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''This document is concerned only with the damage that is created when a missile explodes near a ship. It specifically does not cover aspects of [[Missilery_101|missile weaponry]] such as launcher speed or missile flight time. Nor does it concern itself with the ultimate damage to the ship, which may be [[Shield_tanking|shielded]] or [[Armor_Tanking|armored]] against the kind of damage that the missile creates.'' | :''This document is concerned only with the damage that is created when a missile explodes near a ship. It specifically does not cover aspects of [[Missilery_101|missile weaponry]] such as launcher speed or missile flight time. Nor does it concern itself with the ultimate damage to the ship, which may be [[Shield_tanking|shielded]] or [[Armor_Tanking|armored]] against the kind of damage that the missile creates.'' | ||
== The Basic Picture == | == The Basic Picture == | ||
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If both of these situations apply, EVE chooses the one that reduces the most damage. | If both of these situations apply, EVE chooses the one that reduces the most damage. | ||
{{Note box|In the simplest terms: big, slow ships usually take 100% missile damage. Small, fast ships may take less damage. It is '''NOT''' the speed of the missile that matters; but the speed and size of the explosion.}} | {{Note box|In the simplest terms: big, slow ships usually take 100% missile damage. Small, fast ships may take less damage. It is '''NOT''' the speed of the missile that matters; but the speed and size of the explosion.}} | ||
=== Explosion Details === | === Explosion Details === | ||
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As an illustration, here are the basic statistics for the Inferno Light Missile. These are sorted on Explosion Velocity. | As an illustration, here are the basic statistics for the Inferno Light Missile. These are sorted on Explosion Velocity. | ||
{| class="wikitable" style=" | {| class="wikitable sortable" style="text-align:center; text-size:90%" | ||
! scope="col" width="130px" | Missile | ! scope="col" width="130px" style="background-color:#222222; text-align:left" | Missile | ||
! scope="col" width="90px" | Explosion Radius | ! scope="col" width="90px" style="background-color:#222222;" | Explosion Radius | ||
! scope="col" width="90px" | Explosion Velocity | ! scope="col" width="90px" style="background-color:#222222;" | Explosion Velocity | ||
! scope="col" width="100px" | Base Damage (Thermal) | ! scope="col" width="100px" style="background-color:#222222;" | Base Damage (Thermal) | ||
|- | |- | ||
|Inferno Precision Light Missile|| 25 || 204 || 83 | | style="text-align:left" | Inferno Precision Light Missile|| 25 || 204 || 83 | ||
|- | |- | ||
|Inferno Light Missile|| 40 || 170 || 83 | | style="text-align:left" | Inferno Light Missile|| 40 || 170 || 83 | ||
|- | |- | ||
|Caldari Navy Inferno Light Missile|| 40 || 170 || 95 | | style="text-align:left" | Caldari Navy Inferno Light Missile|| 40 || 170 || 95 | ||
|- | |- | ||
|Inferno Fury Light Missile|| 69 || 143 || 116 | | style="text-align:left" | Inferno Fury Light Missile|| 69 || 143 || 116 | ||
|} | |} | ||
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Other classes of missiles follow the same pattern. Again, the list is sorted on Explosion Velocity. | Other classes of missiles follow the same pattern. Again, the list is sorted on Explosion Velocity. | ||
{| class="wikitable" style= | {| class="wikitable sortable" style=text-align: center; text-size:90%" | ||
! scope="col" width="130px" | Missile | ! scope="col" width="130px" style="background-color:#222222; text-align:left;" | Missile | ||
! scope="col" width="90px" | Explosion Radius | ! scope="col" width="90px" style="background-color:#222222;" | Explosion Radius | ||
! scope="col" width="90px" | Explosion Velocity | ! scope="col" width="90px" style="background-color:#222222;" | Explosion Velocity | ||
! scope="col" width="100px" | Base Damage (Thermal) | ! scope="col" width="100px" style="background-color:#222222;" | Base Damage (Thermal) | ||
|- | |- | ||
|Inferno Light Missile|| 40 || 170 || 83 | | style="text-align:left" |Inferno Light Missile|| 40 || 170 || 83 | ||
|- | |- | ||
|Inferno Rocket|| 20 || 150 || 33 | | style="text-align:left" |Inferno Rocket|| 20 || 150 || 33 | ||
|- | |- | ||
|Inferno Heavy Missile|| 140 || 81 || 135 | | style="text-align:left" |Inferno Heavy Missile|| 140 || 81 || 135 | ||
|- | |- | ||
|Inferno Torpedo|| 450 || 71 || 450 | | style="text-align:left" |Inferno Torpedo|| 450 || 71 || 450 | ||
|} | |} | ||
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While various skills improve a player's [[Missiles_101#Skills_that_affect_Missiles|expertise with missiles]], these three specifically affect the amount of damage done when a missile explodes. | While various skills improve a player's [[Missiles_101#Skills_that_affect_Missiles|expertise with missiles]], these three specifically affect the amount of damage done when a missile explodes. | ||
