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 the same.

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, as it only considers the relative movement between the attacker and the target, and does not take into account any rotation of the attacking ship. From the attacker's point of view, this relative movement appears as a change in the angle to the target.

Turret tracking can be viewed using "Show Info". It is modified by skills, ammunition, modules, hull bonuses, and incoming tracking disruptors and tracking links.

Though tracking can be conceptualized as the ability of a turret to turn and "track" its target, this is not how tracking is calculated. Instead, tracking it behaves similarly to falloff in that it represents a percentage chance to hit, meaning that a turret can miss targets that move slower than its turn speed and hit targets that move faster.

Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat. Most prominently, a target's angular velocity is given in the overview as radians per second (rad/s), which cannot be directly compared to a turret's tracking value.

To convert turret tracking speed to rad/s the following formula can be used:

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

Much of this information is most useful when theorycrafting, as there is often little time or need for complex mathematics during combat. However, pilots who are familiar with these concepts can still use them in a general sense to make decisions when in space.

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

Instead of measuring an object's speed as m/s or miles/hour, a speed can also be measured as an angle. A good example is the suns movement across the sky, where it moves 360° in 24 hours, which makes the angular velocity 15°/hour. If the sun is moving away or towards us wouldn't matter, because that wouldn't change the angle, only sideways movement counts.

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 roughly 57° (360/2π).

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. Two ships will always have the 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 with every non perfect hit. But when the hit chance is reduced, the upper random damage interval will also be reduced. The average damage is thus reduced in two ways, firstly by having some shots miss completely and deal no damage at all, and secondly by having the maximum random damage go down. The average damage will therefore 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, the angular velocity can be minimized (can reach zero) by using Approach. If your ship is slower or less agile, and the opponent is orbiting you, angular velocity can be minimized by using Keep at Range (if set to far away, but be warned: if you reach this range your ship will stop). Alternatively, if your ship has very poor agility, it is better to fly in a straight line to maximize your own speed and let the orbiting ship chase after you. Maximizing the angular velocity is harder but will happen if both ships orbit one another, or if one is using Approach but isn't agile enough to get behind the other. A ships agility is the multiplication of its inertia modifier and mass, a lower value means it can do sharper turns.

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, there is no angular velocity, and the hit chance from the tracking term will be 0.5⁰ = 100%. A battleship can easily hit a frigate for full damage if there is no need to track it.

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 are in combat.

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, because the differance in tracking is too small to make much of a differance.

For short range kiting frigates (around 6-8km) a high tracking can be so critical that the smallest long range guns will have the best performance.

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/