 63: / Line 71: @@
 ***Damage dealt = RAW DAMAGE * (Sum of Resistance modified damages) / (Sum of Ammo Damages)
-The quality of the hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage) for regular hits and there may also perfect hits and misses. On the normal hits this number is multiplied with the turrets average damage. By looking carefully at the damage generation above, it becomes clear that the Hit Chance not only means that a turret can miss but also places a cap on the maximum damage number on the non-perfect hits, the next section looks into how this effects the turrets DPS.
+The quality of the hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage) for regular hits and there may also perfect hits and misses. On the normal hits this number is multiplied with the turrets base damage. By looking carefully at the damage generation above, it becomes clear that the Hit Chance not only means that a turret can miss but also places a cap on the maximum damage number on the non-perfect hits, the next section looks into how this effects the turrets DPS.
 {| class="wikitable" border=0
@@ Line 86: / Line 94: @@
 A turret fires on target. The chance to hit is 0.8981, the EVE server rolls a random number between 0 and 1, and gets 0.6573, its less than the chance to hit so the target is struck. At this point 0.49 is added to the random number which then becomes 1.1473. The turret had a damage multiplier of x2.1 and the ammo does 4 EM and 2 Thermal, so the base damage is 2.1 multiplied with 6 (4+2), which is 12.6. After multiplying this with the random number we get the raw damage, which is 1.1473 x 12.6 = 14.456. In this damage the raw EM part is 1.1473 x 2.1 x 4 = 9.6373 and the raw Thermal part is 4.8187. Assuming the targets shield was hit, and that only the normal 20% resistance to Thermal is in effect, the final damage then becomes 9.6373 + (4.8187*0.8) = 13.492 points, in the log the hit will be described as a well aimed one and be rounded off to one decimal place.
-==Damage reduction due to a decreased hit chance==
+==Damage and DPS reduction due to a decreased hit chance==
 When a turret has less than 100% chance to hit the turrets damage dealing capabilites are reduced in two different ways. The first and obvious one is that it sometimes misses, the other is that the max damage on normal hits (e.g. not perfect ones) are reduced as well. Both of these effects will decrease the DPS output. If you read the previous section, you may remember that the a random number between 0 and 1 is generated to see if a turret hits. If this value is lower than the chance to hit, the turret hits, this number is then used further by adding 0.49, this sum is then multiplied with the turrets base damage to obtain the raw damage done (damage before resistances). What this all means is that targets that are tricky to hit also take less damage since high and juicy rolls now are discarded as misses. This can be seen in the damage log as well, a hard to hit target never recieves excellent or well aimed hits, sometimes barely scratching is the highest (perfect hits still happen). The practical effect is that the DPS decreases more than the chance to hit does.
@@ Line 93: / Line 101: @@
 The table below shows how DPS goes down as a target becomes harder to hit. Do note that the reason for the hit chance reduction doesn't matter, be it because of falloff or just tracking issues, the DPS goes down identically. The table can be used to see both how the damage declines as one goes deeper into falloff, and how the damage declines as a result of a lowered hit chance due to tracking reasons. If you wish to combine the effects of tracking and falloff, you can do this by first picking the hit chance from falloff and then the hit chance from tracking, multiply the values to get the combined hit chance, look in the hit chance column until you find a hit chance that is closest to the product you got, and read your relative DPS from that line.
-Comment: The relative DPS above is over 1 at the start, this is not an error. Its because its relative to the base damage of the turret. What puts it above 1 are the perfect hits since they do extra high damage.
+Comment: The relative DPS below is over 1 at the start, this is not an error. Its because its relative to the base damage of the turret. What puts it above 1 are the perfect hits since they do extra high damage.
 {| class="wikitable" border=0