Difference between revisions of "Missile mechanics"

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{{Weapon Systems Links}}
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{{hatnote|This article details how damage is calculated when a missile explodes near a ship. For details about using missile launchers, as well as other missile stats, see [[Missiles]]. For information about damage as it is received by a target ship, see [[Tanking]].}}
  
This article takes a look at mathematics behind missiles. We look at the equations that govern how far your missiles will travel and how much damage they deal. There's some math at the beginning, but you can skip over this if you wish.  
+
When a missile crosses the signature radius of its target, it explodes. A ship's [[signature radius]] is an invisible "bubble" that most weapon systems see when trying to lock on to a ship. Generally, the bigger the ship, the bigger the signature radius.
  
= Missile Damage Output  =
+
A missile's explosion expands in a bubble of its own. The speed at which this bubble grows is called the <span style="color:#ccffee">''explosion velocity''</span>, and the maximum size that the bubble will reach is called the <span style="color:#ccffee">''explosion radius''</span>. A missile does not so much "hit" a ship as explode near it. EVE uses a [[#Missile damage formula|mathematical formula]] to compute the precise amount of damage that the explosion does to the ship.
 +
[[File:QSG_missile_terms.png|thumb|right|upright=0.8|A Missile Explodes|alt=drawing showing SR and ER]]
  
== First Look at the Damage Equation  ==
+
Of significant note, the [[Vorton Projectors|Arcing Vorton Projectors]] used by [[EDENCOM]] Ships also use missile damage mechanics to determine their damage application. Most other properties of these weapons will not be discussed on this page.
  
Here is the equation for missile damage:
+
==Missile detonation==
  
<br> [[Image:MissileDamageFormula.png|400px]] <br>
+
Every missile has a <span style="color:#ccffee">''Base Damage''</span> – which is listed as "explosive damage", "kinetic damage", or so on in the Attributes tab of the missile's Get Info window.[[File:SampleMissile.png|thumb|Heavy Missile Attributes|alt=Get Info window showing heavy missile attributes]] This amount may be augmented somewhat by certain skills and/or equipment, and when the term "Base Damage" is used here, it means the listed damage of the missile plus any augmented damage … in other words, the damage you expect the missile to do if it scores a direct hit.
  
Here are the terms in the equation:
+
While a missile can apply up to 100% of the Base Damage to a ship in some situations, damage is often reduced by two factors: if the targeted ship is moving faster than the missile's '''explosion velocity''', and if the ship's signature radius is smaller than the missile's '''explosion radius'''.
  
*S&nbsp;: [[Signature radius]] of target
+
*'''Explosion velocity''', in the simplest terms, determines how fast a ship needs to be moving to escape some of the damage the missile inflicts. Think of this as being able to somewhat outrun the shockwave generated by an explosion. The farther away a ship is from a warhead when it detonates, the less powerful the resulting shockwave will be when it hits the ship. [https://www.youtube.com/watch?v=5s3-c2gpbEs This video] is a good example of the principle in action; the explosion is clearly massive enough to kill anyone standing nearby, but the people filming were far enough away that, when it finally reached them, the force behind it had dissipated enough that they only got buffeted by the wind.
*V<sub>t</sub>: velocity of target (equals the speed of the target ship)
+
*'''Explosion radius''' is best described as how small a ship needs to be to only be hit by a part of the explosion it's flying through. A good analogy would be to fragmentation grenades, which cause injury not by the size of the explosion they make, but by filling the air with hundreds of metal fragments moving with the speed of bullets. Something like a human being is going to be hit by many of these fragments and suffer horrible injury as a result, but a sparrow is small enough that it might not be hit by anything large enough to cause it serious injury, and a bee is so small that the chances of it being hurt at all are slim to none.
  
*D&nbsp;: base damage of missile (you can find this in the missile information under" EM damage", "Kinetic damage", "Thermal damage" or "Explosive damage", Base Shield Damage and Base Armor Damage are not relevant here)
+
In practice, damage is usually reduced by the combination of these two factors.
*E&nbsp;: explosion radius of missile (You can find this in the missile information under "Explosion radius")
 
*V<sub>e</sub><sub></sub>: explosion velocity of missile (You can find this in the missile information under "Explosion Velocity")
 
  
*drf: damage reduction factor of missile (You can not find this in the missile information)
+
{{Note box|In the simplest terms: big, slow ships can take up to 100% of missile damage. Small, fast ships often take less damage. It is '''NOT''' the speed of the missile that matters; but the speed and size of the explosion.}}
  
 +
=== Explosion details ===
  
Note that unlike the turret damage equation, the missile damage does not care about angular velocity, but absolute velocity.
+
If you have been using missiles, this probably does not surprise you, and you may want more details, but since the actual damage number depends on target speed, missile speed, signature radius and so on, there is no way to give a simple summary or table of how much damage a particular kind of missile will do against a particular kind of ship.  
  
To find your damage, the game computes each of the three numbers you see, picks the smallest of them, and multiplies that by the base damage.
+
Without going into the mathematical details (''[[#Missile damage formula|discussed below]]''), the other factors that might come into play are these:
  
You can also write the form more abstract as a = b1 * min (c1, c2, c3). the lowest of the 3 numbers (c1, c2, c3) will be multiplied with b to result in a.
+
*If you are using missiles, you want a faster explosion (''more explosion velocity'') and a smaller one (''less explosion radius'') – in other words, a short, tight explosion is more effective than a long, loose one.
 +
*If a missile reaches its target, it will always do ''some'' damage. It is the speed of the explosion that helps determine how much ... not the speed of the missile.
 +
*Unlike with turrets, the angular velocity of the target does not matter ''for computing damage''. The missile still has to get to the target, but once it arrives, damage is computed using the target's absolute velocity.
 +
*Because damage is related to both speed and Signature Radius, using a microwarp drive, which increases both speed AND Signature Radius, will not significantly reduce damage. Afterburners do not affect Signature Radius, however, and so could possibly help.
  
[[File:SampleMissile.png|thumb|800px]]
+
=== Practical example ===
== Finding the target values  ==
 
Target velocity / the speed of the target (*V<sub>t</sub>):
 
if you set up the overview to the [[Overview Guide]], you can see the velocity of any ship near you on your overview.
 
  
Target signature radius (S):
+
As an illustration, here are the basic statistics for the Inferno Light Missile. These are sorted on explosion velocity.
The target signature radius is not displayed in the overview and is affected by various factions. The main factor is the ship size it self, the bigger the ship, the bigger its signature. But other things like modules, rigs, skills and implants and more affect the signature of a target ship. The article [[Signature radius]] can give you a general overview about the expected signature size of a ship.
 
  
== Finding the missile values  ==
+
{| class="wikitable sortable" style="text-align:center; text-size:90%"
 +
! scope="col" width="130px" style="background-color:#222222; text-align:left" | Missile
 +
! scope="col" width="90px" style="background-color:#222222;" | Explosion Radius
 +
! scope="col" width="90px" style="background-color:#222222;" | Explosion Velocity
 +
! scope="col" width="100px" style="background-color:#222222;" | Base Damage (Thermal)
 +
|-
 +
| style="text-align:left" | Inferno Precision Light Missile|| 25 || 204 || 83
 +
|-
 +
| style="text-align:left" | Inferno Light Missile|| 40 || 170 || 83
 +
|-
 +
| style="text-align:left" | Caldari Navy Inferno Light Missile|| 40 || 170 || 95
 +
|-
 +
| style="text-align:left" | Inferno Fury Light Missile|| 69 || 143 || 116
 +
|}
  
Base damage of missile (D): <br>
+
First, notice that the only difference between the regular Inferno and the Caldari Navy Inferno is a change in the base damage.  
You can find this in the missile information under" EM damage", "Kinetic damage", "Thermal damage" or "Explosive damage", Base Shield Damage and Base Armor Damage are not relevant here.
 
