Difference between revisions of "Turret damage"

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(Major rewrite, divided the article into two sections, the first one deals with concepts and should be fairly easy to read, the second one now contains the math)
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[[Category:Guides]]
 
[[Category:Guides]]
  
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=Introduction=
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This article describes how damage from turrets (guns) are generated in EVE and what lessons that can be learned from that. The information here is focused on concepts and game mechanics, and touches only lightly on some modules in order to compare them. It is in no way a fitting guide.
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All the data is based on facts, drawn from the mathematical equations working behind the scene every time someone pulls a trigger. Since not everyone is fond of math, the article will be divided into two sections. The first part is a summary of the results and describes all the concepts you will need to know. The second part is much more detailed and uses several calculations as examples.
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Additional information about turrets can also be found on http://wiki.eveuniversity.org/Turrets and tips and tricks for using turrets more effectively is at http://wiki.eveuniversity.org/Gunnery_Guide
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=The First Part: Summary=
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To understand how turret damage is generated you will need to understand a number of concepts and how they interconnect. Some of them are visible under the attributes tab when you click for info on your guns. Especially falloff and tracking can be tricky to grasp, so be extra careful when reading those.
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==Hit chance==
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A turret always have a 0-100 percent chance to hit a target. The hit chance start at 100% but factors that reduce the hit chance can lower this. Those factors are basically the range to the target and the targets movement, with a few modifications. When the hit chance has been calculated, the EVE server will then "roll a dice" to see if the turret hits or misses the target.
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==DPS==
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DPS stands for Damage Per Second. This number is calculated from the average damage per hit you do (if your hit chance is 100%) divided by the turrets rate of fire (ROF). The fitting window in the game will show you your DPS from turrets, drones and missiles respectively.
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==Average Damage==
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The average damage is the one you do under ideal conditions (a 100% hit chance). But there is always a random element present in turret damage so your actual damage will jump around a bit. When the hit chance is 100% the damage spread will be between 50% and 150% of the average damage, this spread is unavoidable and built into the damage generation. There is an exception to this, so pay extra attention now, because this is a little tricky. When the hit chance is reduced, the highest possible damage also goes down even if all shots did hit. The interval around the average damage is always 50% to (50%+hit chance). So at 30% hit chance the damage interval is down to only 50% to 80% of average damage. This is in addition to the fact that only 30% of your hits will land. Thus there are two things that will reduce the damage you do whenever you loose hit chance. (This description has two tiny intentional errors in it that were used to explain the concept more easily: the first error is that the damage interval is actually spread around what is known as base damage and not average damage, the second error is that the percent interval only has 99 units, more details can be found in the second part below).
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==Perfect hits==
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In the 0-100 percent hit chance interval, there is a 1% chance of doing a perfect hit. It is that first percent unit in the entire interval. Think of it as rolling a 1D100 (a dice with a onehundred sides), if it lands on a 1, you get a perfect hit regardless of the hit chance. This actually means that if your hit chance is a measly two percent, half of your hits will be perfect. If your hit chance is less than one percent, you must first score a hit before it can become a perfect. A perfect hit will always do exactly 300% of the average damage (tiny intentional error, it is base damage).
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==Range==
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The distance to the target you are shooting at. Range is used to determine any penalties to hit chance based on the distance between the shooter and the target.
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==Angular velocity==
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This describes how fast something travels around something else. It is measured in the unit rad/second, where one rad is equal to a 57 degree angle. Your in game overview can show this value if you open its settings and tick a box under the tab called columns. Angular velocity is used to determine the penalty to the hit chance based on the turrets tracking capabilities. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting). A cool headed player can use special manouvers (like keep at range) or modules (turning webs on and off can really mess with orbiting ranges) to drastically reduce the angular velocity of a foe to open up for some heavy handed blows against a target that is otherwise hard to track.
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===Transversal speed===
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The angular velocity is calculated by dividing the Transversal speed with the Range to the target (don't mix meter and km if you calculate this, use just meter for both). Transversal speed is sideways speeds, not speeds towards or from the target (that is called radial speed). If you stand on a straight road and see a car coming, the car will have no sideways movement but a large radial movement towards you. If you stand next to the road and watch a car passing you by, the car will have a large sideway movement but almost no radial. High transversal speeds are important for speed tanking, never fly straight towards or away from a target, if you do the need for tracking drops to zero and you will be shot dead even by the biggest guns.
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==Optimal==
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Inside this range the gun will suffer no reduction in hit chance. If the target is sitting still inside the optimal range, every single attack will hit it.
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==Falloff==
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Falloff is an extra range that goes beyond your optimal range. This is however not a limit value, like the optimal range is. Instead its very fluid. It is best described as a gradual loss of hit chance, where the given number represents the distance at which you are down to a 50% hit chance. At two times your falloff value your hit chance is down to only 6.25%, even though it is unlikely you can still hit your target at that range, and even further out.
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==Tracking==
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Tracking is value that indicates how well you can hit targets that is orbiting you, higher tracking is needed for faster moving targets. This is not a limit value either, in fact it works exactly as falloff does. When the targets angular velocity is equal to the turrets tracking value you will have a 50% hit chance (note: size of the target will also affect this, see below). Just as for falloff, when a targets angular velocity is two times your tracking, the hit chance is down to 6.25%.
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==Turret Signature Resolution==
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This value kind of represents the accuracy of the turret. But only kind of, because it will only be important for tracking, it plays no part when it comes to the range. In EVE, every gun can hit the bullseye of any target in range regardless of its size as long as it is absolutely still. If the target beings to move on the other hand the size suddenly becomes important. All small guns have 40m as value, all medium guns have 125m as value and all large guns have 400m as value. The smaller the better.
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==Target Signature Radius==
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It doesn't matter what a ship looks like physically. They are all treated as if they were spheres when they are shot at. The target signature radius describes how big this sphere is, the bigger it is the easier it will be to track with guns. A big target also takes more damage from missiles, but that is outside the scope of this article.
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==Damage loss from Falloff and Tracking==
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Targets out in falloff, along with targets that must be tracked, are harder to hit. A lower hit chance means less damage done. The real question is, how much less damage? So lets look at that. First of all, one really nice thing with falloff and tracking is that they both behave exactly the same way, so the data table below applies to both of them.
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The "Percent of Tracking or Falloff" values means the percent of your falloff or your tracking, depending on which you want to look at (one at the time). If your falloff is 12km then 33.3% means one third of that, so 4km. If your tracking is 0.06rad/sec then 33.3% means 0.02rad/sec.
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{| class="wikitable" border=0
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| '''Percent of Tracking or Falloff''' || '''Hit chance''' || '''Reduction in DPS by %''' ||
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|-
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|0|| 100%|| 0.0%||
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|-
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|25%|| 95.8%|| -6.1%||
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|-
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|33.3%|| 92.6%|| -10.6%||
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|-
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|50%|| 84.1%|| -22.1%||
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|-
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|84.8%|| 60.8%|| -50.0%||
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|-
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|100%|| 50.0%|| -61.1%||
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|-
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|150%|| 21.0%|| -85.2%||
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|-
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|200%|| 6.25%|| -94.3%||
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|-
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|300%|| 0.20%|| -99.4%||
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|}
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Few players would be able to spot a -10.6% loss in DPS. In fact, this is so small that the normal random distribution sort of drowns this out. Based on this. It is safe to say that you can use 1/3 of your falloff or tracking without any loss of noticeable performance. It is a sweet spot if you will and a good value to remember. Especially so if you often fight in falloff or against hard to track foes.
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===Target size===
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As mentioned above, target size only influence tracking penalties, never range penalties. It may seem counter intuitive, but that is the way the game works. The problem here from a player perspective is that the game will not provide you with the information. If you need to know, you must do the calculations yourself, or at least do rough estimates.
  
