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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.}} | {{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 inner workings of the game by experience and practice over time. Such knowledge is often powerful and can | 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 tip the balance in pvp encounters. Some, but not all, of this practical knowledge stems from the intuitive understanding of the math behind the scene. This article will look into the math that controls the guns and turrets, hopefully this will give the reader insights into the behaviour of damage dealing that otherwise could take many months of playing to develop. The content is not based on experience per se, its based on the math, this ensures that the information is as objective and unbiased as possible and that the reader can verify everything that is written here independantly. | ||
=Governing Equation= | =Governing Equation= | ||
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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. | 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. By looking at the different variables in the equation one can see that many of them are fixed or require certain modules to manipulate. In an unfitted ship the only variables that a pilot can have control over are the distance and the transversal speed. All the other variables are manipulated by fitting in a certain way. Lets look a little closer at the equation and see what more we can learn. | ||
To paraphrase Oli Geist, this can be abstracted to: | To paraphrase Oli Geist, this equation can be abstracted to: | ||
Chance to hit = 0.5 ^ (tracking term + range term). | Chance to hit = 0.5 ^ (tracking term + range term). | ||
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Chance to hit = 0.5^(tracking term) * 0.5^(range term) | Chance to hit = 0.5^(tracking term) * 0.5^(range term) | ||
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. | 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, and vice versa. | ||
=General= | ==General== | ||
Remember that anything to the 0th power = 1, so you'll always hit if (tracking+range) = 0. (1 is 100%.) | Remember that anything to the 0th power = 1, so you'll always hit if (tracking+range) = 0. (1 is 100%.) | ||
Also remember that for any number 'x' < 1, the value of x^y approaches zero as y increases. Since 0.5 is less than one, we'd like the value of (tracking + range) to be as low as possible for better hits. | Also remember that for any number 'x' < 1, the value of x^y approaches zero as y increases. Since 0.5 is less than one, we'd like the value of (tracking + range) to be as low as possible for better hits. | ||
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==Tracking== | ==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 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 | 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 the tracking term is some combination of: | ||
*Keep the target at '''longer''' range | *Keep the target at '''longer''' range | ||
*Lower the transversal speed | *Lower the transversal speed | ||
*Increase your turret's tracking speed | *Increase your turret's tracking speed and/or decrease its signature resolution | ||
*Increase the target's signature radius | *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 automatically miss. | 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. | ||
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==Random damage distribution== | ==Random damage distribution== | ||
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 actually does. Should the randomly generated number be less than 0.01 (1% chance), it will be a perfect hit (aka wrecking), this kind of hit always deal exactly three times the base damage. The thing about perfect hits is that they always occur as long as that random number was lower than 0.01 and at the same time lower than the hit chance. So perfect hits are not scored by 1% of the shots that | 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 actually does. Should the randomly generated number be less than 0.01 (1% chance), it will be a perfect hit (aka wrecking), this kind of hit always deal exactly three times the base damage. The thing about perfect hits is that they always occur as long as that random number was lower than 0.01 and at the same time lower than the hit chance. So perfect hits are not scored by 1% of the shots that can hit, its scored 1% of all hits and misses taken together. This means that if your chance to hit is 1% or below, you can only get perfect hits and misses. Most shots will miss of course, but those that do hit, they will be perfect. | ||
The raw damage dealt by a turret 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. 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 the 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 perfect hits 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. | The raw damage dealt by a turret 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. 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 the 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 perfect hits 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. | ||
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***If (X < 0.01 and X < Hit Chance) Then RAW DAMAGE = 3 * Turret Base Damage ''(these are called perfect or wrecking hits)'' | ***If (X < 0.01 and X < Hit Chance) Then RAW DAMAGE = 3 * Turret Base Damage ''(these are called perfect or wrecking hits)'' | ||
***Else If (X < Hit Chance) Then RAW DAMAGE = (X + 0.49) * Turret Base 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 ''( | ***Else RAW DAMAGE = 0 ''(these are misses)'' | ||
**Calculating damage after resistance | **Calculating damage after resistance | ||
***Resistance modified EM Damage = Ammo EM damage * (100% - Target EM Resistance) | ***Resistance modified EM Damage = Ammo EM damage * (100% - Target EM Resistance) | ||
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***Damage dealt = RAW DAMAGE * (Sum of Resistance modified damages) / (Sum of Ammo Damages) | ***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 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 | 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, it also places a cap on the maximum damage number on the non-perfect hits, the next section will deal with this in more detail. | ||
{| class="wikitable" border=0 | {| class="wikitable" border=0 | ||
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|} | |} | ||
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. | 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. A turret with a 75% hit chance will have a damage spread of 50%-124% on normal hits and do 300% on perfect hits, thus it can never do any excellent hits. | ||
'''Example:''' | '''Example:''' | ||
A turret fires on target | 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 and be rounded off to one decimal place. | ||
==Damage and DPS reduction due to a decreased hit chance== | ==Damage and DPS reduction due to a decreased hit chance== | ||