  
Explosion radius of missile (E):<br>
+
Second, you can see that the Fury missile has a larger base damage, but that the Precision missile has a faster Explosion Velocity and smaller Explosion Radius.  
You can find this in the missile information under "Explosion radius".
 
  
Explosion velocity of missile (V<sub>e</sub><sub></sub>):<br>
+
Explosion radius and velocity come into play whenever the target is small and/or fast. This means that the Fury missile will deliver its full damage against a bigger, slower ship, but is more likely to have its damage reduced against smaller, faster targets. A Precision missile will also deliver its full damage against a bigger, slower ship – though it will do less damage than the Fury because of the lower base damage – but it will also be more likely to deliver full damage to smaller, faster ships.
You can find this in the missile information under "Explosion Velocity".
 
  
== Finding the damage reduction factor of a missile==
+
Other classes of missiles follow the same pattern. Again, the list is sorted on explosion velocity.
  
The quite mysterious "damage reduction factor" of a missile is not mentioned in the game, however it is included in the data that CCP publishes [http://community.eveonline.com/community/toolkit.asp].<br>
+
{| class="wikitable sortable" style="text-align:center; text-size:90%"
The current table is based on Inferno 1.2.
+
! scope="col" width="130px" style="background-color:#222222; text-align:left;" | Missile
 +
! scope="col" width="90px" style="background-color:#222222;" | Explosion Radius
 +
! scope="col" width="90px" style="background-color:#222222;" | Explosion Velocity
 +
! scope="col" width="100px" style="background-color:#222222;" | Base Damage (Thermal)
 +
|-
 +
| style="text-align:left" |Inferno Light Missile|| 40 || 170 || 83
 +
|-
 +
| style="text-align:left" |Inferno Rocket|| 20 || 150 || 33
 +
|-
 +
| style="text-align:left" |Inferno Heavy Missile|| 140 || 85 || 149
 +
|-
 +
| style="text-align:left" |Inferno Torpedo|| 405 || 78 || 450
 +
|}
 +
 
 +
Rockets have the smallest Base Damage (BD), but they have a very small explosion radius (ER) and a fairly fast explosion velocity (EV). So, you would expect them to do very good damage to small targets (due to their ER and EV), but relatively less damage to large ones (due to their BD). Torpedoes have five times the base damage of Light Missiles, but they have ten times the explosion radius and half the explosion velocity. So, you would expect Torpedoes to be very good against large, slow ships (due to their BD), but very poor against small, fast ships (due to their ER and EV).
 +
 
 +
If that all makes sense, then good ... if not, then just keep in mind that, all things being equal, EVE has balanced the damage done by missiles among themselves as well as with the damage done by projectiles, beams and other types of weapons.
 +
 
 +
== Increasing missile damage ==
 +
 
 +
Skills and ship equipment can have a direct impact on missile damage. Many implants do the same. In addition, modules such as Target Painters and Webifiers can affect the target's signature radius and speed, thus making missile damage more effective.
 +
 
 +
=== Skills ===
 +
 
 +
While various skills improve a player's expertise with missiles, these three specifically affect the amount of damage done when a missile explodes.
 +
 
 +
*{{sk|Guided Missile Precision|mult=yes}} reduces the impact of the target signature radius on the damage. This effectively decreases the explosion radius of the missile by 5% per skill level, which makes it more likely to do full damage to a small/fast target.
 +
*{{sk|Target Navigation Prediction|mult=yes}} reduces the impact of the target velocity on the damage. This effectively increases the explosion velocity by 10% per skill level, which makes it more likely to do full damage to a small/fast target.
 +
*{{sk|Warhead Upgrades|mult=yes}} provides a 2% increase in missile damage per level ... this appears to apply to Base Damage.
 +
 
 +
=== Modules, rigs, and ammunition===
 +
 
 +
While there are additional items that affect missiles and launchers, those do not alter the missile damage as such. Here are the ones that do.
 +
 
 +
Ballistic Control System: Among other things, gives a bonus to base missile damage.
 +
 
 +
Missile Launcher Rigs:
 +
 
 +
*Warhead Calefaction Catalyst: increases the base damage of the missile but increases the CPU requirement for the launcher.
 +
*Warhead Flare Catalyst: increases the explosion velocity of the missile but increases the CPU requirement for the launcher.
 +
*Warhead Rigor Catalyst: decreases the explosion radius of the missile but increases the CPU requirement for the launcher.
 +
 
 +
Advanced Tech II Missiles:
 +
 
 +
*Precision Missiles are more effective than Furies against smaller, faster targets, but do less base damage per missile.
 +
*Fury Missiles have a larger base damage per missile, but are less effective than Precisions against smaller, faster targets.
 +
*Both have a somewhat shorter range than regular and Faction missiles.
 +
 
 +
=== Implants ===
 +
 
 +
A variety of [[List_of_Skill_Hardwiring_Implants#Table_of_Implants|Hardwired Implants]] affect weapons systems. Only a few have a direct impact on missile damage creation.
 +
 
 +
==== Specific missile types ====
 +
 
 +
*Zainou 'Snapshot' Cruise Missiles: 1% to 6% bonus to the base damage of Cruise Missiles
 +
*Zainou 'Snapshot' Torpedoes: 1% to 6% bonus to the base damage of Torpedos
 +
*Zainou 'Snapshot' Heavy Missiles: 1% to 6% bonus to the base damage of Heavy Missiles
 +
*Zainou 'Snapshot' Assault Missiles: 1% to 6% bonus to the base damage of Assault Missiles
 +
*Zainou 'Snapshot' Rockets: 1% to 6% bonus to the base damage of Rockets
 +
*Zainou 'Snapshot' Auto-Targeting Explosion Radius: 1% to 6% bonus to explosion radius of Auto-Target Missiles
 +
 
 +
==== All Missiles ====
 +
 
 +
*Zainou 'Deadeye' Guided Missile Precision: 1% to 6% reduced factor of signature radius for all missile explosions
 +
*Zainou 'Deadeye' Target Navigation Prediction: 1% to 6% decrease in factor of target's velocity for all missile explosions
 +
 
 +
=== Missile and electronic warfare ===
 +
 
 +
Missile damage can be substantially increased by using Electronic Warfare Modules to change the Velocity and/or Signature Radius of the target ship.  
 +
 
 +
* [[Target Painter]]s can effectively increase the Signature Radius of the ship. This makes the ship bigger and more likely to take full damage.
 +
* [[Stasis_Webifier_Module#Web | Stasis Webifiers]] can decrease the ship's velocity. This makes the ship slower and more likely to take full damage.
 +
 
 +
Note that both of these are most effective if you are firing missiles at small, fast ships. They may be completely unhelpful if you are firing at very large ships.
 +
 
