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Turret damage: Difference between revisions

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=Turret damage values=
=Turret damage values=
At the very core of turret damage dealing is a single randomly generated value between 0 and 1 that is several digits long, something like 0.317226. This random number is used both to determine if the turret hits the target and also to determine how much damage the hit did. Should the randomly generated number be less than 0.01 (1% chance), it will be a wrecking hit which always deal exactly three times the normal average damage. So in those cases where the chance to hit is 1% or less, all hits on the target will be perfect and do tripple damage.  
At the heart of a turrets damage output is a single randomly generated value between 0 and 1 that is several digits long, something like 0.317226. This random number is used both to determine if the turret hits the target and also to determine how much damage the hit did. Should the randomly generated number be less than 0.01 (1% chance), it will be a wrecking hit which always deal exactly three times the normal average damage. So in those cases where the chance to hit is 1% or less, all hits on the target will be perfect and do tripple damage.  


The raw damage dealt is calculated by taking the randomly generated number that resulted in a hit, adding 0.49, and multiplying this sum with the turrets average damage. Since the first 0.01% of the roll is used for perfect hits, the rolls that hit normally are those between 0.01 and 1. So if the chance to hit was 100%, this means that the normal damage will be between 50% (0.01+0.49) and 149% (1+0.49) of the average damage, or in the case of a perfect hit always exactly 300% of the average damage. This number will then be reduced accordingly by the targets damage resistances in order to obtain the final damage number. The turrets average damage is a fixed number and can be calculated by multiplying the turrets damage multiplier and the sum of the damage types from the ammo.
The raw damage dealt is calculated by taking the randomly generated number that resulted in a hit, adding 0.49, and multiplying this sum with the turrets base damage. A turrets base damage is a fixed number that is calculated by multiplying the turrets damage multiplier and the sum of the damage types from the ammo (the targets resistances is ignored, its dealt with later). Since the first 0.01% of the random value is used for perfect hits, the random values that hit normally are those between 0.01 and up to 1 at most (1 if chance to hit is 100%). So if the chance to hit was 100%, this means that the normal damage will be between 50% (0.01+0.49) and 149% (1+0.49) of the base damage, or in the case of a perfect hit always exactly 300% of the base damage. This number will then be reduced accordingly by the targets damage resistances in order to obtain the final damage number.


*'''Damage generation'''
*'''Damage generation'''
**Calculating variables
**Calculating variables
***Turret Average Damage = Turret Damage Multiplier * Sum of Ammo Damages
***Turret Base Damage = Turret Damage Multiplier * Sum of Ammo Damages
***Hit Chance = ((calculated by the big equation at the top of this page))
***Hit Chance = ((calculated by the big equation at the top of this page))
***X = Random (0 to 1)
***X = Random (0 to 1)
**Calculating raw damage
**Calculating raw damage
***If (X < 0.01) Then RAW DAMAGE = 3 * Turret Average Damage ''(these are called wrecking or perfect hits)''
***If (X < 0.01) Then RAW DAMAGE = 3 * Turret Base Damage ''(these are called wrecking or perfect hits)''
***Else If (X < Hit Chance) Then RAW DAMAGE = (X + 0.49) * Turret Average Damage ''(these are normal hits)''
***Else If (X < Hit Chance) Then RAW DAMAGE = (X + 0.49) * Turret Base Damage ''(these are normal hits)''
***Else RAW DAMAGE = 0 ''(this is a miss)''
***Else RAW DAMAGE = 0 ''(this is a miss)''
**Calculating damage after resistance
**Calculating damage after resistance
***Final EM Damage = Ammo EM damage * (100% - Target EM Resistance)
***Applied EM Damage = Ammo EM damage * (100% - Target EM Resistance)
***Final Thermal Damage = Ammo Thermal damage * (100% - Target Thermal Resistance)
***Applied Thermal Damage = Ammo Thermal damage * (100% - Target Thermal Resistance)
***Final Kinetic Damage = Ammo Kinetic damage * (100% - Target Kinetic Resistance)
***Applied Kinetic Damage = Ammo Kinetic damage * (100% - Target Kinetic Resistance)
***Final Explosive Damage = Ammo Explosive damage * (100% - Target Explosive Resistance)
***Applied Explosive Damage = Ammo Explosive damage * (100% - Target Explosive Resistance)
***DAMAGE = RAW DAMAGE * (Sum of Final Damages) / (Sum of Ammo Damages)
***APPLIED DAMAGE = RAW DAMAGE * (Sum of Applied Damages) / (Sum of Ammo Damages)


