Turret damage

This article describes how damage from turrets is calculated. For general information on turret weapons, see Turrets. For information on how turrets function mechanically, see Turret mechanics.

Hit chance

A turret's chance to hit a target is calculated using the equation below. It will produce a result between 0 and 1, representing a probability between 0% and 100%. This value is then compared to a random number to see if the turret hits or misses.

[math]\pagecolor{Black}\color{White}\text{Chance to Hit} = {0.5^{\left({\left({\frac{V_{angular} \times 40000m}{WAS \times sig_{target}}}\right)^{2} + \left({\frac{max(0, Distance - opt_{turret})}{fall_{turret}}}\right)^{2}}\right)}}[/math]

V_angular is angular velocity (movement between the attacker and the target expressed as an angle (in radians) per second)

WAS is the turrets tracking value (listed on the info window, previously called Weapon Accuracy Score) and means how well the turret can hit a moving target

sig_target is target signature radius (aka target size, a big target is easier to track)

Distance is the range in meters

opt_turret is optimal range of turret

fall_turret is falloff range of turret

Click to enlarge

The hit chance equation has the form of x^(a+b), which can also be written as x^ax^b. In this case, x = 0.5, a = all tracking terms and b = all range terms. In other words, the hit chance equation can be thought of as having two separate parts (tracking and range), which are calculated individually and then multiplied at the end to get the final hit chance. This means that tracking and range don't interfere with one another, they are indeed two seperate things.

The equation also shows that the reduction of hit chance from falloff and tracking respectively follow the same pattern. This is because they both look like 0.5^{(something / x)2}, where x is either tracking or falloff. The only differance between them are the input variables, the output look identical.

Example: At a range equal to optimal+falloff the range part of the equation becomes 0.5¹, which means a 50% chance to hit. Against a target with the same angular velocity (rad/s) as a turrets tracking value multiplied with the targets size and divided by 40000m, the tracking part of the equation becomes 0.5¹, which is also a 50% chance to hit. In the first case the full falloff range was used, in the second case the full turret tracking was used, and since they both follow the same pattern they end up at the same hit chance.

Falloff and optimal range

A target inside the optimal range of a turret will be hit 100% of the time, assuming no tracking is required.

Falloff is an additional range that goes beyond the optimal. Falloff is different than optimal in the sense that it reflects a gradual loss of hit chance. When a target is at optimal+falloff the hit chance is down to 50%. At optimal+(2 x falloff) the hit chance is down to 6.25%, but it's important to note that hits are still possible.

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

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

Turret tracking

Tracking is a value that represents how well a turret can follow a moving target. The equation is not fully realistic, it doesn't consider if the attacking ship is spinning around itself, it only considers the relative movement between the attacker and the target. This relative movement will from the attackers point of view appear as a change in the angle to the target. Don't make the mistake of thinking that a turret has a fixed turn speed, that's not how the equation works. Instead it behaves just like falloff, meaning that the turret can miss targets that move slower than its turn speed and hit targets that move faster.

With the updates to tracking it became much easier to compare the tracking ability between different turrets, but it also made the numbers more abstract and harder to use in combat. In the overview a targets angular velocity is given in rad/s, to know a turrets tracking speed in rad/s the following equation must be used:

turret tracking in rad/s = Turret tracking * Target Signature Resolution / 40000m

There is of course no time or need to use math in combat. But it can still be helpful when one is trying to figure out what a bonus or a penalty to tracking will actually do. As stated earlier, since falloff and tracking follow the same pattern, a +10% bonus to tracking will have the same impact on hitting a moving target, as would a +10% bonus to falloff have on hitting a target out in falloff range.

Turret tracking is visible in turret info window. It is modified by skill, ammo, modules, hull bonuses and incoming tracking disruptors.

A long, long time ago...
The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single mumber simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace 40000 with "Turret Signature Resolution"

Angular velocity

This can be a tricky concept. Instead of measuring the speed as m/s or miles/hour, a speed can also be measured as the percieved change in the angle to an object from a certain location. A good example is the suns movement across the sky, where it moves 360° in 24 hours. If the sun is moving away or towards us is irrelevant, that wouldn't change the angle, only sideways movement will.

Just as a circle can be described as an angle of 360°, it can also be described as an angle of 2π radians. Meaning that one radian equals to (360/2π) roughly 57°.

The ingame overview can show the angular velocity of a target if you open the 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 turret's tracking ability. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting, which is to keep something at range).