 +
==Missile damage formula==
 +
{{Note box|<big>''WARNING: '''Math''' below!''</big>}}
 +
 
 +
The equation for missile damage is as follows:
 +
 
 +
:<math>\displaystyle \text{Damage}= D \cdot \min\left( 1, \frac{S}{E}, \left(\frac{S\,V_\mathrm{e}}{E\,V_\mathrm{t}} \right)^\mathrm{drf} \right)</math>
 +
 
 +
Here are the terms in the equation. Except for the "damage reduction factor", these are the same as were defined in the [[#The_Basic_Picture|Basic Picture]] section, above :
  
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
! Missile Type!! DRF
+
| <math>S</math>&nbsp; || signature radius of target || <i>Note: The bigger the better</i>
 
|-
 
|-
| Precision Light Missile || 2,6
+
| <math>V_{\mathrm t}</math>&nbsp; || velocity of target || <i>Note: The smaller the better</i>
 
|-
 
|-
| Precision Heavy Missile || 2,7
+
| <math>D</math>&nbsp; || base damage of missile || <i>Note: The bigger the better</i>
 
|-
 
|-
| Auto-Targeting Light Missile || 2,8
+
| <math>E</math>&nbsp; || explosion radius of missile || <i>Note: The smaller the better</i>
 
|-
 
|-
| Light Missile || 2,8
+
| <math>V_{\mathrm e}</math>&nbsp; || explosion velocity of missile || <i>Note: The bigger the better</i>
 
|-
 
|-
| Rocket || 3
+
| <math>\mathrm{drf}</math>&nbsp; || damage reduction factor || <i>Note: The smaller the better</i>
 +
|}
 +
 
 +
 
 +
 
 +
Unlike the turret damage formula, missile damage takes the absolute velocity of the target into account, not the angular velocity. To create missile damage, the game computes two values. These values are compared to 1, and the smallest is chosen. That number is then multiplied by the base damage to get the amount of damage applied to the ship.
 +
 
 +
=== Target values  ===
 +
 
 +
Target velocity <math>V_\mathrm{t}</math> is the speed of the target. The maximum speed of a ship can be found in its description, but this speed will vary from the maximum during combat. Keep in mind that the speed of the missile is not a factor. What matters is the speed of the ship at the time the missile arrives.
 +
 
 +
Target [[signature radius]] <math>S</math> is the effective size of a ship. It is affected by various factors, such as the ship type, modules, rigs, skills and/or implants. It cannot displayed in the Overview, but it is listed in the ship's Get Info Attributes.
 +
 
 +
=== Missile values ===
 +
 
 +
The base damage of a missile <math>D</math> can be found in the missile information under “EM damage”, “Kinetic damage”, “Thermal damage” or “Explosive damage”.  Base Shield Damage and Base Armor Damage are not relevant for this calculation.
 +
 
 +
The explosion radius of a missile <math>E</math> represents the size of the explosion. It can be found in the missile information under “Explosion radius”.
 +
 
 +
The explosion velocity of missile <math>V_{\mathrm e}</math> is the rate of expansion of the explosion. It can be found in the missile information under “Explosion velocity”.
 +
 
 +
All three of these can be improved through the use of rigs and/or implants.
 +
 
 +
=== Damage reduction factor ===
 +
 
 +
The “damage reduction factor”, or <math>\mathrm{drf}</math>, of a missile is not mentioned in the game, it is however included in the [https://community.eveonline.com/community/content-creation/toolkit/ data that CCP publishes].
 +
 
 +
{| class="wikitable collapsible collapsed sortable" style="text-size:90%"
 
|-
 
|-
| Heavy Missile || 3,2
+
! style="background-color:#222222;" | Missile Type
 +
! style="background-color:#222222;" | DRF
 
|-
 
|-
| Auto-Targeting Heavy Missile || 3,2
+
| Precision Light Missile || 0.561
 
|-
 
|-
| Javelin Rocket || 3,2
+
| Precision Heavy Missile || 0.583
 
|-
 
|-
| Fury Light Missile || 3,2
+
| Auto-Targeting Light Missile || 0.604
 
|-
 
|-
| Precision Cruise Missile || 3,5
+
| Light Missile || 0.604
 
|-
 
|-
| Cruise Missile || 4,5
+
| Rocket || 0.644
 
|-
 
|-
| Auto-Targeting Cruise Missile || 4,5
+
| Heavy Missile || 0.682
 
|-
 
|-
| Rage Rocket || 4,5
+
| Auto-Targeting Heavy Missile || 0.682
 
|-
 
|-
| Citadel Cruise Missile || 4,5
+
| Javelin Rocket || 0.682
 
|-
 
|-
| Fury Heavy Missile || 4,5
+
| Fury Light Missile || 0.682
 
|-
 
|-
| Heavy Assault Missile || 4,5
+
| Precision Cruise Missile || 0.735
 
|-
 
|-
| Javelin Heavy Assault Missile || 4,6
+
| Cruise Missile || 0.882
 
|-
 
|-
| Fury Cruise Missile || 4,78
+
| Auto-Targeting Cruise Missile || 0.882
 
|-
 
|-
| Rage Heavy Assault Missile || 4,8
+
| Rage Rocket || 0.882
 
|-
 
|-
| Torpedo || 5
+
| Heavy Assault Missile || 0.882
 
|-
 
|-
| Javelin Torpedo || 5,2
+
| Fury Heavy Missile || 0.882
 
|-
 
|-
| Rage Torpedo || 5,2
+
| XL Cruise Missile || 0.882
 
|-
 
|-
| Citadel Torpedo || 5,5
+
| Precision XL Cruise Missile || 0.882
 +
|-
 +
| Fury XL Cruise Missile || 0.882
 +
|-
 +
| Javelin Heavy Assault Missile || 0.895
 +
|-
 +
| Fury Cruise Missile || 0.908
 +
|-
 +
| Rage Heavy Assault Missile || 0.920
 +
|-
 +
| Standup Missiles (all sizes) || 0.944
 +
|-
 +
| Torpedo || 0.944
 +
|-
 +
| Javelin Torpedo || 0.967
 +
|-
 +
| Rage Torpedo || 0.967
 +
|-
 +
| XL Torpedo || 1.00
 +
|-
 +
| Javelin XL Torpedo || 1.00
 +
|-
 +
| Rage XL Torpedo || 1.00
 +
|-
 +
| Small Vorton Projector || 0.40
 +
|-
 +
| Medium Vorton Projector || 0.50
 +
|-
 +
| Large Vorton Projector || 0.70
 
|}
 
|}
  
== Typical S/E Values ==
+
=== Analysis of the equation ===
  
Below is a table that lists some expected values for S/E for each missile type against various hull sizes:  
+
The equation can be written in this format:
  
[[Image:SEvalues.png]]
+
:<math>\displaystyle \mathrm{Damage}= \mathrm{Base damage} \cdot \min\left( 1, \frac{S}{E}, \left(\frac{S\,V_\mathrm{e}}{E\,V_\mathrm{t}} \right)^\mathrm{drf} \right)</math>
  
== Speed Tanking Missile Damage  ==
+
This means that the base damage is multiplied by the smallest of either <math>1</math>, <math>S/E</math> or <math display="inline">[(S/E) \cdot (V_{\mathrm{e}}/ V_{\mathrm{t}})]^\mathrm{drf}</math>. In the equation, then, the number 1 represents 100% of the base damage – since if either of the other values is bigger than 1, they are rejected. Thus, the damage created can be no higher than 100% of the base damage.
  
