Missile mechanics

This article takes a look at mathematics behind missiles. It looks at the equations that govern how much damage missiles deal. There's some math at the beginning, but you can skip over this if you wish.

Missile Damage Output

Damage Equation

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 (V_t) 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 (V_e) 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 [1].
The current table is based on Inferno 1.2.

Missile Type	DRF
Precision Light Missile	2,6
Precision Heavy Missile	2,7
Auto-Targeting Light Missile	2,8
Light Missile	2,8
Rocket	3
Heavy Missile	3,2
Auto-Targeting Heavy Missile	3,2
Javelin Rocket	3,2
Fury Light Missile	3,2
Precision Cruise Missile	3,5
Cruise Missile	4,5
Auto-Targeting Cruise Missile	4,5
Rage Rocket	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
Torpedo	5
Javelin Torpedo	5,2
Rage Torpedo	5,2
Citadel Torpedo	5,5

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. For this purpose 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 S, E and Ve are defined by the missile, (S/E) * Ve can be combined into a single factor for each missile class.

Missile	Minimum velocity factor
Citadel Torpedo	0,01
Citadel Cruise Missile	0,016571429
Rage Torpedo	0,093846154
Fury Cruise Missile	0,105454545
Javelin Torpedo	0,157777778
Torpedo	0,157777778
Auto-Targeting Cruise Missile I	0,23
Cruise Missile	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
Heavy Missile	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
Light Missile	3,4
Rage Rocket	4,666666667
Precision Light Missile	5,114285714
Javelin Rocket	7,5
Rocket	7,5

The signature radius of the ship needs to be multiplied with the minimum velocity factor (mvf) to decrease the missile damage.

Example: 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 (185 (=S) * 0,648 (=mvf) = 119,88). Since the speed of the Drake (140 m/s) is above the required speed (119,88 m/s), the speed affects the missile damage. The damage is determined by (S/E*Ve/Vt)^(ln(drf)/ln(5.5) * base damage (=150), the damage is ~135.

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 by (S/E*Ve/Vt)^(ln(drf)/ln(5.5) * base damage, the damage is ~125. (10 damage less)

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 anymore. The damage is determined by (S/E)* base damage (=150), the damage is ~ 135.

Example 4: The heavy missile has a mvf of 0,648 The drake fits a Core X-Type 100MN MicroWarpdrive, increasing the speed by 500 %, the maximum speed is 700 m/s, signature radius is increased by 400% to 1140m.

Required speed is therefore changed to 738,72 (1140(=S) * 0,648 (=mvf) = 738,72). Since the speed of the Drake with a MWD (700 m/s) is below the required speed (738,72), the speed does not affect the missile damage anymore. The damage is determined by (S/E)* base damage (=150), the damage is ~ 125.

As one can notice, the damage from example 3 is the same as example 1. This is to be expected since velocity and signature radius increase at the same factor. The use of the MWD on this ship does not increases the missile damage upon usage. Rather then an Afterburner it does not decrease the damage either.

If the a module or skill is able to increase the speed above the minimum threshold, this will decrease the damage a ship takes (speed tanking missiles). The MWD can also decrease the missile damage if the signature size penalty is smaller then the speed bonus are identical.

Increasing Missile Damage

There are many things a player can do to increase thier missile damage.

Skills

• Guided Missile Precision

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

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

Warhead Upgrades provides a straight forward 2% increase in missile damage per level.

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 System

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.

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

Target Painters can increase the signature size of the ship by a percentage.

• Stasis Webifier

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 is essentially 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.