The quality of the hit as seen in the log will be described by the value of the random number. In the list below, 0.49 is added to the random number to show more clearly which number it is that the turrets average damage is multiplied with for each description.
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.  


{| class="wikitable" border=0
{| class="wikitable" border=0
| '''Hit description''' || '''Intervall of the random number + 0.490''' ||
| '''Hit description''' || '''Random damage modifier''' ||
|-
|-
| Perfectly || 0.490 to 0.500, 3x the average damage instead ||
| Perfectly || 0.490 to 0.500 (special case, 3x the average damage instead) ||
|-
|-
| Barely scratches || 0.500 to 0.625 ||
| Barely scratches || 0.500 to 0.625 ||
Line 60: Line 60:
| Excellent || 1.250 to 1.490 ||
| Excellent || 1.250 to 1.490 ||
|}
|}
A turret with a 100% hit chance will see a natural and unavoidable damage spread between 50-149% of its base damage for normal hits, and always do exactly 300% of its base damage on perfect hits.


'''Example:'''
'''Example:'''
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. The total raw (before resistances) EM damage becomes 1.1473*2.1*4=9.6373 and the raw Thermal damage becomes 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 to one decimal place.
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==
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 scrathing is the highest (perfect hits still happen ofc). The practical effect is that the DPS decreases more than the chance to hit does.


==Damage reduction in falloff==
'''Example:''' (please note that perfect hits are not considered in this example to make the numbers easier to follow) A turret has 50% chance to hit at optimal+falloff. The highest randomly rolled number that can result in a hit is thus 0.5, higher numbers means a miss. This will shrink the damage interval down to 0.5 to 0.99 for normal hits, which on average is 0.745 ((0.5+0.99)/2). Compare that with a case inside optimal range where the chance to hit is 100%, where the damage interval is 0.5 to 1.49 and the average is 0.995. At optimal+falloff (and ignoring perfect hits) the DPS is hence reduced to 50% x 0.745=37.25% of normal. (If perfect hits are taken into consideration, the DPS value will become 39.5%, see table below)
When a target is inside falloff range there is a reduction to the chance to hit as well as a reduction in the max damage that can be dealt. Both of these 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 average damage to obtain the raw damage done (before resistance). What this all means is that targets that are tricky to hit also take less damage since high rolls are discarded as misses. This can be seen in the damage log since the good hits (like excellent) no longer appear when a ship becomes harder to hit. The practical effect is that the DPS decreases more than the chance to hit does.


'''Example:''' (please note that perfect hits are not considered in this example to make the numbers easier to follow) A turret has 50% chance to hit at optimal+falloff. The highest randomly rolled number that can result in a hit is thus 0.5, higher numbers means a miss. This will shrink the damage interval down to 0.5 to 0.99 for normal hits, which on average is 0.745 ((0.5+0.99)/2). Compare that with a case inside optimal range where the chance to hit is 100%, where the damage interval is 0.5 to 1.49 and the average is 0.995. At optimal+falloff (and ignoring perfect hits) the DPS is hence reduced to 50% x 0.745=37.25% of normal. (If perfect hits are taken into consideration, the DPS value becomes 39.5%)
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.


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 decline as you go deeper into falloff, and how the damage decline as the hit chance is lowered due to tracking reasons. If you wish to combine the effects of tracking and falloff, 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, go down in the table 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.


{| class="wikitable" border=0
{| class="wikitable" border=0
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The relative DPS above is over 1 at the start, this is because the value is relative to the turrets average damage, and the perfect hits push the relative number above 1.


The formulas used to calculate this table were:
The formulas used to calculate this table were:
Retrieved from "https://wiki.eveuniversity.org/Turret_damage"