We will now look at what velocities you can speed tank missile damage, and how much damage reduction you can get from speed tanking. To start, we'll assume that S/E = 1. Of course, the table above shows that this is very wrong, but you can factor in this by multiplying the explosion velocity V<sub>e</sub> by S/E, which will adjust the figures appropriately. Hence, if a ship fires a standard light missile at a frigate then we multiply the explosion velocity of 170 by S/E, which will be about 80%, which gives us an effectively explosion velocity of about 136. Below is a list of explosion velocities for most missiles.  
+
When the target's signature radius is larger than the missile's explosion radius, <code>S/E</code> will be greater than 1, and that term will be rejected. If target signature radius is smaller than explosion velocity, then <code>S/E</code> will be computed and compared with the third term. The smaller of these will be chosen and multiplied times the Base Damage.
  
<br>  
+
Since the part of the equation that is affected by velocity ... <code>(S/E*Ve/Vt)^drf</code> ... only matters if it is less than 1, it can be set to 1 and solved to find the point where it begins to matter.  Doing that gives <code>Vt = S/ (1^(1/ ADRF) * E) * Ve</code>. Since <code>1^x = 1</code>, then <code>1^(1/ drf) </code> also must equal 1, and the equation reduces to <code>Vt = (S/E) * Ve</code>. This can be rewritten as
  
{| width="300" border="1" cellpadding="1" cellspacing="1"
+
:<math>\displaystyle V_\text{t} = S \times \frac{V_\text{e} }{E }</math>
|+ Explosion Velocities for Missiles
+
 
 +
Since <code>Ve</code> and <code>E</code> are both attributes of the missile, <code>Ve/E</code> can be combined into a single "minimum velocity factor" for each missile class.
 +
 
 +
{| class="wikitable collapsible collapsed sortable"
 +
|-
 +
! style="background-color:#222222;" | Missile
 +
! style="background-color:#222222;" | Minimum Velocity<br />Factor (V<sub>e</sub>/E)
 +
|-
 +
| Standup XL Cruise Missile || 0.001
 +
|-
 +
| Standup Super Heavy Torpedo || 0.002
 +
|-
 +
| Standup Cruise Missile || 0.12
 +
|-
 +
| Standup Heavy Missile || 0.5
 +
|-
 +
| Standup Light Missile || 2
 
|-
 
|-
|  
+
| XL Torpedo || 0.0035
Rockets
+
|-
 
+
| XL Cruise Missile || 0.00666
| Standard
+
|-
| 150
+
| Rage Torpedo || 0.0788
 +
|-
 +
| Fury Cruise Missile || 0.102
 +
|-
 +
| Javelin Torpedo || 0.158
 +
|-
 +
| Torpedo || 0.158
 +
|-
 +
| Auto-Targeting Cruise Missile I || 0.209
 +
|-
 +
| Cruise Missile || 0.209
 +
|-
 +
| Precision Cruise Missile || 0.279
 +
|-
 +
| Fury Heavy Missile || 0.294
 +
|-
 +
| Rage Heavy Assault Missile || 0.405
 +
|-
 +
| Auto-Targeting Heavy Missile I || 0.579
 +
|-
 +
| Heavy Missile || 0.607
 +
|-
 +
| Precision Heavy Missile || 0.816
 +
|-
 +
| Heavy Assault Missile || 0.808
 +
|-
 +
| Javelin Heavy Assault Missile || 0.808
 +
|-
 +
| Fury Light Missile || 2.07
 +
|-
 +
| Auto-Targeting Light Missile I || 4.25
 +
|-
 +
| Light Missile || 4.25
 +
|-
 +
| Rage Rocket || 3.79
 +
|-
 +
| Precision Light Missile || 8.16
 
|-
 
|-
|  
+
| Javelin Rocket || 7.50
| Anti-Ship
 
| 150
 
 
|-
 
|-
|  
+
| Rocket || 7.50
| Range
+
|}
| 150
+
 
 +
So, the target velocity at which the damage created begins to be reduced is equal to the signature radius of the target times the minimum velocity factor.
 +
 
 +
:<math>\displaystyle V_\text{t} = S \times \text{MVF} </math>
 +
 
 +
This means that a rocket will begin doing less damage when the target velocity is at 7.5 * <code>S</code>,  a light missile at  3.4 * <code>S</code>, and a torpedo at 0.158 * <code>S</code>.  Thus, the same sized ship has to be going much faster to reduce damage from a rocket than it does to reduce damage from a torpedo.
 +
 
 +
The equations also show that there is a minimum speed that a ship needs to fly before its velocity can reduce the missile damage at all. If the ship is moving below a specific threshold, the explosion velocity and the speed of the ship do not affect the missile damage. In that case, only the signature radius of the target and the explosion radius of the missile can have an effect, and further decreases in the ship's speed will not increase the damage. However, increases the signature radius can, until the damage reaches 100%.
 +
 
 +
==== Application Modules and Stacking Penalties ====
 +
As you see in the Formula (assuming the minimum is the third term), reducing the explosion radius by 20% means multiplying the explosion radius with 0.8 which is equivalent to multiplying the explosion velocity by 1/0.8=1.25. This shows that the first rigor (20% reduction to explosion radius) is flat out better than the flare (20% increase in explosion velocity). If you assume that the minimum is the second term then the rigor is better anyway and for the first term it doesn't matter. Now you have stacking penalties though, so does the flare become better at some point?
 +
For that purpose I calculated various combinations of rigs always as a multiplicator of the term inside the drf bracket. If you rise that multiplicator to the appropriate drf you get the damage multiplicator compared to no application modules (Assuming you stay in the third case).
 +
 
 +
Multiplicator (higher is better) of various combinations of t2 rigor/flare rigs and t2 guidance computer scripted with the precision script assuming imperfect application:
 +
 
 +
{| class="wikitable"
 +
| 0 Comp. (Prec)
 
|-
 
|-
| Light
+
| #rigor\#flare || 0 || 1
| Standard
 
| 170
 
 
|-
 
|-
|  
+
| 0 || 1 || 1.2
| Anti-Ship
 
| 174
 
 
|-
 
|-
|  
+
| 1 || 1.25 || 1.5
| Precision
 
| 179
 
 
|-
 
|-
| Heavy
+
| 2 || 1.513 || 1.816
| Standard
 
| 81
 
 
|-
 
|-
|  
+
| 3 || 1.708 || -
| High Damage
+
|}
| 97
+
 
 +
{| class="wikitable"
 +
| 1 Comp. (Prec)
 
|-
 
|-
|  
+
| #rigor\#flare || 0 || 1
| High Precision
 
| 87
 
 
|-
 
|-
| Heavy Assault
+
| 0 || 1.395 || 1.2
| Standard
 
| 101
 
 
|-
 
|-
|  
+
| 1 || 1.700 || 2.002
| Anti-Ship
 
| 93
 
 
|-
 
|-
|  
+
| 2 || 1.946 || 2.292
| Range
 
| 101
 
 
|-
 
|-
| Cruise
+
| 3 || 2.087 || -
| Standard
+
|}
| 69
+
 
 +
{| class="wikitable"
 +
| 2 Comp. (Prec)
 
|-
 
|-
|  
+
| #rigor\#flare || 0 || 1
| High Damage
 
| 58
 
 
|-
 
|-
|  
+
| 0 || 1.862 ||  2.099
| High Precision
 
| 71
 
 
|-
 
|-
| Torpedoes
+
| 1 || 2.146 ||  2.419
| Standard
 
| 71
 
 
|-
 
|-
|  
+
| 2 || 2.334 ||  2.631
| High Damage
 
| 61
 
 
|-
 
|-
|  
+
| 3 || 2.429 || -
| Range
 
| 71
 
 
|}
 
|}
  
One final chart will be needed. This chart will indicate how many times faster than the missile's effective explosion velocity you must travel to reduce the incoming damage by a given amount, roughly.
+
=== Additional examples ===
  
[[File:damage_reduction_chart.png]]
+
Note that all examples assume all 0 skills.  Higher acceleration control will result in propulsion mods being significantly more effective at mitigating damage.
  