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=Introduction=
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This is not as hard as it sounds, there is a rather neat way to quickly estimate what kind of tracking you really have against smaller or bigger targets. First you need to know the tracking value of your guns, the second thing is the Turret Signature Resolution value of your guns, and the third is to guess (yes, guess, but qualified guesses can be made) the Signature Size of your target. Guns always come in the resolution of 40m (small), 125m (medium) and 400m (large). In a similar fashion, you can use 40m for frigates, 125m for cruisers, 200-300m for battlecruisers and 400m for battleships. Shield tanked ships will always be a bit bigger while armor tanked ships have a normal size. Now you estimate the ratio between the target size and your gun size, multiply that ratio with your own tracking and now you know what you have in practice against that target.
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Difficulty: Advanced (requires a previous knowledge of concepts such as tracking, falloff, DPS and more)
 
  
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This article takes a detailed look into how the damage from turrets (guns) is determined. The To-Hit-Equation (which determines the effects from falloff and tracking) is given a thorough explanation and a datatable is provided to show the practical consequences of it, the random damage distribution is also looked at, as well as its connection with the chance to hit.
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Example: A battleship (400m resolution on guns) fires on a frigate (40m radius). Target size divided by gun size gives us 40m / 400m = 0.1, or 10%. When the battleship fires on the frigate it can thus only use 10% of its actual tracking value (which is already low), due to the size differance. This is why it is so freakin hard to hit small things with big guns (if they are moving).
  
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To be unbiased and as accurate as possible, there is some math. You will however not be required to do any calculations of your own unless you want to double check something, so if you don't like math you can just keep on reading, all of the important things are explained with words as well.
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Example 2: An Incursion Machariel with 3 Tracking Enhancer II's and T2 large autocannons have a tracking value of 0.067rad/sec. While shooting at a Sansha frigate (49m size), its real tracking value is only 49m / 400m = 0.1225 or 12% of the stated one, 0.067rad/sec x 0.1225 =
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0.0082rad/sec. A typical Sansha frigate orbits at 14km at roughly 500m/s, that corresponds to an angular velocity of 500m/s / 14000m = 0.036rad/sec. Which is over 4 times higher than the Machariels tracking value and practically impossible to hit. No wonder why incursion fleets love webs (tracking links are nice too).
  
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==Grouping guns, does it affect the damage?==
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No. Even if the guns are grouped on your screen, they are still treated separately. This can be seen by collecting damage data and comparing that with the normal expected damage distribution, its very clear that its a combination of several seperate turret shots. It can also be deduced by looking at the turret group's damage output when shooting at hard to hit objects, like things deep into falloff, its quite easy to tell when one, two or more guns hit the target.
  
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Additional information about turrets can also be found on http://wiki.eveuniversity.org/Turrets and tips and tricks for using turrets more effectively is at http://wiki.eveuniversity.org/Gunnery_Guide
 
  
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=Turret damage output=
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=The Second Part: Mechanics and equations=
  
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==An initial look at the To-Hit-Equation==
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==Tools==
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This is the To-Hit-Equation:
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E-UNI member Junker Jan created a [https://spreadsheets.google.com/ccc?key=0Ag79e9sxtWMcdGRVYXJCeWRDR2V2MTU1UmFEcTRSWkE&hl=en spreadsheet] primarily focused on determining your chance of hitting a target given a set of criterion.  Made Public via Google Docs the document won't be editable when you click the above link, otherwise one accidental click could destroy all the carefully crafted formulae!  You will need to either click '''File --> Download As''' to download the spreadsheet into your format of choice, or '''File --> Make a copy...''' to copy the document to your personal Google Docs store if you have a Google Account.
  
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The values you should input should be in their final state, i.e. after all implants, modules, boosters, or fleet boosts you want included for the calculations are activated.  All of the required information is available from the ''Show Info'' context-menu of the turret or ship in question, so for an in-game test simply undock and turn on everything you want to get your real-world actual values.  For NPC ships you could use a resource like [http://eveinfo.com/npcship EVE Info] to find out their signature radii or typical armor resistance values.
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==The To-Hit-Equation==
 
[[File:TurretHitChance1.JPG]]
 
[[File:TurretHitChance1.JPG]]
  
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If you get a headache by just looking at this, don't worry, you will never have to actually do anything with it yourself. And there will not be a test. It is however important, since it works behind the scenes whenever someone uses a turret based weapon. But it isn't really the equation itself that is of interest in a fight, it is how it affects the fight. So that is what we will be looking at.
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This equation is used every single time someone fires a turret weapon in the game. The purpose of it is to determine the odds the turret has to hit its target. The value will always be between 0 and 1, or 0% and 100% if you will. The computer will then 'roll a dice' to see if a hit is scored or not.  
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An example of how this is useful, is with autocannons. They have very short optimals and large falloffs, in practice they always fight in falloff. So the question is, how far can they go into falloff without having any major loss of damage? The equation can help us answer this.
 
  
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But now we have rushed ahead. We should start with the very basics, by looking at the variables inside the equation, so we see what it is that actually effect the chance to hit. Most of these variables are determined before you undock. From your choice of ship, your skill points and your fitting. But two of them actually depends on how you fly your ship when in space, those are Transversal Speed and Range To Target. This is an important insight: Your own piloting will have an impact on the damage your guns do.
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Let's start by taking a look at variables inside the equation. Most of these variables are actually determined before you even undock. From things like your choice of ship, your skill points and your fitting. There are only two that depend on you as a player (how you fly your ship), those are called 'Transversal Speed' and 'Range To Target'. This is the first important insight: How you fly will affect the damage you do.
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*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.
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*Transversal speed = Movement up/down/left/right relative to an object, but not towards or away from it (that thing is called radial speed). Measured in m/s.
 
*Range to target = The range to an object. Measured in meters.
 
*Range to target = The range to an object. Measured in meters.
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*Turret tracking = Found on the attributes tab of a turret. Measured in rad/second.
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*Turret tracking = Found on the attributes tab of a turret. Measured in rad/second (one rad is equal to 57 degrees, 360 degress is equal to 6.28 rad)
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*Turret signature resolution = Higher values make it harder to hit small signature radii. Measured in meters.
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*Turret signature resolution = Higher values make it harder to hit small signature radii, it can be thought of as accuracy but it isn't entirely correct. Measured in meters.
 
*Target signature radius = The size of the target, or more precisly the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.
 
*Target signature radius = The size of the target, or more precisly the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.
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*max(0, x) = Takes the highest value of zero or x. Used to set all negative values to zero in this case.
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*max(0, x) = a math function that takes the highest value of zero or x. It is used to prevent negative values in this case, any negative numbers a replaced with a zero instead.  
 
*Turret optimal range = Found on the attributes tab of a turret. Inside this range no range penalites from distance are applied. Measured in meters.
 
*Turret optimal range = Found on the attributes tab of a turret. Inside this range no range penalites from distance are applied. Measured in meters.
 
*Falloff = Found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.
 
*Falloff = Found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.
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  Chance to hit = 0.5 ^ (tracking term) * 0.5 ^ (range term)
 
  Chance to hit = 0.5 ^ (tracking term) * 0.5 ^ (range term)
  
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Why is this interesting? From this we can see that tracking and range are actually calculated completely seperately before the results from each are multiplied. This means that Range and Tracking are two entirely separate things that has nothing to do with eachother, and you will need both.
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Why is this interesting? From this we can see that tracking and range are actually calculated seperately, then the results from each are multiplied. This shows that Range and Tracking are indeed two different and independant things, and both will be used to score a hit.
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There is one more thing we can find out by just looking at the equation. This is however a little tricker to grasp. The aim here is to compare the tracking term and the range term for similarities in their behaviour. Do they have anything in common? To do this, we will freeze all values in those terms except for one variable in each, turret tracking and falloff respectively. Then we can look at how that single variable effects the outcome and if there is any similarities between the two cases.
 
  
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All guns have their tracking value expressed in something called angular velocity, this is identical to Transversal speed divided by Range to Target, this is inside the tracking term, and basically it means how fast something moves around something else. Lets freeze the angular velocity, this means that it is still moving but that the value will not change. In the tracking term we also have Turret signature resolution divided by Target signature radius, for easy comparison later on we will assume that both these number are the same, then we freeze them as well. What we are left over with is: a fixed number divided by Turret tracking.
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There is also one more thing we can find out by just looking at the equation. This is however a little tricker to follow, but the conclusion is easy. The aim is to compare the tracking term and the range term for similarities in how they behave. Do they have anything in common? To do this, we will freeze all values in those respective terms except for one variable in each, that will be 'turret tracking' and 'falloff' respectively. Then we can look at how that single variable effects the outcome in each case and see if there is any similarities between them.
  
