This article takes a look at mathematics behind missiles. It looks at the equations that govern how much damage missiles deal.
Missile Damage Output
Here is the equation for missile damage:
Here are the terms in the equation:
|S||Signature radius of target||Note: The bigger the better|
|Vt||velocity of target||Note: The smaller the better|
|D||base damage of missile||Note: The bigger the better|
|E||explosion radius of missile||Note: The smaller the better|
|Ve||explosion velocity of missile||Note: The bigger the better|
|drf||damage reduction factor||Note: The smaller the better|
Note that unlike the turret damage equation, missile damage takes absolute velocity into account, not angular velocity.
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.
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.
Finding the target values
Target velocity (Vt) is the speed of the target. If your overview is set up according to the Overview Guide, you can see the velocity of any ship near you on your overview.
Target signature radius (S) is the effective size of a ship. It is affected by various factors, for example the ship type, modules, rigs, skills or implants. It is not displayed in the overview.
Finding the missile values
The Base damage of a missile (D) 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 (E) represents the size of the explosion. It can be found in the missile information under “Explosion radius”.
The Explosion velocity of missile (Ve) is the rate of expansion of the explosion. It can be found in the missile information under “Explosion velocity”.
Finding the damage reduction factor of a missile
The “damage reduction factor” (drf) of a missile is not mentioned in the game, it is however included in the data that CCP publishes , and you can easily view it in the EVEMon item browser (you can also see the value 5.5 from the above equation in the same data, where it is called the Damage Reduction Sensitivity).
|Precision Light Missile||2.6|
|Precision Heavy Missile||2.7|
|Auto-Targeting Light Missile||2.8|
|Auto-Targeting Heavy Missile||3.2|
|Fury Light Missile||3.2|
|Precision Cruise Missile||3.5|
|Auto-Targeting Cruise Missile||4.5|
|Citadel Cruise Missile||4.5|
|Fury Heavy Missile||4.5|
|Heavy Assault Missile||4.5|
|Javelin Heavy Assault Missile||4.6|
|Fury Cruise Missile||4.7|
|Rage Heavy Assault Missile||4.8|
Practical application of the equation
The equation provides us with some basic information.
The base damage of the missile is multiplied by min(1, S/E, (S/E*Ve/Vt)^(ln(drf)/ln(5.5)). This means that the base damage is multiplied by the smallest of either 1, S/E or (S/E*Ve/Vt)^(ln(drf)/ln(5.5). This leads to the base damage being no higher than 100%, due to the fact that as soon as the other values exceed 1, 1 will always be selected in the calculation.
The damage of the missile is dependent on four things: Signature radius of the target, speed of the target, explosion Radius of the missile and explosion velocity of the missile.
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 this case, only the signature radius of the target and the explosion radius of the missile affect the missile damage. Further decreases the ships speed will not increase the damage; however increases the signature size will, until the damage reaches 100%.
An important fact that derives from the equations is the fact that there is a minimum speed that a ship needs to fly before the velocity can reduce the missile damage at all. Looking at the case where the target's base sig radius is larger than the missile explosion radius then the equations part that is affected by velocity, (S/E*Ve/Vt)^(ln(drf)/ln(5.5), is set to be 1 and solved to Vt = (S/ (1^(1/ (ln(drf)/ln(5.5)) * E)) * Ve. Since 1^x = 1 this means 1^(1/ (ln(drf)/ln(5.5) = 1, reducing the equation to (S/E) * Ve = Vt. The drf gets removed from the equation. Since E and Ve are defined by the missile, Ve/E can be combined into a single factor for each missile class.
|Missile||Minimum velocity factor|
|Citadel Cruise Missile||0,016571429|
|Fury Cruise Missile||0,105454545|
|Auto-Targeting Cruise Missile I||0,23|
|Precision Cruise Missile||0,262962963|
|Fury Heavy Missile||0,451162791|
|Rage Heavy Assault Missile||0,516666667|
|Auto-Targeting Heavy Missile I||0,648|
|Precision Heavy Missile||0,776785714|
|Heavy Assault Missile||0,808|
|Javelin Heavy Assault Missile||0,808|
|Fury Light Missile||2,047058824|
|Auto-Targeting Light Missile I||3,4|
|Precision Light Missile||5,114285714|
The signature radius of the ship needs to be multiplied with the minimum velocity factor (mvf) to decrease the missile damage.
Example 1: The heavy missile has a mvf of 0,648. Drake has 140 m/s speed, the signature radius of 285 m.
Required speed is therefore 119,88 (285 (=S) * 0,648 (=mvf) = 184,68). Since the speed of the Drake (140 m/s) is below the required speed (184,68 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 a mvf of 0,648. The drake fits a 10mn Afterburner I, increasing the speed by 125 %, the maximum speed is 157,5 m/s, signature size is unchanged. The required speed stays the same. The damage is determined again by 1 as both other options are greater than 1. The drake again takes full damage.
Example 3: The heavy missile has a mvf of 0,648 The drake fits a 10mn Microwarpdrive I, increasing the speed by 500 %, the maximum speed is 700 m/s, signature radius is increased by 500% to 1425 m.
Required speed is therefore changed to 923,4 (1425 (=S) * 0,648 (=mvf) = 923,4). Since the speed of the Drake with a MWD (700 m/s) is below the required speed (923,4), 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 recieves without the MWD.
Increasing Missile Damage
There are many things a player can do to increase thier missile damage.
Guided Missile Precision 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. Notice that this only affects guided missiles (Light, Heavy and Cruise Missile).
Target Navigation Prediction reduces the impact of the target velocity on the damage. This effectively increases the explosion velocity by 10% per skill level. Works for all missiles, guided and unguided.
Warhead Upgrades provides a straight forward 2% increase in missile damage per level.
- Missile Specialization (to be added)
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.
Modules and Rigs
Ballistic Control Systems increase, amongst other things, missile damage.
- Warhead Calefaction Catalyst
A Warhead Calefaction Catalyst increases the damage of the missile by 10% but increases the CPU requirement for the launcher.
- Warhead Flare Catalyst
A Warhead Flare Catalyst increases the explosion velocity of the missile by 15% but increases the CPU requirement for the launcher.
- Warhead Rigor Catalyst
A Warhead Rigor Catalyst decreases the explosion radius by 15% but increases the CPU requirement for the launcher.
While other rigs affect missiles and launchers as well, they do not affect the missile damage as such.
There are also a wide array of implants that can modify the missile damage. (to be added)
Affecting the target ship
Due to the fact that missile damage is affected by signature radius and velocity (speed) of the target ship, the missile damage can be substantially increased by affecting the target ship in order to change these parameters.
Target Painters can increase the signature size of the ship by a percentage.
A Stasis Webifier can decrease the ships velocity (speed) by a percentage.
Due to the fact that the usual MWD increases the ships signature and speed, these effects nullify each other. The missile damage on a target flying with MWD at maximum speed (!) is essentially (exceptions as mentioned above) identical to the one flying without it, as the bigger signature radius offsets the faster speed. Keep in mind that this is only applicable to the most basic T1 MWD; T2 versions of the drive increase the velocity bonus without increasing the signature radius penalty which decreases the missile damage. The same goes for other effects that increase the velocity bonus of the MWD. For afterburner this is not applicable since afterburners only increase the speed, but do not penalize the signature size.