== Using These Charts ==
+
{{Example |  Example 1:
 +
The Heavy Missile has an MVF of 0.648.
 +
The Drake has 140 m/s speed and a signature radius of 295 m.
  
How can we possibly use these charts effectively? Well, suppose I'm firing standard light missiles at a target. My explosion velocity sits at about 170. If I'm shooting this missile at a frigate, then my effective explosion velocity becomes 136. Since he's webbed and has his afterburner on, he's going at about 400 m/s, which is roughly 3 times my explosion velocity. We look at the proper row in the table above and scan across until we see which columns 3 lies between. We then look up and see that I'm doing about 50% reduced damage on him. If we were allowed to travel without the web, he could easily hit 10 times my explosion velocity, at which point the damage drops to 30-40%. From this, you should take away the fact that even a target that's the right size for your missiles moving even at very normal speeds might cut your DPS by 50%, much like a turret tracking something of the right speed and size might take a similar DPS cut.
+
The required speed is therefore 191.16. (''295  * 0.648'')
 +
Since the speed of the Drake (140 m/s) is below the required speed (191.16 m/s), the speed does not affect the missile damage. The damage is determined by 1, the lowest of the three factors and the missile does full damage.}}
  
From this, take away that ships do not need to be moving very quickly to slice missile damage, as the explosion radii are typically quite low.
 
  
= Increasing Missile Damage =
+
{{Example | Example 2:
 +
The Heavy Missile has an MVF of 0.648.
 +
The Drake fits a 10MN meta afterburner, increasing top speed to 273m/s; signature size is unchanged.
  
There are many things a player can do to increase the missile damage.  
+
The required speed stays the same. As the drake is now significantly faster than the required speed (273m/s vs 191.16m/s) some damage is lost (the missile does approximately 72.6% of maximum damage).}}
  
== Skills ==
 
  
 +
{{Example |  Example 3:
 +
The Heavy Missile has an MVF of 0.648.
 +
The Drake fits a 50MN Quad LiF Restrained Microwarpdrive, increasing top speed to 675m/s and signature radius to 1622.5m.
  
*[[Skills:Missiles#Guided_Missile_Precision|Guided Missile Precision]]
+
Required speed is therefore changed to 1051.38m/s  (''1622.5  * 0.648'')
The target signature radius has less impact on the damage. This effectively decreases the explosion radius of the missile by 5% per skill level. Notice that this only affects guided missiles (Light, Heavy and Cruise Missile).
+
Since the speed of the Drake with a MWD (675m/s) is below the required speed (1051.38 m/s), the speed does not affect the missile damage. The damage is determined by 1, the damage is 100% of the possible damage and it is no different than the damage the ship receives without the MWD.}}
  
*[[Skills:Missiles#Target_Navigation_Prediction|Target Navigation Prediction]]
 
The target velocity has less impact on the damage. This effectively increases the explosion velocity by 10% per skill level. Works for all missiles, guided and unguided.
 
  
*[[Skills:Missiles#Warhead_Upgrades|Warhead Upgrades]]  
+
{{Example |  Example 4:
A straight forward 2% more missile damage per skill level.
+
The Heavy Missile has an MVF of 0.648 and explosion radius E of 140m.
 +
Griffin frigate has signature radius S of about 42m
 +
 
 +
Since signature radius of Griffin is smaller than missile's explosion radius, we are limited by the second term in the missile damage formula - S/E, which is 0.3. That means that at the best we can do only 30% of Heavy Missile's damage when firing at Griffin, even when Griffin is not moving at all. Also, we can notice that in this case, Griffin's speed will take effect much later than at required speed. While required speed is 27.216m/s (42 * 0.648), at this speed third term in the missile damage formula is 1, however, it still does not have any effect because second term is 0.30. We will need to solve different (and more complicated) equation to get the speed of Griffin which will lower damage further below those 30%. After calculation we see that speed of the Griffin needs to be at least 141.89m/s to have further effect on reducing damage, which is more than 5 times more than required speed of 27.216m/s.
 +
}}
 +
 
 +
== Missile range ==
 +
When fired, a missile will leave the launcher, quickly accelerate, and then  proceed at its best speed directly at the target until it runs out of fuel. If it encounters the target during that time, it will explode - otherwise it will vanish. The approximate maximum distance that a missile will travel can be found by multiplying the speed of the missile by the number of seconds that its fuel will last. (''The approximation is due to eve running at 1 second intervals while missile flight time may not be a whole number. Also the missiles start at slower speed as the missile accelerates ''.)
 +
::''Maximum Distance ≈ Speed x Seconds of Fuel''
 +
[[File:QSM_missleHeadsUp.jpg‎|369px|thumb|Missile Launcher On-Screen Pop-Up shows its attributes.]]
 +
 
 +
For example:
 +
* A Light Missile has a flight time of 5 seconds at a speed of 3750 m/s. The maximum distance it can travel is 5 x 3750 ≈ 18,750 m.
 +
* A torpedo has a flight time of 6 seconds at a speed of 1500 m/s. The maximum distance it can travel is 6 x 1500 ≈ 9,000 m.
 +
 
 +
There are two special cases to missile flight time.
 +
 
 +
Eve uses 1 second ticks. If the missile flight time is not an integer then the missile will fly for the integer number of seconds shown and has a chance to fly one more second. For example a missile with a flight time of 7.5 seconds has a 50% probability to fly for 7 seconds and a 50% probability to fly for 8 seconds.<ref>If the flight time is a fraction EVE rounds it up or down. At times this produces considerable departures from the computed range. See [https://youtu.be/fyKTHfDYeqU Missile flight time demonstration]</ref>
 +
 
 +
The second exception is a result of the fact that missile ranges are calculated from center of the ship while ranges on overview are calculated from "edge" of the ship. To counter this large ships get small bonus to missile flight time.<ref>https://forums.eveonline.com/default.aspx?g=posts&m=6523910#post6523910</ref>
 +
 
 +
This information, as modified by your skills and equipment bonuses, along with the missile's dps and type of damage, is shown when you move your mouse over the icon for a missile launcher while in space.
 +
 
 +
Although the terms "range" and "distance" are often used interchangeably, technically, the range answers the question of whether the missile can reach its target: is it "in" or "out" of range? If the target is stationary, then the maximum distance will be the missile's range. Normally, however, the target is moving, and the range depends on this motion.
 +
If the target is moving directly away from the missile, then it will take the missile longer to reach the target than it would a stationary one. If the target is moving fast enough, the missile may not be able to reach it at all - in this case, the target would be considered "out of range." Note that the target does not have to be moving faster than the missile ... just fast enough to stay ahead of the missile until it runs out of fuel.
 +
 
