Turret damage

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This article describes how damage from turrets is calculated. For general information on turret weapons, see Gunnery. For information on missile weapons, see Missiles and Missile damage.


The information here is focused on concepts and game mechanics. The practical use of this lies mostly in the understanding of how falloff and tracking works, and how far you can push them without losing any noticeable performance.

An overview of turrets can be found on Turrets.

Contents

Hit chance

A turret always has a 0–100 percent chance to hit a target. The hit chance is affected by turret tracking, optimal and falloff ranges, target angular velocity, target distance and target signature radius.

Falloff and optimal range

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

Falloff is an extra range that goes beyond your optimal range. This is, however, not a limit value, like the optimal range is. It is best described as a gradual loss of hit chance. Distance of falloff + optimal represents the distance at which you are down to a 50% hit chance. At optimal plus two times your falloff value your hit chance is down to 6.25%, even though it is unlikely you can still hit your target at that range, and at three times your falloff range the chance to hit is only 0.2%.

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

Turret tracking

Tracking is a value that indicates how well you can hit targets that are passing you by, higher tracking is needed for faster moving targets. This is not a limit value either, in fact it works exactly as falloff does but without any optimal range. When the target's angular velocity is equal to the turret's tracking value divided by 40000 you will have a 50% hit chance (note: size of the target will also affect this, see below). Just as for falloff, when a target's angular velocity is two times your tracking, the hit chance is down to 6.25%.

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

Note that the turret tracking was recently changed. Any info that mentions turret signature resolution is outdated.

Angular velocity

This can be a tricky concept. It describes how fast something passes by something else. It is measured in in radians per second (rad/s), where one radian is equal to about a 57° angle (more accurately, 360° = 2π radians). Your ingame 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 turret's 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 maneuvers (like keep at range) or modules 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.

Angular velovity is calculated as ω=vt/d, where vt 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

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. Target signature radius only affects tracking and has no effect when shooting a stationary target.

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

Hit chance formula

The chance to hit formula calculates the chance to hit a target based on the parameters listed above. The hit chance is always a number between 0 and 1, or 0% and 100% if you will. The computer then generates a random number to see if a hit is scored or not. The hit chance of a turret is given by formula

\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)}}

where Vangular is angular velocity of target, WAS is weapon tracking speed, sigtarget is target signature radius, distance is distance to target, optturret is optimal range of turret and fallturret is falloff of turret.

When a turret shots a target a random number between 0 and 1 is generated. If the random number is greater than the hit chance the shot misses. One thing that needs to be emphasized is that your own piloting can change your hit chance, by actively trying to control the range and the movements relative to your opponents.

This equation can be abstracted to

  • \pagecolor{Black}\color{White}\text{Chance to Hit} = 0.5^{\text{tracking term} + \text{range term}}

Math students may recognize that something of the form x(a+b) is identical to xaxb, so we can rewrite the above as

  • \pagecolor{Black}\color{White}\text{Chance to Hit} = 0.5^{\text{tracking term}} \cdot 0.5^{\text{range term}}

From this we can see that tracking and range are actually calculated separately, then the results from each are multiplied. This shows that Range and Tracking are indeed two different and independent 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 trickier 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 turrets measure tracking speed as a Turret tracking, which describes how well a turret can cope with targets moving around the turret in circles (or how well the turret can cope with its own ship moving around the target in circles; as far as the equation is concerned, these are the same situation). Let's freeze the angular velocity, meaning the ships are orbiting each other at a constant speed. In the tracking term we also have a 40000 meters term (a true constant) and target signature radius (which is usually constant except when any effects that affect signature radius are applied or removed). The result: 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 to see any changes in the to-hit equation's output values. Lets freeze everything apart from falloff. The result: a fixed number divided by falloff.

Did you see what they have 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 behave identically. Also, they are not fixed limits, they become ratios that describes how quickly you lose hit chance as you start to push range and orbiting speeds. Also, the hit chance loss is gradual.