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Now lets look at the range part. Being inside optimal never incurs a hit penalty, so we must move out into falloff ranges too see any changes in the to-hit-equation's output values. Lets freeze everything apart from falloff. What we are left with is: a fixed number divided by Falloff.
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The tracking part: All guns have their tracking value expressed in something called 'angular velocity', this is identical to 'Transversal speed' divided by 'Range to Target', this is all inside the tracking term if you look at it, and basically it just means how fast something moves around something else. Lets freeze the angular velocity, this means that it is still moving but that the speed will not change. In the tracking term we also have 'Turret signature resolution' divided by 'Target signature radius', for easy comparison later on we will assume that both these number are the same (so their ratio is one, which means no effect), then we freeze them as well. What we are left over with is this: a fixed number divided by 'Turret tracking'.
  
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Did you see what they had in common? In the tracking term, we now have ''something / Turret tracking'', in the range term we have ''something / Falloff''. In both cases there is a value that is divided by the variable we are interested in. So mathematically the same thing happens in both cases. That means that tracking and falloff behave the exact same way. So if you understand one of them, you have actually also understood the other.
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The range part: Being inside optimal never incurs a hit penalty, so we must move out into falloff ranges too see any changes in the to-hit-equation's output values. Lets freeze everything apart from 'falloff'. What we are left with is: a fixed number divided by 'Falloff'.
  
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Did you see what they had in common? In the tracking term, we now have ''something / Turret tracking'', in the range term we have ''something / Falloff''. In both cases there is a value that is divided by the variable we were interested in. There is an important insight here: tracking and falloff behaves identically. And they are not fixed limits, they become ratios that describes how quickly you loose hit chance as you start to push range and orbiting speeds, and the hit chance loss is gradual.
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===Tools===
 
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E-UNI member Junker Jan created a [https://spreadsheets.google.com/ccc?key=0Ag79e9sxtWMcdGRVYXJCeWRDR2V2MTU1UmFEcTRSWkE&hl=en spreadsheet] primarily focused on determining your chance of hitting a target given a set of criterion.  Made Public via Google Docs the document won't be editable when you click the above link, otherwise one accidental click could destroy all the carefully crafted formulae!  You will need to either click '''File --> Download As''' to download the spreadsheet into your format of choice, or '''File --> Make a copy...''' to copy the document to your personal Google Docs store if you have a Google Account.
 
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The values you should input should be in their final state, i.e. after all implants, modules, boosters, or fleet boosts you want included for the calculations are activated.  All of the required information is available from the ''Show Info'' context-menu of the turret or ship in question, so for an in-game test simply undock and turn on everything you want to get your real-world actual values.  For NPC ships you could use a resource like [http://eveinfo.com/npcship EVE Info] to find out their signature radii or typical armor resistance values.
 
  
  
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==Random damage distribution==
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==The random damage distribution==
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At the heart of a turret's 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 hit the target and then to determine how much damage the hit actually did. Should the randomly generated number be less than 0.01 (1% chance), it will be a perfect hit (aka 'wrecking'). A wrecking hit always deals exactly three times the base damage, exactly, there is no random element in perfect hits. 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, but by 1% of all hits and misses taken together. This means that if your chance to hit is 1% or less, you will either hit perfectly or you will miss, there are no normal hits.
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At the heart of a turret's 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 then to determine how much damage the hit actually did. Should the randomly generated number be less than 0.01 (1% chance), it will be a perfect hit (aka 'wrecking'). A wrecking hit always deals exactly three times the base damage, exactly, there is no random element in damage from perfect hits. 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, but by 1% of all hits and misses taken together. This means that if your chance to hit is 1% or less, you will either hit perfectly or you will miss, there are no normal hits.
  
 
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 turret's base damage. Since the first 0.01% of the random value is used for perfect hits, normal hits have a damage spread between 0.50 to 1.49, or 50% to 149% 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 target's 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 turret's base damage. Since the first 0.01% of the random value is used for perfect hits, normal hits have a damage spread between 0.50 to 1.49, or 50% to 149% 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 target's damage resistances in order to obtain the final damage number.
  
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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, on top of which there may also perfect hits and misses.  
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The quality of a non perfect hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage).
  
 
{| class="wikitable" border=0
 
{| class="wikitable" border=0
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|}
 
|}
  
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A turret with a 100% hit chance will see a natural and unavoidable damage spread between 50% to 149% of its base damage for normal hits, and will 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 because they are now misses.
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A turret with a 100% hit chance will see a natural and unavoidable damage spread between 50% to 149% of its base damage for normal hits, and will 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, so with a 75% hit chance there can be no excellent hits because they are now turned into misses.
  
 
'''Example:'''
 
'''Example:'''
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==Damage and DPS reduction in the presence of a chance to miss==
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==Damage and DPS reduction due to a lower hit chance==
 
When a turret has less than 100% chance to hit the damage is 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.  
 
When a turret has less than 100% chance to hit the damage is 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.  
  
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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 higher than the chance to hit, the turret misses. What this really means, is that the random rolls that would have caused high damage are converted into misses instead. This can be seen in the damage log: a hard-to-hit target never recieves excellent or well aimed hits, sometimes barely scratching is the highest possible (though of course perfect hits can still happen).
 
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The practical effect from this is that the effective DPS always decreases more than the chance to hit does.
 
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==Detailed DPS loss from Tracking and Falloff==
 
 
Since it was established earlier that Tracking and Falloff behave exactly the same way. We can use the same data table and the same graphs to describe both, but only one at the time.
 
Since it was established earlier that Tracking and Falloff behave exactly the same way. We can use the same data table and the same graphs to describe both, but only one at the time.
  
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The true strength with the table and graphs below are not to calculate what your DPS might be in a given situation. But rather to see how much you can push your falloff and tracking while still maintaining a decent DPS output.
 
The true strength with the table and graphs below are not to calculate what your DPS might be in a given situation. But rather to see how much you can push your falloff and tracking while still maintaining a decent DPS output.
  
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Now consider the following values, they are especially notable because they are easy to calculate. They are one third, one half and one full of either your tracking or your falloff value:
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'''Notes:''' Parts into means the value you multiply either your falloff or your tracking with. 0.25 means 25% or a quarter of that value. Likewise, the hit chance is expressed the same way. The relative DPS is a multiple to the base damage of the turret, it starts above 1 because of the perfect hits, since they do extra high damage.
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*Below 0.333 parts into ... : the DPS loss is at most 10%, a very small effect, being at 0.333 or below means pretty much that you have nearly top performance, you are still in a really sweet spot.
 
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*Above 0.50 parts into... : the DPS loss is now 22% and noticeable, you can try manual piloting to rectify this unless you have a tactical reason for keeping the current conditions, for example a situation where your opponant have an even higher loss of DPS.
 
−
*Above 1.0 parts into... : at this point the DPS loss is 60% or more. Some damage is still better than no damage, but keep in mind that you have a pretty lousy performance under these circumstances.
 
−
Especially the 0.333 value is good to remember (one third of your tracking or falloff). If you want to maintain a high DPS, this is how deep you can go into either tracking or falloff (if you are pushing both of them at once use 0.25 instead). If you go above this, your DPS will start dropping fairly quickly and if you go further in there is only a small increase in damage. This is kind of the golden limit that comes out from studying the To-Hit-Equation. Like all guidelines, this one comes with an exception too, see the next section for that.
 
−
 
 
−
 
 
−
'''Comment on the table below:''' The relative DPS below is over 1 at the start, this is not an error. It's because it's relative to the base damage of the turret. What puts it above 1 are the perfect hits, since they do extra high damage.
 
  
 
[[File:HitChanceVsFalloff.JPG|500px|thumb|right|Click to enlarge]]
 
[[File:HitChanceVsFalloff.JPG|500px|thumb|right|Click to enlarge]]
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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%
−
 
−
 
−
==The effects of Signature radius==
 
−
Turret Signature Resolution and Target Signature Radius play an important role inside the tracking term. So far we assumed that they are the same, meaning that their ratio is always 1, and hence have no effect on tracking. But they do have an impact. To better understand what effect it really has, we must go back up to the To-Hit-Equation and look closer at the tracking term again.
 