 +
If the target is moving directly at the missile, then the missile will reach it much faster than it would reach a stationary target. In this case, the target may be "in range" even when it seems too far away to hit.
 +
 
 +
In most cases, however, the target will be moving in a curve with regard to the missile ship - possibly in an orbit, possibly curving towards or away from the launch. It is hard to specify the range, exactly, in these cases, but as always, the missile will head directly for the target, and it will continue as long as it has fuel. Its path is likely to be some sort of a spiral.
 +
 
 +
There is no way to control the path of a missile once it has been launched. It will point itself at its target and follow the target until it hits or runs out of fuel.
 +
{| class="wikitable"
 +
|-
 +
! Missile Chases the Target!! Missile Catches Fleeing Target!! Missile Does Not Catch Fleeing Target
 +
|-
 +
| [[File:Qsg_missile_chase.mov]]|| [[File:QSM_missile_catchyes.gif‎‎]]|| [[File:QSM_missile_catchno.gif‎]]
 +
|}
 +
{{clear}}
  
 +
== Footnotes and references ==
 +
{{reflist}}
  
Keep in mind these are only skills that affect the missile damage as such. For a more information about skills that affect missiles and their launchers in general review the article about [[Missile Launchers]].
+
[[Category:Weapons]]
 +
[[Category:Game mechanics]]

Latest revision as of 07:43, 26 June 2024

This article details how damage is calculated when a missile explodes near a ship. For details about using missile launchers, as well as other missile stats, see Missiles. For information about damage as it is received by a target ship, see Tanking.

When a missile crosses the signature radius of its target, it explodes. A ship's signature radius is an invisible "bubble" that most weapon systems see when trying to lock on to a ship. Generally, the bigger the ship, the bigger the signature radius.

A missile's explosion expands in a bubble of its own. The speed at which this bubble grows is called the explosion velocity, and the maximum size that the bubble will reach is called the explosion radius. A missile does not so much "hit" a ship as explode near it. EVE uses a mathematical formula to compute the precise amount of damage that the explosion does to the ship.

drawing showing SR and ER
A Missile Explodes

Of significant note, the Arcing Vorton Projectors used by EDENCOM Ships also use missile damage mechanics to determine their damage application. Most other properties of these weapons will not be discussed on this page.

Missile detonation

Every missile has a Base Damage – which is listed as "explosive damage", "kinetic damage", or so on in the Attributes tab of the missile's Get Info window.

Get Info window showing heavy missile attributes
Heavy Missile Attributes

This amount may be augmented somewhat by certain skills and/or equipment, and when the term "Base Damage" is used here, it means the listed damage of the missile plus any augmented damage … in other words, the damage you expect the missile to do if it scores a direct hit.

While a missile can apply up to 100% of the Base Damage to a ship in some situations, damage is often reduced by two factors: if the targeted ship is moving faster than the missile's explosion velocity, and if the ship's signature radius is smaller than the missile's explosion radius.

  • Explosion velocity, in the simplest terms, determines how fast a ship needs to be moving to escape some of the damage the missile inflicts. Think of this as being able to somewhat outrun the shockwave generated by an explosion. The farther away a ship is from a warhead when it detonates, the less powerful the resulting shockwave will be when it hits the ship. This video is a good example of the principle in action; the explosion is clearly massive enough to kill anyone standing nearby, but the people filming were far enough away that, when it finally reached them, the force behind it had dissipated enough that they only got buffeted by the wind.
  • Explosion radius is best described as how small a ship needs to be to only be hit by a part of the explosion it's flying through. A good analogy would be to fragmentation grenades, which cause injury not by the size of the explosion they make, but by filling the air with hundreds of metal fragments moving with the speed of bullets. Something like a human being is going to be hit by many of these fragments and suffer horrible injury as a result, but a sparrow is small enough that it might not be hit by anything large enough to cause it serious injury, and a bee is so small that the chances of it being hurt at all are slim to none.

In practice, damage is usually reduced by the combination of these two factors.

In the simplest terms: big, slow ships can take up to 100% of missile damage. Small, fast ships often take less damage. It is NOT the speed of the missile that matters; but the speed and size of the explosion.

Explosion details

If you have been using missiles, this probably does not surprise you, and you may want more details, but since the actual damage number depends on target speed, missile speed, signature radius and so on, there is no way to give a simple summary or table of how much damage a particular kind of missile will do against a particular kind of ship.

Without going into the mathematical details (discussed below), the other factors that might come into play are these:

  • If you are using missiles, you want a faster explosion (more explosion velocity) and a smaller one (less explosion radius) – in other words, a short, tight explosion is more effective than a long, loose one.
  • If a missile reaches its target, it will always do some damage. It is the speed of the explosion that helps determine how much ... not the speed of the missile.
  • Unlike with turrets, the angular velocity of the target does not matter for computing damage. The missile still has to get to the target, but once it arrives, damage is computed using the target's absolute velocity.
  • Because damage is related to both speed and Signature Radius, using a microwarp drive, which increases both speed AND Signature Radius, will not significantly reduce damage. Afterburners do not affect Signature Radius, however, and so could possibly help.

Practical example

As an illustration, here are the basic statistics for the Inferno Light Missile. These are sorted on explosion velocity.

Missile Explosion Radius Explosion Velocity Base Damage (Thermal)
Inferno Precision Light Missile 25 204 83
Inferno Light Missile 40 170 83
Caldari Navy Inferno Light Missile 40 170 95
Inferno Fury Light Missile 69 143 116

First, notice that the only difference between the regular Inferno and the Caldari Navy Inferno is a change in the base damage.

Second, you can see that the Fury missile has a larger base damage, but that the Precision missile has a faster Explosion Velocity and smaller Explosion Radius.

Explosion radius and velocity come into play whenever the target is small and/or fast. This means that the Fury missile will deliver its full damage against a bigger, slower ship, but is more likely to have its damage reduced against smaller, faster targets. A Precision missile will also deliver its full damage against a bigger, slower ship – though it will do less damage than the Fury because of the lower base damage – but it will also be more likely to deliver full damage to smaller, faster ships.

Other classes of missiles follow the same pattern. Again, the list is sorted on explosion velocity.

Missile Explosion Radius Explosion Velocity Base Damage (Thermal)
Inferno Light Missile 40 170 83
Inferno Rocket 20 150 33
Inferno Heavy Missile 140 85 149
Inferno Torpedo 405 78 450

Rockets have the smallest Base Damage (BD), but they have a very small explosion radius (ER) and a fairly fast explosion velocity (EV). So, you would expect them to do very good damage to small targets (due to their ER and EV), but relatively less damage to large ones (due to their BD). Torpedoes have five times the base damage of Light Missiles, but they have ten times the explosion radius and half the explosion velocity. So, you would expect Torpedoes to be very good against large, slow ships (due to their BD), but very poor against small, fast ships (due to their ER and EV).

If that all makes sense, then good ... if not, then just keep in mind that, all things being equal, EVE has balanced the damage done by missiles among themselves as well as with the damage done by projectiles, beams and other types of weapons.