Angular velocity is calculated as ω=v_t/d, where v_t is tranversal velocity of the target relative to shooter and d is distance to target. The shooter and target will both have same angular velocity to each other.

Target Signature Radius

Every ship has a size that is treated as a sphere when they are being shot at. The target signature radius describes how big this sphere is. The signature radius is only used in the tracking part of the hit chance equation. So it only matters for tracking, it has no impact on the loss of hit chance due to long ranges.

Target signature radius is visible in ship fitting window. It is modified by modules, hull bonuses and incoming target painters.

Damage

The damage that a turret deal will be randomly spread around a fixed value called base damage. The base damage is calculated from the turret's Damage Multiplier attribute, the ammo's damage values, hull modifiers and skills.

Random damage interval

At the heart of each turret's damage output is a single randomly generated value between 0 and 1 that is several digits long. This random number is used to determine both if the turret hits and how much damage it does. Unfortunately, the misses are those random numbers that would have caused the most damage. If the random number is less than 0.01 (1% chance) a special case occurs, a perfect hit, these will always deal exactly 300% of the base damage. A funny result of this is that when the hit chance is 1% or less, only misses and perfect hits can occur.

The damage modifier for a normal hit is calculated with the following formula

Random Damage modifier = Random number[0.01,1] + 0.49

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

Hit description	Random damage modifier
Barely scratches	0.500–0.625
Hits lightly	0.625–0.750
Hits	0.750–1.000
Well aimed	1.000–1.250
Excellent	1.250–1.490
Perfectly	3.000

Average damage

A turret with a hit chance of 100% will strike for 50% - 149% of its base damage in every non perfect hit. But since the same random number is used to determine both hit or miss as well as the damage modifier, this means that the upper damage interval will begin to shrink when the hit chance is decreased. The average damage is thus reduced in two ways, firstly by having some shots miss and deal no damage at all, and secondly by having the upper damage interval decrease. The average damage will always be reduced more than the hit chance is.

Example: When the hit chance of a turret is 70% the damage interval has shrunk to 50% - 119% for all non perfect hits. When combined, these two things results in an average damage of just 61.3% (69%*(50%+119%)/2+1%*3) of the base damage.

Will grouping guns change 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 expected damage distribution, it's very clear that it's a combination of several separate turret shots instead of a single one. 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, it's then possible to tell when one, two or more guns hit the target.

Fighting with and against turret ships

Two ships always have the same range and angular velocity towards eachother. The pilot who can control these two values, can control how much damage turrets will be able to do.

If your ship is faster and more agile, and the opponent is orbiting you, you can drop the angular velocity towards zero by using Approach. If your ship is slower, and the opponent is orbiting you, you can make the angular velocity oscillate up and down by flying in a straight line as fast as you can. If you use Keep at Range with the same distance as your opponents orbit distance, your speed will drop down to zero (which can be suicidal if there are more enemies around). It's hard to maximize the angular velocity, but it will happen as long as both ships try to orbit eachother at a short distance.

A ships mass and inertia values determine how quickly it can turn. If a ship turns slowly, it will loose more speed and angular velocity when orbiting something. Turning fast is mostly important for small ships that are fighting larger ones, so they can fly "under the guns" of their target and also be harder to hit by others. When two ships of similar sizes are fighting, raw speed seems more important than agility, because the one with the most speed has the most control.

A tackler (typically a frigate whose job is to prevent an enemy from warping away) needs to keep his or hers angular velocity in mind to survive. If they approach a distant target straight on, they are easy to track and even the biggest guns with the worst tracking will hit for full damage. To be safe, a tackler need to approach at an angle, to keep the angular velocity up.

The Disruption EWAR module will reduce a turrets tracking and/or range. Since ships are often fitted around an idea, like fighting at a certain range, a disruptor can really mess with that. Always bring both range and tracking disruption scripts, you won't know which one you'll need until you start fighting.

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

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

Choosing turrets

Each group of weapon have several choices. For blasters (short range hybrid weapon) there are three different kinds: Electron, Ion and Neutron (from weakest to strongest). The electron have the best tracking, the neutron have the best damage and range. Which one is best? It turns out that the higher damage choice is pretty much always better. This is because the higher tracking weapon can only start to compete when the average damage output has already dropped significantly.

References

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

https://www.reddit.com/r/Eve/comments/5h24bk/turrets_listed_signature_resolution_is_40km/