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*Relative DPS: if(HitChance>0.01 then (HitChance-0.01)*((0.50)+(HitChance+0.49))/2+0.01*3 else HitChance*3) | *Relative DPS: if(HitChance>0.01 then (HitChance-0.01)*((0.50)+(HitChance+0.49))/2+0.01*3 else HitChance*3) | ||
*Reduction in DPS: (RelativeDPSatCurrent/RelativeDPSat100%hit)*100%-100% | *Reduction in DPS: (RelativeDPSatCurrent/RelativeDPSat100%hit)*100%-100% | ||
==Damage and DPS dependancy on tracking in fast ship dogfights== | |||
(not finished) | |||
=Answers to some questions= | =Answers to some questions= | ||
==Do small targets take less damage from big guns?== | ==Do small targets take less damage from big guns?== | ||
Usually they do. If they have zero transversal speed, they will take full damage from any attacks in optimal range. If they have a transversal speed however this will result in two things, first of all they become harder to hit and secondly the maximum damage they can receive goes down as well. A hit will never deal less than half the guns base damage, | Usually they do. If they have zero transversal speed, they will take full damage from any attacks in optimal range. If they have a transversal speed however this will result in two things, first of all they become harder to hit and secondly the maximum damage they can receive goes down as well. A hit will never deal less than half the guns base damage, half of something very high still hurts. | ||
Since big guns have large values in signature resolution and low values in turret tracking, it becomes harder to hit a small target and the hits will have a lower maximum damage. Unless of course the small ship pilot drops his transversal to 0, at which point the big guns will hit easily and deal full damage, the award for such piloting is a brand new noob ship. | Since big guns have large values in signature resolution and low values in turret tracking, it becomes harder to hit a small target and the hits will have a lower maximum damage. Unless of course the small ship pilot drops his transversal to 0, at which point the big guns will hit easily and deal full damage, the award for such piloting is a brand new noob ship. | ||
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No. Even if the guns are grouped on your screen, they are still treated as separate turrets. This can be seen by looking at the turret groups average damage distribution. Its also quite easy to see by looking at the damage output when shooting deep into falloff (or against hard to track targets). | No. Even if the guns are grouped on your screen, they are still treated as separate turrets. This can be seen by looking at the turret groups average damage distribution. Its also quite easy to see by looking at the damage output when shooting deep into falloff (or against hard to track targets). | ||
==+0.49? It says +0.50 on | ==+0.49? It says +0.50 on EVEonline wiki== | ||
Yes it does. But a test | Yes it does. But a test were made to ensure the validity of this article and it showed a small deviance. The data is too big to present here, so results and the method to collect it will be presented instead. Should you wish to check for yourself feel free to follow this procedure. A frigate was named 'Ouch' and abandoned at a safespot. An Osprey was fitted with lasers (infinite ammo, perfect for afk:ing), a remote shield transfer and shield transfer drones. The guns and the ammo was chosen so that the damage would never go below 10.0 and to give as large of a damage interval as possible (an interval of at least 10.0 units (resistances must be accounted for) is needed to get a precision of 1%), this assures that the data will be good enough to draw accurate conclusions. The damage was also only done to the shields, they where never allowed to drop below 25% since a bleed through into armor can happen that can mess with the observed damage numbers. Finally, the ships were positioned within optimal range and the speed set to zero to ensure that the chance to hit is 0.5^0 = 100% and nothing less. After 10,656 shots on the poor frigate, enough data was collected to make some conclusions about how the random damage distribution looks like. The data ends up in the My Documents\EVE\gamelogs on windows, and was easily copied into a prepared Excel sheet for analysis. | ||
*Base damage | *Base damage | ||
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**Compensating for resistance (20% thermal) the modified base damage is: 22.8308 | **Compensating for resistance (20% thermal) the modified base damage is: 22.8308 | ||
Analysis of the data and interpretation of some reduced frequencies of min and max results in the normal damage span: | |||
Of the 10,656 shots the lowest recorded damage was 11.4 (recorded 15 times) and the highest non-perfect was 34.0 (recorded 33 times), perfect hits dealt 68.5 damage (recorded 101 times). On average, each damage number (anything between 11.5 to 33.9) was recorded 46.7 times (standard deviation = 7.02). The reason for the lower occurances of the min and max results on normal hits comes from rounding effects. Any damage in between has an interval of 0.1 units (22.2500 to 22.3499 both produce the 22.3 in the log). However the min and max values do not have that span. The lowest theoretical number is Base Damage x 0.5 = 11.415, hence the interval to get 11.4 in the log is between 11.415 and 11.4499, that is only 0.0345 differance. So the expected number of occurances of the value 11.4 is only 34.6% of the average number, 15 recorded values / 34.6% = 43.4, close to average and inside the standard deviation. The upper interval is 67.8%, 33 times / 67.8% = 48.7, also close to average and inside the standard deviation. (Note: 34.6%+67.8%=102.4%, which is impossible ofc, the error comes from rounding errors in the 4th decimal of the basedamage, awesome precision isn't needed for this comparative calculation since the natural random deviation is much larger anyhow, so good enough). | Of the 10,656 shots the lowest recorded damage was 11.4 (recorded 15 times) and the highest non-perfect was 34.0 (recorded 33 times), perfect hits dealt 68.5 damage (recorded 101 times). On average, each damage number (anything between 11.5 to 33.9) was recorded 46.7 times (standard deviation = 7.02). The reason for the lower occurances of the min and max results on normal hits comes from rounding effects. Any damage in between has an interval of 0.1 units (22.2500 to 22.3499 both produce the 22.3 in the log). However the min and max values do not have that span. The lowest theoretical number is Base Damage x 0.5 = 11.415, hence the interval to get 11.4 in the log is between 11.415 and 11.4499, that is only 0.0345 differance. So the expected number of occurances of the value 11.4 is only 34.6% of the average number, 15 recorded values / 34.6% = 43.4, close to average and inside the standard deviation. The upper interval is 67.8%, 33 times / 67.8% = 48.7, also close to average and inside the standard deviation. (Note: 34.6%+67.8%=102.4%, which is impossible ofc, the error comes from rounding errors in the 4th decimal of the basedamage, awesome precision isn't needed for this comparative calculation since the natural random deviation is much larger anyhow, so good enough). | ||