Increasing missile damage

Skills and ship equipment can have a direct impact on missile damage. Many implants do the same. In addition, modules such as Target Painters and Webifiers can affect the target's signature radius and speed, thus making missile damage more effective.

Skills

While various skills improve a player's expertise with missiles, these three specifically affect the amount of damage done when a missile explodes.

  • Guided Missile Precision (5x) reduces the impact of the target signature radius on the damage. This effectively decreases the explosion radius of the missile by 5% per skill level, which makes it more likely to do full damage to a small/fast target.
  • Target Navigation Prediction (2x) reduces the impact of the target velocity on the damage. This effectively increases the explosion velocity by 10% per skill level, which makes it more likely to do full damage to a small/fast target.
  • Warhead Upgrades (5x) provides a 2% increase in missile damage per level ... this appears to apply to Base Damage.

Modules, rigs, and ammunition

While there are additional items that affect missiles and launchers, those do not alter the missile damage as such. Here are the ones that do.

Ballistic Control System: Among other things, gives a bonus to base missile damage.

Missile Launcher Rigs:

  • Warhead Calefaction Catalyst: increases the base damage of the missile but increases the CPU requirement for the launcher.
  • Warhead Flare Catalyst: increases the explosion velocity of the missile but increases the CPU requirement for the launcher.
  • Warhead Rigor Catalyst: decreases the explosion radius of the missile but increases the CPU requirement for the launcher.

Advanced Tech II Missiles:

  • Precision Missiles are more effective than Furies against smaller, faster targets, but do less base damage per missile.
  • Fury Missiles have a larger base damage per missile, but are less effective than Precisions against smaller, faster targets.
  • Both have a somewhat shorter range than regular and Faction missiles.

Implants

A variety of Hardwired Implants affect weapons systems. Only a few have a direct impact on missile damage creation.

Specific missile types

  • Zainou 'Snapshot' Cruise Missiles: 1% to 6% bonus to the base damage of Cruise Missiles
  • Zainou 'Snapshot' Torpedoes: 1% to 6% bonus to the base damage of Torpedos
  • Zainou 'Snapshot' Heavy Missiles: 1% to 6% bonus to the base damage of Heavy Missiles
  • Zainou 'Snapshot' Assault Missiles: 1% to 6% bonus to the base damage of Assault Missiles
  • Zainou 'Snapshot' Rockets: 1% to 6% bonus to the base damage of Rockets
  • Zainou 'Snapshot' Auto-Targeting Explosion Radius: 1% to 6% bonus to explosion radius of Auto-Target Missiles

All Missiles

  • Zainou 'Deadeye' Guided Missile Precision: 1% to 6% reduced factor of signature radius for all missile explosions
  • Zainou 'Deadeye' Target Navigation Prediction: 1% to 6% decrease in factor of target's velocity for all missile explosions

Missile and electronic warfare

Missile damage can be substantially increased by using Electronic Warfare Modules to change the Velocity and/or Signature Radius of the target ship.

  • Target Painters can effectively increase the Signature Radius of the ship. This makes the ship bigger and more likely to take full damage.
  • Stasis Webifiers can decrease the ship's velocity. This makes the ship slower and more likely to take full damage.

Note that both of these are most effective if you are firing missiles at small, fast ships. They may be completely unhelpful if you are firing at very large ships.

Missile damage formula

WARNING: Math below!

The equation for missile damage is as follows:

[math]\displaystyle \text{Damage}= D \cdot \min\left( 1, \frac{S}{E}, \left(\frac{S\,V_\mathrm{e}}{E\,V_\mathrm{t}} \right)^\mathrm{drf} \right)[/math]

Here are the terms in the equation. Except for the "damage reduction factor", these are the same as were defined in the Basic Picture section, above :

[math]S[/math]  signature radius of target Note: The bigger the better
[math]V_{\mathrm t}[/math]  velocity of target Note: The smaller the better
[math]D[/math]  base damage of missile Note: The bigger the better
[math]E[/math]  explosion radius of missile Note: The smaller the better
[math]V_{\mathrm e}[/math]  explosion velocity of missile Note: The bigger the better
[math]\mathrm{drf}[/math]  damage reduction factor Note: The smaller the better


Unlike the turret damage formula, missile damage takes the absolute velocity of the target into account, not the angular velocity. To create missile damage, the game computes two values. These values are compared to 1, and the smallest is chosen. That number is then multiplied by the base damage to get the amount of damage applied to the ship.

Target values

Target velocity [math]V_\mathrm{t}[/math] is the speed of the target. The maximum speed of a ship can be found in its description, but this speed will vary from the maximum during combat. Keep in mind that the speed of the missile is not a factor. What matters is the speed of the ship at the time the missile arrives.

Target signature radius [math]S[/math] is the effective size of a ship. It is affected by various factors, such as the ship type, modules, rigs, skills and/or implants. It cannot displayed in the Overview, but it is listed in the ship's Get Info Attributes.

Missile values

The base damage of a missile [math]D[/math] can be found in the missile information under “EM damage”, “Kinetic damage”, “Thermal damage” or “Explosive damage”. Base Shield Damage and Base Armor Damage are not relevant for this calculation.

The explosion radius of a missile [math]E[/math] represents the size of the explosion. It can be found in the missile information under “Explosion radius”.

The explosion velocity of missile [math]V_{\mathrm e}[/math] is the rate of expansion of the explosion. It can be found in the missile information under “Explosion velocity”.

All three of these can be improved through the use of rigs and/or implants.

Damage reduction factor

The “damage reduction factor”, or [math]\mathrm{drf}[/math], of a missile is not mentioned in the game, it is however included in the data that CCP publishes.

Analysis of the equation

The equation can be written in this format:

[math]\displaystyle \mathrm{Damage}= \mathrm{Base damage} \cdot \min\left( 1, \frac{S}{E}, \left(\frac{S\,V_\mathrm{e}}{E\,V_\mathrm{t}} \right)^\mathrm{drf} \right)[/math]

This means that the base damage is multiplied by the smallest of either [math]1[/math], [math]S/E[/math] or [math][(S/E) \cdot (V_{\mathrm{e}}/ V_{\mathrm{t}})]^\mathrm{drf}[/math]. In the equation, then, the number 1 represents 100% of the base damage – since if either of the other values is bigger than 1, they are rejected. Thus, the damage created can be no higher than 100% of the base damage.

When the target's signature radius is larger than the missile's explosion radius, S/E will be greater than 1, and that term will be rejected. If target signature radius is smaller than explosion velocity, then S/E will be computed and compared with the third term. The smaller of these will be chosen and multiplied times the Base Damage.

Since the part of the equation that is affected by velocity ... (S/E*Ve/Vt)^drf ... only matters if it is less than 1, it can be set to 1 and solved to find the point where it begins to matter. Doing that gives Vt = S/ (1^(1/ ADRF) * E) * Ve. Since 1^x = 1, then 1^(1/ drf) also must equal 1, and the equation reduces to Vt = (S/E) * Ve. This can be rewritten as

[math]\displaystyle V_\text{t} = S \times \frac{V_\text{e} }{E }[/math]

Since Ve and E are both attributes of the missile, Ve/E can be combined into a single "minimum velocity factor" for each missile class.

So, the target velocity at which the damage created begins to be reduced is equal to the signature radius of the target times the minimum velocity factor.