−
 
−
Instead of thinking about ''Turret Signature Resolution / Target Signature Radius'' as an expression, think of it as a single number that the Transversal Speed is multiplied with. This makes sense if you look at the equation. Now, if this number is 1, it has no effect at all and tracking works as normal. But if the number is higher than 1, this would have the same effect as if the Transversal Speed went up, which means it is harder to hit. And if the number is lower than 1, this would have the same effect as if the Transversal Speed went down, which means it is easier to hit.
 
−
 
−
If you know how many parts into tracking a certain ship is, and you want to adjust for the signature part too, you must multiply ''parts into tracking'' with ''Turret Signature Resolution / Target Signature Radius'' to get the ''true'' parts into tracking. There is no other way. This is not something that can be done in combat, mostly because you will not know the signature radius of your target. What you can do is to use your gut feeling and guess from what it is you see. A shield tank means a bigger ship, an armor tank a normal size. And then you compensate for it if needed.
 
−
 
−
To better illustrate this, consider the following examples:
 
−
 
−
'''Example:''' A Rifter is attacking a Hurricane. The angular velocity is about 0.3 rad/sec and the Hurrican has a tracking of 0.15. From the Hurricane pilots view, the Rifter is already 2.0 parts into tracking from just its speed. But this is not entirely true, since the signature resolution and the signature radius has not been accounted for yet. The guns have a signature resolution of 125m and the rifter has a radius of 35m. The ratio here is 125/35 = 3.57. So the Rifter counts as if being 3.57 times deeper into tracking just because of its smaller size. Taking this into account means that the Rifter is actually 7.14 parts into tracking under the mentioned conditions, and impossible to hit. The Hurricane must rely on its drones to fend off the Rifter. With luck the Rifter will die before it can kill all the drones.
 
−
 
−
'''Example:''' A shield tanked and an armor tanked Rifter are fighting. The angular velocity is very high at about 0.5 and they both have a tracking of 0.49 with their 200mm autocannons. So we say one full part into tracking. They are using small guns which always has a Turret Signature Resolution of 40m. The shield tanked Rifter has a signature radius of 48m and the armor tanked one has 35m. From the shield tanked Rifters point of view, his opponant counts as being 1 x 40m/35m = 1.14 parts into tracking, where the DPS loss from turrets are about -70%. From the armor tanked Rifters point of view, his opponant counts as if being 1x 40m/48m = 0.833 parts into tracking, where the DPS loss from turrets are about -50%. The shield tanked Rifter pilot is at a disadvantage from just being bigger, his guns do roughly half the damage compared to his opponant. If he doesn't compensate for this by flying in a way that reduces the angular velocity, he is likely to loose.
 
  
  
 
==Tracking upgrades vs Damage upgrades==
 
==Tracking upgrades vs Damage upgrades==
−
Weapon upgrade modules can improve raw damage, tracking and range. Making use of an increased range is fairly obvious. However, comparing tracking and damage can be harder to do. This section is written to help with that.
+
Weapon upgrade modules can improve raw damage, tracking and range. Making use of an increased range is fairly obvious. However, comparing tracking and damage can be harder to do. The tricky thing with this comparison is that the need for tracking in a fight often varies depending on how the pilots fly their ships. So to make any sense of the following you must have some rough ideas of what the angular velocities will be. The only way to get that is through experience.
−
 
 
−
The tricky thing with this comparison is that the need for tracking in a fight often varies depending on how the pilots fly their ships. So to make any sense of the following you must have some rough ideas of what the angular velocity can be expected to be. The only way to get that is through experience.
 
  
 
Here are some guidelines for comparisons: (note that only the bonus of the 1st module is considered for all tracking modules, additional ones will suffer from a stacking penalty).
 
Here are some guidelines for comparisons: (note that only the bonus of the 1st module is considered for all tracking modules, additional ones will suffer from a stacking penalty).
Line 258: Line 304:
 
Webs:
 
Webs:
  
−
The effect from a web is hard to predict, since its use can change both the transversal speed and the range between the ships. Experience and practice will be your best guide here. The drawback with webs is that they can help your opponants tracking as well as your own. The web is more often used for its tactical benefits, such as giving control over the range, than to help with tracking.
+
The effect from a web is hard to predict, since its use can change both the transversal speed and the range between the ships. Experience and practice will be your best guide here. The drawback with webs is that they can help your opponants tracking as well as your own. The web is more often used for its tactical benefits, such as giving control over the range. But it is also the best tool to reduce the need for tracking when large guns are used against small targets.
  
  
 
==Choosing turrets==
 
==Choosing turrets==
−
Is it better with high damage or high tracking? It is almost always better to go for the higest possible damage, which also gives a higer range. This is true for long range (like artillery) and short range (like autocannons) guns alike.  
+
Is it better with high damage or high tracking turrets? It is almost always better to go for the higest possible damage, which also gives a higer range. This is true for long range (like artillery) and short range (like autocannons) guns alike. The reason for this is because the gain in tracking isn't enough to compete with the lost damage.
  
  
−
The only turret type where higher tracking can possibly outweigh the extra damage and range is for autocannons, the other types simply doesn't gain enough tracking to be worth even looking into. The lighter autocannon type has +32% tracking, -23% damage and -17% falloff compard to the heavier type. The following example will compare heavy vs light, it is heavy in numbers, but there is a summary at the end of it of it if you want to skip ahead.
+
The only turret type where higher tracking can possibly outweigh the extra damage and range is for autocannons, the other types simply doesn't gain enough tracking to be worth even looking into. The lighter autocannon type has +32% tracking, -23% damage and -17% falloff compard to the heavier type (for small, mediums and large alike). The following example will compare heavy vs light, there will be lots of numbers, but there is a summary at the end of it of it all if you want to skip ahead.
  
 
'''Example:''' ''This is a comparison of when the lighter type overtakes the heavier type against a target with high angular velocity. For this example it is assumed that that the targets signature radius is identical to the guns signature size, the range is also assumed to be the same in both cases so that the angular velocity will be identical.'' A pilot is using the heavier autocannons (for example small 200mm, but this comparison is true for medium and large as well) and is fighting at 0.333 parts into falloff (corresponds to about 2200m with hard hitting ammo and T2 guns (for T1 it would be 2100m, so no real differance)), this corresponds to a -10% DPS loss from range, tracking isn't considered yet. If the pilot instead had been using the lighter autocannons (small 125mm) the range is the same (2200m for T2 guns) but this time it corresponds to 0.4 parts into falloff where the DPS loss from falloff is -15%. Now we will compare the guns damage output, we must remember that the lighter version does -23% damage as well. So in this range case the relative DPS from the heavier one is 0.90 and for the lighter it is (0.85 x 0x77) 0.655, we can divide them (0.9 / 0.655) to find out that the heavier ones do +37% more DPS over the lighter ones. Now the question is, at how many parts into tracking will these guns do the same damage? Since the lighter ones track better, the heavier ones will loose DPS faster and we are looking for the point where they do the same damage. It turns out that when the heavier type is at 0.9 parts into tracking, they loose -53% DPS, at the same time the lighter version is only 0.68 parts into tracking (0.9 / 1.32, +32% faster tracking), where it loose -36% DPS. Comparing the relative DPS we get that the lighter do 0.64 and the heavier 0.47, we divide them (0.64 / 0.47) and see that the lighter ones do +36% more DPS (from just tracking) at this point. This is close to the +37% advantage that the heavier had from before.  
 