*{{sk|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, which makes it more likely to do full damage to a small/fast target. | *{{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}} 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|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}} provides a 2% increase in missile damage per level ... this appears to apply to Base Damage. | *{{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=== | === Modules, Rigs and Ammunition=== | ||
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[http://wiki.eveonline.com/en/wiki/Ballistic_Control_System_I Ballistic Control System]: among other things, gives a bonus to base missile damage. | [http://wiki.eveonline.com/en/wiki/Ballistic_Control_System_I Ballistic Control System]: among other things, gives a bonus to base missile damage. | ||
[https://wiki.eveonline.com/en/wiki/Item_Database:Ship_Modifications:Rigs:Missile_Launcher_Rigs Missile Launcher Rigs] | [https://wiki.eveonline.com/en/wiki/Item_Database:Ship_Modifications:Rigs:Missile_Launcher_Rigs Missile Launcher Rigs]: | ||
*Warhead Calefaction Catalyst: increases the base damage of the missile but increases the CPU requirement for the launcher. | *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 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. | *Warhead Rigor Catalyst: decreases the explosion radius of the missile but increases the CPU requirement for the launcher. | ||
[https://wiki.eveonline.com/en/wiki/Missiles#Tech_II_Missiles Advanced Tech II Missiles] | [https://wiki.eveonline.com/en/wiki/Missiles#Tech_II_Missiles Advanced Tech II Missiles]: | ||
*Precision Missiles are more effective than Furies against smaller, faster targets, but do less base damage per missile. | *Precision Missiles are more effective than Furies against smaller, faster targets, but do less base damage per missile. | ||
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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. | 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 Classes ==== | |||
*Zainou 'Snapshot' Cruise Missiles: 1% to 6% bonus to the base damage of Cruise Missiles | *Zainou 'Snapshot' Cruise Missiles: 1% to 6% bonus to the base damage of Cruise Missiles | ||
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*Zainou 'Snapshot' FOF Explosion Radius: 1% to 6% bonus to explosion radius of Auto-Target Missiles | *Zainou 'Snapshot' FOF 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' Guided Missile Precision: 1% to 6% reduced factor of signature radius for all missile explosions | ||
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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. | 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. | ||
==Technical Section: The Missile Damage Equation== | ==Technical Section: The Missile Damage Equation== | ||
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Here is the equation for missile damage: | Here is the equation for missile damage: | ||
[[Image:MissileDamageFormula.png|center|400px]] | [[Image:MissileDamageFormula.png|center|400px]] | ||
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 : | 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 : | ||
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=== Finding the Damage Reduction Factor of a Missile=== | === Finding the Damage Reduction Factor of a Missile=== | ||
The “damage reduction factor” <b>(drf)</b> of a missile is not mentioned in the game, it is however included in the | The “damage reduction factor” <b>(drf)</b> of a missile is not mentioned in the game, it is however included in the [http://community.eveonline.com/community/fansites/toolkit/ 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 – it is called the Damage Reduction Sensitivity. | ||
{| class="wikitable collapsible collapsed sortable" style="text-size:90%" | |||
{| class="wikitable" | |||
|- | |- | ||
! Missile Type! | ! style="background-color:#222222;" | Missile Type | ||
! style="background-color:#222222;" | DRF | |||
|- | |- | ||
| Precision Light Missile || 2.6 | | Precision Light Missile || 2.6 | ||
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| Citadel Torpedo || 5.5 | | Citadel Torpedo || 5.5 | ||
|} | |} | ||
=== Analysis of the Equation === | === Analysis of the Equation === | ||