[math]\displaystyle V_\text{t} = S \times \text{MVF} [/math]

This means that a rocket will begin doing less damage when the target velocity is at 7.5 * S, a light missile at 3.4 * S, and a torpedo at 0.158 * S. Thus, the same sized ship has to be going much faster to reduce damage from a rocket than it does to reduce damage from a torpedo.

The equations also show that there is a minimum speed that a ship needs to fly before its velocity can reduce the missile damage at all. If the ship is moving below a specific threshold, the explosion velocity and the speed of the ship do not affect the missile damage. In that case, only the signature radius of the target and the explosion radius of the missile can have an effect, and further decreases in the ship's speed will not increase the damage. However, increases the signature radius can, until the damage reaches 100%.

Application Modules and Stacking Penalties

As you see in the Formula (assuming the minimum is the third term), reducing the explosion radius by 20% means multiplying the explosion radius with 0.8 which is equivalent to multiplying the explosion velocity by 1/0.8=1.25. This shows that the first rigor (20% reduction to explosion radius) is flat out better than the flare (20% increase in explosion velocity). If you assume that the minimum is the second term then the rigor is better anyway and for the first term it doesn't matter. Now you have stacking penalties though, so does the flare become better at some point? For that purpose I calculated various combinations of rigs always as a multiplicator of the term inside the drf bracket. If you rise that multiplicator to the appropriate drf you get the damage multiplicator compared to no application modules (Assuming you stay in the third case).

Multiplicator (higher is better) of various combinations of t2 rigor/flare rigs and t2 guidance computer scripted with the precision script assuming imperfect application:

0 Comp. (Prec)
#rigor\#flare 0 1
0 1 1.2
1 1.25 1.5
2 1.513 1.816
3 1.708 -
1 Comp. (Prec)
#rigor\#flare 0 1
0 1.395 1.2
1 1.700 2.002
2 1.946 2.292
3 2.087 -
2 Comp. (Prec)
#rigor\#flare 0 1
0 1.862 2.099
1 2.146 2.419
2 2.334 2.631
3 2.429 -

Additional examples

Note that all examples assume all 0 skills. Higher acceleration control will result in propulsion mods being significantly more effective at mitigating damage.

Example 1:

The Heavy Missile has an MVF of 0.648. The Drake has 140 m/s speed and a signature radius of 295 m.

The required speed is therefore 191.16. (295 * 0.648) Since the speed of the Drake (140 m/s) is below the required speed (191.16 m/s), the speed does not affect the missile damage. The damage is determined by 1, the lowest of the three factors and the missile does full damage.


Example 2:

The Heavy Missile has an MVF of 0.648. The Drake fits a 10MN meta afterburner, increasing top speed to 273m/s; signature size is unchanged.

The required speed stays the same. As the drake is now significantly faster than the required speed (273m/s vs 191.16m/s) some damage is lost (the missile does approximately 72.6% of maximum damage).


Example 3:

The Heavy Missile has an MVF of 0.648. The Drake fits a 50MN Quad LiF Restrained Microwarpdrive, increasing top speed to 675m/s and signature radius to 1622.5m.

Required speed is therefore changed to 1051.38m/s (1622.5 * 0.648) Since the speed of the Drake with a MWD (675m/s) is below the required speed (1051.38 m/s), the speed does not affect the missile damage. The damage is determined by 1, the damage is 100% of the possible damage and it is no different than the damage the ship receives without the MWD.


Example 4:

The Heavy Missile has an MVF of 0.648 and explosion radius E of 140m. Griffin frigate has signature radius S of about 42m

Since signature radius of Griffin is smaller than missile's explosion radius, we are limited by the second term in the missile damage formula - S/E, which is 0.3. That means that at the best we can do only 30% of Heavy Missile's damage when firing at Griffin, even when Griffin is not moving at all. Also, we can notice that in this case, Griffin's speed will take effect much later than at required speed. While required speed is 27.216m/s (42 * 0.648), at this speed third term in the missile damage formula is 1, however, it still does not have any effect because second term is 0.30. We will need to solve different (and more complicated) equation to get the speed of Griffin which will lower damage further below those 30%. After calculation we see that speed of the Griffin needs to be at least 141.89m/s to have further effect on reducing damage, which is more than 5 times more than required speed of 27.216m/s.

Missile range

When fired, a missile will leave the launcher, quickly accelerate, and then proceed at its best speed directly at the target until it runs out of fuel. If it encounters the target during that time, it will explode - otherwise it will vanish. The approximate maximum distance that a missile will travel can be found by multiplying the speed of the missile by the number of seconds that its fuel will last. (The approximation is due to eve running at 1 second intervals while missile flight time may not be a whole number. Also the missiles start at slower speed as the missile accelerates .)

Maximum Distance ≈ Speed x Seconds of Fuel
Missile Launcher On-Screen Pop-Up shows its attributes.

For example:

  • A Light Missile has a flight time of 5 seconds at a speed of 3750 m/s. The maximum distance it can travel is 5 x 3750 ≈ 18,750 m.
  • A torpedo has a flight time of 6 seconds at a speed of 1500 m/s. The maximum distance it can travel is 6 x 1500 ≈ 9,000 m.

There are two special cases to missile flight time.

Eve uses 1 second ticks. If the missile flight time is not an integer then the missile will fly for the integer number of seconds shown and has a chance to fly one more second. For example a missile with a flight time of 7.5 seconds has a 50% probability to fly for 7 seconds and a 50% probability to fly for 8 seconds.[1]

The second exception is a result of the fact that missile ranges are calculated from center of the ship while ranges on overview are calculated from "edge" of the ship. To counter this large ships get small bonus to missile flight time.[2]

This information, as modified by your skills and equipment bonuses, along with the missile's dps and type of damage, is shown when you move your mouse over the icon for a missile launcher while in space.

Although the terms "range" and "distance" are often used interchangeably, technically, the range answers the question of whether the missile can reach its target: is it "in" or "out" of range? If the target is stationary, then the maximum distance will be the missile's range. Normally, however, the target is moving, and the range depends on this motion. If the target is moving directly away from the missile, then it will take the missile longer to reach the target than it would a stationary one. If the target is moving fast enough, the missile may not be able to reach it at all - in this case, the target would be considered "out of range." Note that the target does not have to be moving faster than the missile ... just fast enough to stay ahead of the missile until it runs out of fuel.

If the target is moving directly at the missile, then the missile will reach it much faster than it would reach a stationary target. In this case, the target may be "in range" even when it seems too far away to hit.

In most cases, however, the target will be moving in a curve with regard to the missile ship - possibly in an orbit, possibly curving towards or away from the launch. It is hard to specify the range, exactly, in these cases, but as always, the missile will head directly for the target, and it will continue as long as it has fuel. Its path is likely to be some sort of a spiral.

There is no way to control the path of a missile once it has been launched. It will point itself at its target and follow the target until it hits or runs out of fuel.

Missile Chases the Target Missile Catches Fleeing Target Missile Does Not Catch Fleeing Target
QSM missile catchyes.gif QSM missile catchno.gif

Footnotes and references

  1. ^ If the flight time is a fraction EVE rounds it up or down. At times this produces considerable departures from the computed range. See Missile flight time demonstration
  2. ^ https://forums.eveonline.com/default.aspx?g=posts&m=6523910#post6523910