'''Example:''' ''This is a comparison of when the lighter type overtakes the heavier type against a target with high angular velocity. For this example it is assumed that that the targets signature radius is identical to the guns signature size, the range is also assumed to be the same in both cases so that the angular velocity will be identical.'' A pilot is using the heavier autocannons (for example small 200mm, but this comparison is true for medium and large as well) and is fighting at 0.333 parts into falloff (corresponds to about 2200m with hard hitting ammo and T2 guns (for T1 it would be 2100m, so no real differance)), this corresponds to a -10% DPS loss from range, tracking isn't considered yet. If the pilot instead had been using the lighter autocannons (small 125mm) the range is the same (2200m for T2 guns) but this time it corresponds to 0.4 parts into falloff where the DPS loss from falloff is -15%. Now we will compare the guns damage output, we must remember that the lighter version does -23% damage as well. So in this range case the relative DPS from the heavier one is 0.90 and for the lighter it is (0.85 x 0x77) 0.655, we can divide them (0.9 / 0.655) to find out that the heavier ones do +37% more DPS over the lighter ones. Now the question is, at how many parts into tracking will these guns do the same damage? Since the lighter ones track better, the heavier ones will loose DPS faster and we are looking for the point where they do the same damage. It turns out that when the heavier type is at 0.9 parts into tracking, they loose -53% DPS, at the same time the lighter version is only 0.68 parts into tracking (0.9 / 1.32, +32% faster tracking), where it loose -36% DPS. Comparing the relative DPS we get that the lighter do 0.64 and the heavier 0.47, we divide them (0.64 / 0.47) and see that the lighter ones do +36% more DPS (from just tracking) at this point. This is close to the +37% advantage that the heavier had from before.  
  
−
'''Summary:''' Only when the heavier autocannons get near 1.0 parts of their tracking, will the lighter ones start performing better. At this point, the drop in DPS is already big (like half). It is therefor generally more useful to fit the heaviest type you can and then fly in a way that reduce the demand for tracking if need be, unless there is a tactical reason for using the lighter type.
+
'''Summary:''' Only when the heavier autocannons get near 1.0 parts of their tracking, will the lighter ones start performing better. At this point, the drop in DPS is already big (like half). It is therefor generally more useful to fit the heaviest type you can and then fly in a way that reduce the demand for tracking if need be. Lighter weapons are mostly only useful when a ship uses up its CPU and PG on other things.
−
 
 
−
=Answers to some questions=
 
−
 
 
−
==Do rails suck?==
 
−
There is no denying that they are worse than either beam lasers or artillery. But they are not far enough behind to say that they suck.
 
−
 
 
−
Beam lasers have the highest DPS (damage per second) and artillery cannons have the highest damage per hit (per volley). Both of these things are valuable, especially in PvP. High DPS is good because it makes tough ships die faster. A high damage per hit is also good because it can instantly kill a target (something that is important when the target has logistic support that repairs it). Railguns have slightly more DPS than artillery and the worst damage per hit. They also have a slightly longer range than beam lasers, but pay for that with a comparatively higher penalty to tracking.
 
−
 
 
−
It isn't enough to just look at the guns. One must also look at the ammo each type of turret use. Lasers use crystals, changing them is immediate and they never run out of ammo. Projectiles use various ammo types that deal different damage types, which makes it easier to match the damage with the target. The hybrid ammo on the other hand is stuck with the same two damage types (like lasers are) and have a reload time (like projectiles do), if one feel a little mean one could say that hybrid ammo combines the worst of the other two types.
 
−
 
 
−
Beam lasers and artillery cannons have drawbacks too of course. Generally speaking: The beam lasers uses a lot of capacitor energy and require immense amounts of power grid, they will mostly only work on Amarr ships. The artillery cannons also needs a lot of power grid and are designed to be used on ships with a bonus for projectile firing speed, otherwise it takes forever before they can shoot again. So for Gallente and Caldari ships, the railguns will still be the overall prefered pick.
 
−
 
 
−
A more detailed comparison can be found at http://www.eveonline.com/ingameboard.asp?a=topic&threadID=1332697
 
−
 
 
−
==Do small targets take less damage from big guns?==
 
−
Yes, but only if it has a transversal speed. Since big guns have large signature resolution values and low tracking values, it becomes harder to hit a small and fast target. The lowered hit chance is what reduces the damage, nothing else. The lowered hit chance results both in less DPS and lower maximum damage (not counting perfect hits, which always do three times the base damage). If the transversal speed is zero on the other hand, and the small ship inside optimal range, then it will be hit just as hard as a large ship would be. That is why the #1 survival tip for small ships is to keep up their transversal at all times.
 
−
 
 
−
==Can a turret hit a target with a larger angular velocity than its own tracking?==
 
−
Yes it can. But at an angular velocity identical to a turrets tracking value the turret already suffer 50% misses. Preferably you should never go above half your turrets tracking value, your sweet spot is at one third and below, assuming that you are shooting at a target with a size your guns were designed to hit (small guns for small targets, large guns for large targets).
 
−
 
 
−
==Are frigates with a smaller signature radius better than larger frigates in frigate pvp?==
 
−
They have an advantage from it when the angular velocities are getting high, which makes them harder to hit. But not all frigate pvp is fought by orbiting closely at high speeds, some try to keep a range of maybe 5km and at that range the signature radius is less important.
 
  
−
==Are target painters useful for turrets?==
 
−
Yes, but only if the turret have difficulties in tracking the target or if big guns are used against small targets. Although unusual, a T2 target painter can be better than a T2 Tracking Computer (with a tracking script) when it comes to solving tracking issues. Especially since a target painter also helps others and may be stacked by different people for an even higher gain. But it requires a bit of cap and must also be activated by the pilot.
 
  
−
==If I group my guns, does it affect the damage?==
 
−
No. Even if the guns are grouped on your screen, they are still treated separately. This can be seen by collecting damage data and comparing that with the normal expected damage distribution, its very clear that its a combination of several seperate turret shots. It can also be deduced by looking at the turret group's damage output when shooting at hard to hit objects, like deep into falloff, its quite easy to tell when one, two or more guns hit the target.
 
  
−
==+0.49? It says +0.5 on EVEonline wiki==
+
==Experiment to determine the damage interval around base damage==
−
Yes it does and the differance isn't exactly noticeable. But the test that was made to ensure the validity of this article showed a small deviance, and it should be noted in case anyone wants to reproduce the numbers. The test has too much data to present all of it here, so the method and results will be presented instead. Should you wish to check for yourself feel free to follow this procedure:
+
This test has too much data to show all of it here, so the method and the results will be presented instead. Should you wish to check for yourself feel free to follow this procedure:
  
 
A frigate (named 'Ouch') was 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 were 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 at least 1% in the damage values) -- this ensured that the data would be good enough to draw accurate conclusions. The damage was 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 their speeds set to zero to ensure that the chance to hit is 0.5^0 = 100% and nothing less.
 
A frigate (named 'Ouch') was 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 were 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 at least 1% in the damage values) -- this ensured that the data would be good enough to draw accurate conclusions. The damage was 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 their speeds set to zero to ensure that the chance to hit is 0.5^0 = 100% and nothing less.
Line 328: Line 348:
 
**Modified base damage x 3 = 68.5
 
**Modified base damage x 3 = 68.5
  
−
The collected data shows that the normal damage is distributed within 50%-149%. Since the first 1% unit is used for critical rolls (this is most likely, if the last % unit was used additional calculations will be needed if the to hit chance is less than 1%), this means that the constant has to be 0.49.
+
The collected data shows that the normal damage is distributed within 50%-149%. Since the first 1% unit is used for critical rolls (this is most likely, if the last % unit was used additional calculations will be needed if the to hit chance is less than 1%).
  
  
−
References:  
+
=References:=
  
 
http://wiki.eveonline.com/wiki/Turret_damage
 
http://wiki.eveonline.com/wiki/Turret_damage

Revision as of 18:52, 10 February 2012


Introduction

This article describes how damage from turrets (guns) are generated in EVE and what lessons that can be learned from that. The information here is focused on concepts and game mechanics, and touches only lightly on some modules in order to compare them. It is in no way a fitting guide.

All the data is based on facts, drawn from the mathematical equations working behind the scene every time someone pulls a trigger. Since not everyone is fond of math, the article will be divided into two sections. The first part is a summary of the results and describes all the concepts you will need to know. The second part is much more detailed and uses several calculations as examples.


Additional information about turrets can also be found on http://wiki.eveuniversity.org/Turrets and tips and tricks for using turrets more effectively is at http://wiki.eveuniversity.org/Gunnery_Guide

The First Part: Summary

To understand how turret damage is generated you will need to understand a number of concepts and how they interconnect. Some of them are visible under the attributes tab when you click for info on your guns. Especially falloff and tracking can be tricky to grasp, so be extra careful when reading those.

