Turret damage

This page underwent a major update the 13th august 2011.

Introduction

This article looks at the To-Hit-Equation. But rather than explaining the math behind it, it will focus on the practical results. A lot of attention will be given to Falloff and Tracking, since they are two major components of this equation. Occasionally there will be examples involvning number crunching, these examples are there to clarify certain things, but there is no real need to understand them.

Governing Equation

This is the To-Hit-Equation. Yes, it can look daunting, but you will never have to actually use it. What makes it so interesting is that it determines how turrets will perform in battle. So by understanding how it works, it will be a little easier to hit things.

We will begin by looking at the basics, 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, by things like what ship you choose and how you have fitted it. There are only two variables that are based on how you actually fly your ship, those two are Transversal speed and Range To Target.

• 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.
• 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.
• Turret signature resolution = Higher values make it harder to hit small signature radii. 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) = Takes the highest value of zero or x. Used to set all negative values to zero in this case.
• 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 completely seperately before the results from each are multiplied. This means that Range and Tracking are two separate terms and can not replace eachother. So a lack of range can never be compensated for by an increase in tracking. You may have guessed this already.

There is one more thing we can find out by just looking at the equation. This is a little tricker to grasp. The aim here is to compare the tracking term and the range term for similarities in their behaviour. To do this, we will freeze all values in those terms except for one variable in each, then we can look at how that single variable effects the outcome and if there is any similarities between the two cases.

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 frozen number divided by Turret tracking.

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 frozen number divided by Falloff.

Did you see the smiliarity here? In the tracking term, we now have something / Turret tracking, in the range term we have something / Falloff. Since both of them are calculated by 0.5 ^ (term), this means that tracking values and falloff ranges will behave in exactly the same way. The words and their meanings in each case are a little different, but the behaviour is identical. So if you understand how one of them works, you have already understood how the other one works. That is pretty nice, isn't it?

General

What does an expression like 0.5^(tracking term) mean? This article is not about the math itself, so this will not be explained here. Anyone who wish to know more can read about Exponents or Exponantiation in wikipedia and many other places.

Tools & Links

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.

Turret damage output

Base damage

All turrets have a base damage, this is a fixed 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

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 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. 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 below, you can actually only hit perfectly or miss. Almost all shots will miss of course, but those that do hit they will be perfect.

The raw damage dealt by a turret is calculated by taking the randomly generated number that resulted in a hit, adding 0.49, and multiplying this sum with the 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 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.

By looking carefully at the damage generation above, it becomes clear that the Hit Chance not only means that a turret can miss, it also places a cap on the maximum damage a non-perfect hit can do. Suppose that a gun has 55% chance to hit, not only will almost half of the shots miss but those that do hit will do between (0.49+0.01) 50% and (0.49+0.55) 104% of the base damage. So by loosing chance to hit, we also loose the high damage hits.

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%-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.

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. In this damage the raw EM part is 1.1473 x 2.1 x 4 = 9.6373 and the raw Thermal part is 4.8187 (half of EM). Assuming the target's shield was hit, and that only the normal 20% resistance to Thermal is in effect, the final damage then becomes 9.6373 + (4.8187*(100%-20%)) = 13.492 points. In the combat log the hit will be described as 'well aimed' and be rounded off to one decimal place.

Damage and DPS reduction

When a turret has less than 100% chance to hit its damage dealing capabilites are 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) is reduced as well. Both of these effects will decrease the DPS output. 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 lower than the chance to hit, the shot lands and this number is then used further: 0.49 is added to it, and the result is then multiplied with the turret's base damage to obtain the raw damage done (damage before resistances)

What this all means is that targets that are tricky to hit also take less damage since high rolls now are discarded as misses. 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). The practical effect from this is that the DPS always decreases more than the chance to hit does.

Example: (please note that perfect hits are not considered in this example to make the numbers easier to follow) A turret has 50% chance to hit at optimal+falloff, ignoring tracking. The highest randomly rolled number that can result in a hit is thus 0.5 -- higher numbers mean a miss. This will shrink the damage interval down to 0.5 to 0.99 for normal hits, which on average is 0.745 ((0.5+0.99)/2). Compare that with a case inside optimal range where the chance to hit is 100%, ignoring tracking. Here the damage interval is 0.5 to 1.49 and the average is 0.995. At optimal+falloff (and ignoring perfect hits) the DPS from normal hits are hence reduced to 50% (number of hits) x 0.745 (average damage per hit) = 37.25% of normal. (When perfect hits are taken into consideration the DPS value becomes 39.5% instead, see the table below)

Tracking or Falloff

The table below shows how damage and DPS goes down as a result of lower hit chance. Note that the reason for the hit chance reduction doesn't matter, be it because of falloff or tracking issues, the DPS goes down identically. If you wish to combine the effects of tracking and falloff, look them up individuall and then multiply them (note: this only works for the columns Hit Chance and Relative DPS; the clumn 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 range and tracking while still maintaining a decent DPS output. Also, remember that the decrease in DPS from tracking and range are multiplied. Now consider the following notable values.

• Below 0.33 parts into ... : the DPS loss is at most 10%, a very small effect, being at 0.33 or below means pretty much that you have nearly top performance, you are still in your sweet spot.
• Above 0.50 parts into... : the DPS loss is now 22% or more and may start to become a problem, 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.

Comment to the table: 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

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%
0.3	0.9395	0.9268	-8.7%
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%
0.9	0.5704	0.4672	-54.0%
1	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	0.0625	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%

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. This section will try to shed some light on that. The tricky thing with this 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 you expect to be up against and what the angular velocity can be expected to be at.

Here are some guidelines for comparisons:

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 depends on how close a ship is to its max speed. This makes the effect hard to predict. But one can accurately say that the need for tracking will be reduced with at most the webs value. Relatively speaking, this can be compared to a 150% boost (at most) to tracking if a T2 web is used (-60% speed). The drawback is that your opponent also benefits from this.

Answers to some questions

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?

When comparing small signature radii, say 35m and 43m, the differance is only noticeable at short distances (up to 1 or 2 km). The one with the smallest radius get a small advantage from this factor. However, other factors come into play as well, and this advantage is many times offset by the fact that the larger-signature frigates use guns that generally have higher tracking values (the trend is: projectiles have the worst tracking, lasers are in between, hybrids have the best; when compared on an equal basis). So it really doesn't seem to matter. What is clear is that a high tracking can be more important than the damage multiplier on the gun, especially since the max damage drops if the gun can't track well enough.

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

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.

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 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 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 means that the constant has to be 0.49.

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