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 turret's Damage Multiplier attribute, the ammo's damage values and skills. This is before any resistances are taken into consideration. A high base damage means that your guns hit hard (but do not mistake this for DPS (damage per second). The base damage is always a bit below the average damage (about 1.5% lower) when there is a 100% hit chance because of the rare-but-powerful perfect hits.

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

Randomness of damage

The damage from turrets always has a random factor in it, this is built into the game and can't be avoided. Under ideal conditions, when your hit chance is 100%, the damage done by your turrets will be inside an interval of 50% to 149% of your base damage with 1% chance of perfect 300% damage hit. However, things are different when your hit chance decreases. Not only will you have a chance to miss your target, which means no damage done. But also, the damage interval will change as well. That interval is actually from 50% but only up to (49% + hit chance). So if your hit chance is 70%, not only will you miss a few shots, the shots that do hit are now in the damage interval of 50% to 119% with 1% chance of 300% damage. There are thus two simultaneous factors that reduce your damage when your chance to hit goes down.

Perfect hits

With any shot 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 hundred-sided die; 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 get that hit, before it can become a perfect one. A perfect hit will always do exactly 300% of your base damage. Note that the 1% propability is for all shots including misses.

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, with no normal hits.

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. 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. If the random number is less than 0.01 (1% chance) the hit is perfect hit and deals 300% damage. If the hit chance is less than 1% this perfect hit can also miss and any non perfect hit will miss.

In non perfect hits the damage modifier of the shot is calculated with formula

Damage modifier = Random number[0,1] + 0.49

The base damage is multiplied by this modifier to get the final damage. The result is that the turret can deal 50% - 149% of its damage in single non perfect hit. Also note that since the same random number is used for hit and damage calculations the possible damage range gets lower as hit chance lowers. At 70% hit chance the turret can deal 50% - 119% damage with non perfect hit.

The quality of the hit is also visible on combat log.

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

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 ×2.1 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 × 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."

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, 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 possible to tell when one, two or more guns hit the target.

Combined effects of hit chance and damage distribution

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 "Percent of Tracking or Falloff" values means how much of the listed falloff or tracking you are looking at. If your falloff is 12 km then 33.3% means one third of that, so 4 km. If your tracking is 0.4 rad/s then 50% would mean 0.2 rad/s.

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 individually 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.

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 Hit Chance' > 0.01 then (Hit Chance − 0.01) × (0.50 + (Hit Chance + 0.49))/2 + 0.01 × 3, else Hit Chance × 3
  • Reduction in DPS: (Relative DPS at Current/Relative DPS at 100% hit) × 100% − 100%

The best performance is up to 1/4 (quarter) of your falloff or tracking, the DPS loss is almost unnoticeable. At 1/2 (half) the DPS reduction is starting to be noticeable but it is still not too bad. Exactly at your falloff or tracking your DPS will be less than half, which is bad. As a rule of thumb, avoid using more than half of your falloff or tracking when you are trying to deal high damage.

Tracking upgrades vs Damage upgrades vs Target painter Vs Stasis webifier

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

Note that a target painter helps everyone who shoots at the targetwhile damage/tracking upgrades help only one ship.

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 opponents 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. Stasis webifier alsoo has limited range compared to other modules.

Choosing turrets

Is it better with high damage or high tracking turrets? It is almost always better to go for the highest possible damage, which also gives a higher 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 don't gain enough tracking to be worth even looking into. The lighter autocannon type has +32% tracking, −23% damage and −17% falloff compared 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 the range is same in both cases so that the angular velocity will be identical. A pilot is using the heavier autocannons (for example small 200 mm, but this comparison is true for medium and large as well) and is fighting at 0.333 parts into falloff (corresponds to about 2200 m with hard hitting ammo and T2 guns (for T1 it would be 2100 m, so no real difference)), 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 125 mm) the range is the same (2200 m 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 × 0.77 =) 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 lose 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 lose 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 loses 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 therefore 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.

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

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