Hit chance

A turret always have a 0-100 percent chance to hit a target. The hit chance start at 100% but factors that reduce the hit chance can lower this. Those factors are basically the range to the target and the targets movement, with a few modifications. When the hit chance has been calculated, the EVE server will then "roll a dice" to see if the turret hits or misses the target.

DPS

DPS stands for Damage Per Second. This number is calculated from the average damage per hit you do (if your hit chance is 100%) divided by the turrets rate of fire (ROF). The fitting window in the game will show you your DPS from turrets, drones and missiles respectively.

Average Damage

The average damage is the one you do under ideal conditions (a 100% hit chance). But there is always a random element present in turret damage so your actual damage will jump around a bit. When the hit chance is 100% the damage spread will be between 50% and 150% of the average damage, this spread is unavoidable and built into the damage generation. There is an exception to this, so pay extra attention now, because this is a little tricky. When the hit chance is reduced, the highest possible damage also goes down even if all shots did hit. The interval around the average damage is always 50% to (50%+hit chance). So at 30% hit chance the damage interval is down to only 50% to 80% of average damage. This is in addition to the fact that only 30% of your hits will land. Thus there are two things that will reduce the damage you do whenever you loose hit chance. (This description has two tiny intentional errors in it that were used to explain the concept more easily: the first error is that the damage interval is actually spread around what is known as base damage and not average damage, the second error is that the percent interval only has 99 units, more details can be found in the second part below).

Perfect hits

In the 0-100 percent hit chance interval, there is a 1% chance of doing a perfect hit. It is that first percent unit in the entire interval. Think of it as rolling a 1D100 (a dice with a onehundred sides), if it lands on a 1, you get a perfect hit regardless of the hit chance. This actually means that if your hit chance is a measly two percent, half of your hits will be perfect. If your hit chance is less than one percent, you must first score a hit before it can become a perfect. A perfect hit will always do exactly 300% of the average damage (tiny intentional error, it is base damage).

Range

The distance to the target you are shooting at. Range is used to determine any penalties to hit chance based on the distance between the shooter and the target.

Angular velocity

This describes how fast something travels around something else. It is measured in the unit rad/second, where one rad is equal to a 57 degree angle. Your in game overview can show this value if you open its settings and tick a box under the tab called columns. Angular velocity is used to determine the penalty to the hit chance based on the turrets tracking capabilities. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting). A cool headed player can use special manouvers (like keep at range) or modules (turning webs on and off can really mess with orbiting ranges) to drastically reduce the angular velocity of a foe to open up for some heavy handed blows against a target that is otherwise hard to track.

Transversal speed

The angular velocity is calculated by dividing the Transversal speed with the Range to the target (don't mix meter and km if you calculate this, use just meter for both). Transversal speed is sideways speeds, not speeds towards or from the target (that is called radial speed). If you stand on a straight road and see a car coming, the car will have no sideways movement but a large radial movement towards you. If you stand next to the road and watch a car passing you by, the car will have a large sideway movement but almost no radial. High transversal speeds are important for speed tanking, never fly straight towards or away from a target, if you do the need for tracking drops to zero and you will be shot dead even by the biggest guns.

Optimal

Inside this range the gun will suffer no reduction in hit chance. If the target is sitting still inside the optimal range, every single attack will hit it.

Falloff

Falloff is an extra range that goes beyond your optimal range. This is however not a limit value, like the optimal range is. Instead its very fluid. It is best described as a gradual loss of hit chance, where the given number represents the distance at which you are down to a 50% hit chance. At two times your falloff value your hit chance is down to only 6.25%, even though it is unlikely you can still hit your target at that range, and even further out.

Tracking

Tracking is value that indicates how well you can hit targets that is orbiting you, higher tracking is needed for faster moving targets. This is not a limit value either, in fact it works exactly as falloff does. When the targets angular velocity is equal to the turrets tracking value you will have a 50% hit chance (note: size of the target will also affect this, see below). Just as for falloff, when a targets angular velocity is two times your tracking, the hit chance is down to 6.25%.

Turret Signature Resolution

This value kind of represents the accuracy of the turret. But only kind of, because it will only be important for tracking, it plays no part when it comes to the range. In EVE, every gun can hit the bullseye of any target in range regardless of its size as long as it is absolutely still. If the target beings to move on the other hand the size suddenly becomes important. All small guns have 40m as value, all medium guns have 125m as value and all large guns have 400m as value. The smaller the better.

Target Signature Radius

It doesn't matter what a ship looks like physically. They are all treated as if they were spheres when they are shot at. The target signature radius describes how big this sphere is, the bigger it is the easier it will be to track with guns. A big target also takes more damage from missiles, but that is outside the scope of this article.

Damage loss from Falloff and Tracking

Targets out in falloff, along with targets that must be tracked, are harder to hit. A lower hit chance means less damage done. The real question is, how much less damage? So lets look at that. First of all, one really nice thing with falloff and tracking is that they both behave exactly the same way, so the data table below applies to both of them.

The "Percent of Tracking or Falloff" values means the percent of your falloff or your tracking, depending on which you want to look at (one at the time). If your falloff is 12km then 33.3% means one third of that, so 4km. If your tracking is 0.06rad/sec then 33.3% means 0.02rad/sec.

Percent of Tracking or Falloff Hit chance Reduction in DPS by %
0 100% 0.0%
25% 95.8% -6.1%
33.3% 92.6% -10.6%
50% 84.1% -22.1%
84.8% 60.8% -50.0%
100% 50.0% -61.1%
150% 21.0% -85.2%
200% 6.25% -94.3%
300% 0.20% -99.4%


Few players would be able to spot a -10.6% loss in DPS. In fact, this is so small that the normal random distribution sort of drowns this out. Based on this. It is safe to say that you can use 1/3 of your falloff or tracking without any loss of noticeable performance. It is a sweet spot if you will and a good value to remember. Especially so if you often fight in falloff or against hard to track foes.

Target size

As mentioned above, target size only influence tracking penalties, never range penalties. It may seem counter intuitive, but that is the way the game works. The problem here from a player perspective is that the game will not provide you with the information. If you need to know, you must do the calculations yourself, or at least do rough estimates.

This is not as hard as it sounds, there is a rather neat way to quickly estimate what kind of tracking you really have against smaller or bigger targets. First you need to know the tracking value of your guns, the second thing is the Turret Signature Resolution value of your guns, and the third is to guess (yes, guess, but qualified guesses can be made) the Signature Size of your target. Guns always come in the resolution of 40m (small), 125m (medium) and 400m (large). In a similar fashion, you can use 40m for frigates, 125m for cruisers, 200-300m for battlecruisers and 400m for battleships. Shield tanked ships will always be a bit bigger while armor tanked ships have a normal size. Now you estimate the ratio between the target size and your gun size, multiply that ratio with your own tracking and now you know what you have in practice against that target.

Example: A battleship (400m resolution on guns) fires on a frigate (40m radius). Target size divided by gun size gives us 40m / 400m = 0.1, or 10%. When the battleship fires on the frigate it can thus only use 10% of its actual tracking value (which is already low), due to the size differance. This is why it is so freakin hard to hit small things with big guns (if they are moving).

Example 2: An Incursion Machariel with 3 Tracking Enhancer II's and T2 large autocannons have a tracking value of 0.067rad/sec. While shooting at a Sansha frigate (49m size), its real tracking value is only 49m / 400m = 0.1225 or 12% of the stated one, 0.067rad/sec x 0.1225 = 0.0082rad/sec. A typical Sansha frigate orbits at 14km at roughly 500m/s, that corresponds to an angular velocity of 500m/s / 14000m = 0.036rad/sec. Which is over 4 times higher than the Machariels tracking value and practically impossible to hit. No wonder why incursion fleets love webs (tracking links are nice too).

Grouping guns, does it affect the damage?