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damage created = base damage * min[1, S/E, (S/E*Ve/Vt)^(ln(drf)/ln(5.5)] | damage created = base damage * 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). 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. | This means that the base damage is multiplied by the smallest of either <code>1</code>, <code>S/E</code> or <code>(S/E*Ve/Vt)^(ln(drf)/ln(5.5)</code>. 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 S is smaller than E, 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. | 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 <code>S</code> is smaller than <code>E</code>, 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. | ||
Since the part of the equation that is affected by velocity ... <code>(S/E*Ve/Vt)^(ln(drf)/ln(5.5)</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/ (ln(drf)/ln(5.5)) * E)) * Ve</code>. Since <code>1^x = 1</code>, then <code>1^(1/ (ln(drf)/ln(5.5)</code> also must equal 1, and the equation reduces to <code>Vt = (S/E) * Ve</code>. This can be rewritten as | |||
Since the part of the equation that is affected by velocity ... (S/E*Ve/Vt)^(ln(drf)/ln(5.5) ... 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/ (ln(drf)/ln(5.5)) * E)) * Ve. Since 1^x = 1, then 1^(1/ (ln(drf)/ln(5.5) also must equal 1, and the equation reduces to Vt = (S/E) * Ve. This can be rewritten as | |||
Vt = S * Ve/E | Vt = S * Ve/E | ||
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. | 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" | |||
{| class="wikitable" | |||
|- | |- | ||
!Missile ! | ! style="background-color:#222222;" | Missile | ||
! style="background-color:#222222;" | Minimum Velocity<br />Factor (Ve/E) | |||
|- | |- | ||
| Citadel Torpedo || 0. | | Citadel Torpedo || 0.0100 | ||
|- | |- | ||
| Citadel Cruise Missile || 0. | | Citadel Cruise Missile || 0.0166 | ||
|- | |- | ||
| Rage Torpedo || 0. | | Rage Torpedo || 0.0938 | ||
|- | |- | ||
| Fury Cruise Missile || 0. | | Fury Cruise Missile || 0.105 | ||
|- | |- | ||
| Javelin Torpedo || 0. | | Javelin Torpedo || 0.158 | ||
|- | |- | ||
| Torpedo || 0. | | Torpedo || 0.158 | ||
|- | |- | ||
| Auto-Targeting Cruise Missile I || 0. | | Auto-Targeting Cruise Missile I || 0.230 | ||
|- | |- | ||
| Cruise Missile || 0. | | Cruise Missile || 0.230 | ||
|- | |- | ||
| Precision Cruise Missile || 0. | | Precision Cruise Missile || 0.263 | ||
|- | |- | ||
| Fury Heavy Missile || 0. | | Fury Heavy Missile || 0.451 | ||
|- | |- | ||
| Rage Heavy Assault Missile || 0. | | Rage Heavy Assault Missile || 0.517 | ||
|- | |- | ||
| Auto-Targeting Heavy Missile I || 0.648 | | Auto-Targeting Heavy Missile I || 0.648 | ||
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| Heavy Missile || 0.648 | | Heavy Missile || 0.648 | ||
|- | |- | ||
| Precision Heavy Missile || 0. | | Precision Heavy Missile || 0.777 | ||
|- | |- | ||
| Heavy Assault Missile || 0.808 | | Heavy Assault Missile || 0.808 | ||
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| Javelin Heavy Assault Missile || 0.808 | | Javelin Heavy Assault Missile || 0.808 | ||
|- | |- | ||
| Fury Light Missile || 2. | | Fury Light Missile || 2.05 | ||
|- | |- | ||
| Auto-Targeting Light Missile I || 3. | | Auto-Targeting Light Missile I || 3.40 | ||
|- | |- | ||
| Light Missile || 3. | | Light Missile || 3.40 | ||
|- | |- | ||
| Rage Rocket || 4. | | Rage Rocket || 4.67 | ||
|- | |- | ||
| Precision Light Missile || 5. | | Precision Light Missile || 5.11 | ||
|- | |- | ||
| Javelin Rocket || 7. | | Javelin Rocket || 7.50 | ||
|- | |- | ||
| Rocket || 7. | | Rocket || 7.50 | ||
|} | |} | ||
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. | 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. | ||
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Vt = S * MVF | Vt = S * MVF | ||
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. | 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%. | 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%. | ||
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{{Example | Example 1: | {{Example | Example 1: | ||
The | The Heavy Missile has a MVF of 0.648. | ||
The Drake has 140 m/s speed and a signature radius of 285 m. | The Drake has 140 m/s speed and a signature radius of 285 m. | ||
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{{Example | Example 2: | {{Example | Example 2: | ||
The | The Heavy Missile has a MVF of 0.648. | ||
The Drake fits a | 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.}} | 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.}} | ||
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{{Example | Example 3: | {{Example | Example 3: | ||
The | The Heavy Missile has a MVF of 0.648. | ||
The | 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 * 0.648'') | Required speed is therefore changed to 923.4 (''1425 * 0.648'') | ||
Since the speed of the Drake with a MWD (700 m/s) is below the required speed (923.4 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.}} | Since the speed of the Drake with a MWD (700 m/s) is below the required speed (923.4 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.}} | ||