No. Even if the guns are grouped on your screen, they are still treated separately. This can be seen by collecting damage data and comparing that with the normal expected damage distribution, its very clear that its a combination of several seperate turret shots. It can also be deduced by looking at the turret group's damage output when shooting at hard to hit objects, like things deep into falloff, its quite easy to tell when one, two or more guns hit the target.


The Second Part: Mechanics and equations

Tools

E-UNI member Junker Jan created a spreadsheet primarily focused on determining your chance of hitting a target given a set of criterion. Made Public via Google Docs the document won't be editable when you click the above link, otherwise one accidental click could destroy all the carefully crafted formulae! You will need to either click File --> Download As to download the spreadsheet into your format of choice, or File --> Make a copy... to copy the document to your personal Google Docs store if you have a Google Account.

The values you should input should be in their final state, i.e. after all implants, modules, boosters, or fleet boosts you want included for the calculations are activated. All of the required information is available from the Show Info context-menu of the turret or ship in question, so for an in-game test simply undock and turn on everything you want to get your real-world actual values. For NPC ships you could use a resource like EVE Info to find out their signature radii or typical armor resistance values.


The To-Hit-Equation

TurretHitChance1.JPG

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

Let's start by taking a look at variables inside the equation. Most of these variables are actually determined before you even undock. From things like your choice of ship, your skill points and your fitting. There are only two that depend on you as a player (how you fly your ship), those are called 'Transversal Speed' and 'Range To Target'. This is the first important insight: How you fly will affect the damage you do.

  • Transversal speed = Movement up/down/left/right relative to an object, but not towards or away from it (that thing is called radial speed). Measured in m/s.
  • Range to target = The range to an object. Measured in meters.
  • Turret tracking = Found on the attributes tab of a turret. Measured in rad/second (one rad is equal to 57 degrees, 360 degress is equal to 6.28 rad)
  • Turret signature resolution = Higher values make it harder to hit small signature radii, it can be thought of as accuracy but it isn't entirely correct. Measured in meters.
  • Target signature radius = The size of the target, or more precisly the radius of an imagined circle that represents the target's sensor footprint. Measured in meters.
  • max(0, x) = a math function that takes the highest value of zero or x. It is used to prevent negative values in this case, any negative numbers a replaced with a zero instead.
  • Turret optimal range = Found on the attributes tab of a turret. Inside this range no range penalites from distance are applied. Measured in meters.
  • Falloff = Found on the attributes tab of a turret. Represents how rapidly a turret's accuracy declines as the target moves beyond optimal range. Measured in meters.

Now let's look a little closer at the equation itself, there is something to be learned from that.

To paraphrase Oli Geist, this equation can be abstracted to: 

Chance to hit = 0.5 ^ (tracking term + range term).

Those who have studied math may recognize that something of the form x^(a+b) is identical to (x^a)*(x^b), so we can rewrite the above as : 

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

Why is this interesting? From this we can see that tracking and range are actually calculated seperately, then the results from each are multiplied. This shows that Range and Tracking are indeed two different and independant things, and both will be used to score a hit.

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

The tracking part: All guns have their tracking value expressed in something called 'angular velocity', this is identical to 'Transversal speed' divided by 'Range to Target', this is all inside the tracking term if you look at it, and basically it just means how fast something moves around something else. Lets freeze the angular velocity, this means that it is still moving but that the speed will not change. In the tracking term we also have 'Turret signature resolution' divided by 'Target signature radius', for easy comparison later on we will assume that both these number are the same (so their ratio is one, which means no effect), then we freeze them as well. What we are left over with is this: a fixed number divided by 'Turret tracking'.

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

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


Base damage

All turrets have a base damage, this is a fixed number. The volley damage that your turrets do will be spread around this number. The higher the number the more damage the turret will do when it hits. It is calculated from the turrets Damage Multiplier attribute and the ammo's damage values. This is before any resistances is taken into consideration. A high base damage means that your guns hit hard (but do not mistake this for DPS (damage per second) since that also depends on how often the guns may fire). The base damage is always a bit below the average damage (about 1.5% lower) when there is a 100% hit chance -- the reason for this are those rare but highly damaging perfect hits.

Example: A small turret has a damage multiplier of x1.725, and is loaded with an ammo type that does 7 EM and 5 Thermal damage. The base damage is then 1.725*(7+5) = 20.7


The random damage distribution

At the heart of a turret's 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 then to determine how much damage the hit actually did. Should the randomly generated number be less than 0.01 (1% chance), it will be a perfect hit (aka 'wrecking'). A wrecking hit always deals exactly three times the base damage, exactly, there is no random element in damage from perfect hits. 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, but by 1% of all hits and misses taken together. This means that if your chance to hit is 1% or less, you will either hit perfectly or you will miss, there are no normal hits.

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 turret's base damage. Since the first 0.01% of the random value is used for perfect hits, normal hits have a damage spread between 0.50 to 1.49, or 50% to 149% 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 target's damage resistances in order to obtain the final damage number.

The quality of a non perfect hit will be described by the value of the random number + 0.49, ranging from barely scratching (least damage) to excellent (highest damage).

Hit description Random damage modifier
Perfectly 0.490 to 0.500 (special case, 3x the base damage instead)
Barely scratches 0.500 to 0.625
Hits lightly 0.625 to 0.750
Hits 0.750 to 1.000
Well aimed 1.000 to 1.250
Excellent 1.250 to 1.490

A turret with a 100% hit chance will see a natural and unavoidable damage spread between 50% to 149% of its base damage for normal hits, and will 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, so with a 75% hit chance there can be no excellent hits because they are now turned into misses.

Example: A small gatling laser 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 -- this is less than the chance to hit so the shot lands on the target. 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. This damage will become lower when resistances have been accounted for. In the combat log the hit will be described as 'well aimed'.


Damage and DPS reduction due to a lower hit chance

When a turret has less than 100% chance to hit the damage is 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.

Since it was established earlier that Tracking and Falloff behave exactly the same way. We can use the same data table and the same graphs to describe both, but only one at the time.

The table below shows how damage and DPS goes down as a result of lower hit chance. The decrease is identical for tracking and falloff so either one can be used. If you wish to combine the effects of tracking and falloff, look them up individualy and then multiply them (note: this only works for the columns Hit Chance and Relative DPS; the column Reduction in DPS by % can not be used for this).

The true strength with the table and graphs below are not to calculate what your DPS might be in a given situation. But rather to see how much you can push your falloff and tracking while still maintaining a decent DPS output.

Notes: Parts into means the value you multiply either your falloff or your tracking with. 0.25 means 25% or a quarter of that value. Likewise, the hit chance is expressed the same way. The relative DPS is a multiple to the base damage of the turret, it starts above 1 because of the perfect hits, since they do extra high damage.

File:HitChanceVsFalloff.JPG
Click to enlarge
File:HitChanceVsRelativeDPS.JPG
Click to enlarge
Parts into Tracking or Falloff Hit chance Relative DPS Reduction in DPS by %
0 1.0000 1.0151 0.0%
0.1 0.9931 1.0048 -1.0%
0.2 0.9727 0.9747 -4.0%
0.25 0.9576 0.9528 -6.1%
0.3 0.9395 0.9268 -8.7%
0.333 0.9260 0.9076 -10.6%
0.4 0.8950 0.8641 -14.9%
0.5 0.8409 0.7906 -22.1%
0.6 0.7792 0.7104 -30.0%
0.7 0.7120 0.6274 -38.2%
0.8 0.6417 0.5454 -46.3%
0.848 0.6075 0.5072 -50.0%
0.9 0.5704 0.4672 -54.0%
1.0 0.5000 0.3951 -61.1%
1.1 0.4323 0.3303 -67.5%
1.2 0.3686 0.2736 -73.0%
1.3 0.3099 0.2249 -77.8%
1.4 0.2570 0.1840 -81.9%
1.5 0.2102 0.1502 -85.2%
1.6 0.1696 0.1225 -87.9%
1.7 0.1349 0.1003 -90.1%
1.8 0.1058 0.0825 -91.9%
1.9 0.0819 0.0685 -93.2%
2.0 0.0625 0.0576 -94.3%
2.1 0.0470 0.0492 -95.2%
2.2 0.0349 0.0428 -95.8%
2.3 0.0256 0.0379 -96.3%
2.4 0.0185 0.0343 -96.6%
2.5 0.0131 0.0316 -96.9%
2.6 0.0092 0.0277 -97.3%
2.7 0.0064 0.0192 -98.1%
2.8 0.0044 0.0131 -98.7%
2.9 0.0029 0.0088 -99.1%
3.0 0.0020 0.0059 -99.4%


The formulas used to calculate this table were:

  • Chance to Hit: 0.5^(0+(Falloff parts / 1)^2)
  • 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%


Tracking upgrades vs Damage upgrades

Weapon upgrade modules can improve raw damage, tracking and range. Making use of an increased range is fairly obvious. However, comparing tracking and damage can be harder to do. The tricky thing with this comparison is that the need for tracking in a fight often varies depending on how the pilots fly their ships. So to make any sense of the following you must have some rough ideas of what the angular velocities will be. The only way to get that is through experience.

Here are some guidelines for comparisons: (note that only the bonus of the 1st module is considered for all tracking modules, additional ones will suffer from a stacking penalty).

Damage Upgrade module, T2 (such as Gyrostabilizer, Heat Sink etc):

  • The 1st T2 Damage Upgrade module increase damage with +23.5%
  • The 2nd T2 Damage Upgrade module increase damage with +20%
  • The 3rd T2 Damage Upgrade module increase damage with +13%
  • The 4th T2 Damage Upgrade module increase damage with +6.5%

Tracking Enchancer, T2:

  • When Angular velocity = 25% of your Tracking: +9.5% more tracking is the same as +1.1% damage
  • When Angular velocity = 50% of your Tracking: +9.5% more tracking is the same as +4.2% damage
  • When Angular velocity = 75% of your Tracking: +9.5% more tracking is the same as +9.5% damage
  • When Angular velocity = 100% of your Tracking: +9.5% more tracking is the same as +16.6% damage

Tracking Rig, T1:

  • When Angular velocity = 25% of your Tracking: +15% more tracking is the same as +1.5% damage
  • When Angular velocity = 50% of your Tracking: +15% more tracking is the same as +6.3% damage
  • When Angular velocity = 75% of your Tracking: +15% more tracking is the same as +14.3% damage
  • When Angular velocity = 100% of your Tracking: +15% more tracking is the same as +25.4% damage

Tracking Computer, T2 with tracking script:

  • When Angular velocity = 25% of your Tracking: +30% more tracking is the same as +2.7% damage
  • When Angular velocity = 50% of your Tracking: +30% more tracking is the same as +10.8% damage
  • When Angular velocity = 75% of your Tracking: +30% more tracking is the same as +25.2% damage
  • When Angular velocity = 100% of your Tracking: +30% more tracking is the same as +46.7% damage

Target Painter, T2 with Signature Focusing at level IV (increasing sig radius have the exact same result on damage as an increase in tracking has)

  • When Angular velocity = 25% of your Tracking: +36% higher sig radius is the same as +3.0% damage
  • When Angular velocity = 50% of your Tracking: +36% higher sig radius is the same as +12.3% damage
  • When Angular velocity = 75% of your Tracking: +36% higher sig radius is the same as +28.8% damage
  • When Angular velocity = 100% of your Tracking: +36% higher sig radius is the same as +54.1% damage

Webs:

The effect from a web is hard to predict, since its use can change both the transversal speed and the range between the ships. Experience and practice will be your best guide here. The drawback with webs is that they can help your opponants tracking as well as your own. The web is more often used for its tactical benefits, such as giving control over the range. But it is also the best tool to reduce the need for tracking when large guns are used against small targets.


Choosing turrets

Is it better with high damage or high tracking turrets? It is almost always better to go for the higest possible damage, which also gives a higer range. This is true for long range (like artillery) and short range (like autocannons) guns alike. The reason for this is because the gain in tracking isn't enough to compete with the lost damage.


The only turret type where higher tracking can possibly outweigh the extra damage and range is for autocannons, the other types simply doesn't gain enough tracking to be worth even looking into. The lighter autocannon type has +32% tracking, -23% damage and -17% falloff compard to the heavier type (for small, mediums and large alike). The following example will compare heavy vs light, there will be lots of numbers, but there is a summary at the end of it of it all if you want to skip ahead.

Example: This is a comparison of when the lighter type overtakes the heavier type against a target with high angular velocity. For this example it is assumed that that the targets signature radius is identical to the guns signature size, the range is also assumed to be the same in both cases so that the angular velocity will be identical. A pilot is using the heavier autocannons (for example small 200mm, but this comparison is true for medium and large as well) and is fighting at 0.333 parts into falloff (corresponds to about 2200m with hard hitting ammo and T2 guns (for T1 it would be 2100m, so no real differance)), this corresponds to a -10% DPS loss from range, tracking isn't considered yet. If the pilot instead had been using the lighter autocannons (small 125mm) the range is the same (2200m for T2 guns) but this time it corresponds to 0.4 parts into falloff where the DPS loss from falloff is -15%. Now we will compare the guns damage output, we must remember that the lighter version does -23% damage as well. So in this range case the relative DPS from the heavier one is 0.90 and for the lighter it is (0.85 x 0x77) 0.655, we can divide them (0.9 / 0.655) to find out that the heavier ones do +37% more DPS over the lighter ones. Now the question is, at how many parts into tracking will these guns do the same damage? Since the lighter ones track better, the heavier ones will loose DPS faster and we are looking for the point where they do the same damage. It turns out that when the heavier type is at 0.9 parts into tracking, they loose -53% DPS, at the same time the lighter version is only 0.68 parts into tracking (0.9 / 1.32, +32% faster tracking), where it loose -36% DPS. Comparing the relative DPS we get that the lighter do 0.64 and the heavier 0.47, we divide them (0.64 / 0.47) and see that the lighter ones do +36% more DPS (from just tracking) at this point. This is close to the +37% advantage that the heavier had from before.

Summary: Only when the heavier autocannons get near 1.0 parts of their tracking, will the lighter ones start performing better. At this point, the drop in DPS is already big (like half). It is therefor generally more useful to fit the heaviest type you can and then fly in a way that reduce the demand for tracking if need be. Lighter weapons are mostly only useful when a ship uses up its CPU and PG on other things.


Experiment to determine the damage interval around base damage

This test has too much data to show all of it here, so the method and the results will be presented instead. Should you wish to check for yourself feel free to follow this procedure:

A frigate (named 'Ouch') was 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 were 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 at least 1% in the damage values) -- this ensured that the data would be good enough to draw accurate conclusions. The damage was 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 their speeds set to zero to ensure that the chance to hit is 0.5^0 = 100% and nothing less.

After 10,656 shots at 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 folder (in Windows), and was easily copied into a prepared Excel sheet for analysis.

  • Base damage
    • The ammo type dealt: 7 EM and 5 Thermal
    • The base damage on the lasers were: 24.9063
    • 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 occurences 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 of course impossible -- the error comes from rounding errors in the 4th decimal of the base damage, awesome precision isn't needed for this comparative calculation since the natural random deviation is much larger anyhow, so this is good enough, the objective was to explain the lower frequencies of the end points which now has been done).

  • Lowest damage random multiple
    • Modified base damage x 0.51 = 11.6
    • Modified base damage x 0.50 = 11.4
    • Modified base damage x 0.49 = 11.2
    • The lowest observed damage is 11.4, thus 50%
  • Highest non-perfect random multiple
    • Modified base damage x 1.50 = 34.2
    • Modified base damage x 1.49 = 34.0
    • Modified base damage x 1.48 = 33.8
    • The highest non-perfect damage is 34.0, thus 149%
  • Perfect hits deal 68.5 damage
    • Modified base damage x 3 = 68.5

The collected data shows that the normal damage is distributed within 50%-149%. Since the first 1% unit is used for critical rolls (this is most likely, if the last % unit was used additional calculations will be needed if the to hit chance is less than 1%).


References:

http://wiki.eveonline.com/wiki/Turret_damage

http://forum.eveuniversity.org/viewtopic.php?p=201888#201888

http://forum.eveuniversity.org/viewtopic.php?p=216525#p216525

http://www.hostile.dk/files/eve/eve-tracking101.swf

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