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Damage
From EVEWiki
Contents 
Hit Points
Ships in EVE have three wells of hit points: shield, armor, and structure (or hull). When a ship begins receiving damage, damage is dealt to the shield first. If the ship's shield is depleted, damage is then dealt to the ship's armor. If armor is depleted, damage then goes to structure. If a ship is reduced to 0 structure it explodes, destroying the ship and most of the modules equipped on it.
Damage Types and Resistances
There are four damage types:
Damage to shields or armor is reduced by that subsystem's resistance to that type of damage before being applied. For example, consider a ship with 500 shield points and 60% shield resistance to explosive damage. If that ship were to be hit with 150 points of explosive damage (from a Havoc Heavy Missile, for instance), that ship's new shield total would be:
 500  ( ( 1  .6 ) * 150 ) =
 500  (.4 * 150) =
 500  60 =
 440
Faction Damage Types  Strengths and Weakneses
Faction  Names  Damage type to shoot  Damage type to resist 
Amarr Empire 
Amarr 
Explosive EM 
EM 48% 
Angel Cartel 
Angel Domination 
Explosive 
Explosive 59% 
Blood Raiders 
Blood Corpior 
EM Kinetic 
EM 45% 
Caldari State 
Caldari 
Kinetic 
Kinetic 73% 
CONCORD 
CONCORD 
Kinetic 
Kinetic 28% 
Gallente Federation 
Gallente 
Thermal Kinetic 
Kinetic 44% Explosive 0% 
Guristas Pirates 
Guristas Pithum 
Kinetic 
Kinetic 84% 
Mercenaries 
Mercenary 
Kinetic 
Kinetic 
Minmatar Republic 
Minmatar 
Explosive EM 
Thermal 8% Kinetic 19% 
Mordu's Legion 
Mordus 
Thermal EM 
Kinetic 81% Explosive 0% 
Rogue Drones 
Alvatis 
EM 
Explosive 55% 
Sansha's Nation 
Sansha Centior 
EM Kinetic 
EM 60% Explosive 0% 
Serpentis 
Serpentis 
Kinetic 
Thermal 62% 
Turrets (and Drones)
Optimal Range
The Optimal Range is the innermost sphere surrounding your ship on your tac array. You can observe this sphere, in flight, by turning on the tac array (radial button with many circles on the left), then hovering the mouse pointer over the button of an equipped turret (loaded with ammunition if needed).
If you are AT or BELOW Optimal Range, then your accuracy is unaffected by this variable. If you're ABOVE... well, then you're not in Optimal Range anymore... you'd be in Falloff Range, and thus subject to the effects of Falloff.
That's it. That's all there is to it.
Falloff Range
The Falloff Range begins just beyond the edge of the Optimal sphere. Likewise, you'll be able to see the Falloff sphere just outside the Optimal sphere.
It should be noted that Falloff range is always ADDED to Optimal range... so if the Optimal range is altered in any manner, the Falloff range is also altered as a consequence. It is also, therefore, not possible for the Falloff sphere to be "inside of" the Optimal sphere.
At the very beginning of the Falloff sphere, you won't notice much of a difference in shot accuracy... but as you get closer and closer to the edge, your accuracy begins to go down. At the very edge you'll have a 50% hit chance, roughly (and not counting other accuracy modifiers). Worse, if you actually do hit, the damage is reduced by about the same amount as your accuracy (in percent). If the target moves beyond the Falloff sphere, and it continues to degrade. If the target resides at about double the Falloff range, you have almost no chance of hitting your target.
Taking long shots at the edge of your Falloff sphere is not necessarily a bad tactic... each individual shot may have low accuracy, but that accuracy will be tested multiple times per volley if you have many turrets firing at the target. You may, indeed, be able to hit many times within a short time period anyway... and even if the damage quality isn't nearly as high, it may be enough to deal out healthy amounts of damage, while avoiding that of your opponents. NPC opponents tend to be weak anyway, so you can often use this method to finish them quickly, regardless.
Note: Ammunition types affect your optimal range, and consequently, your falloff range.
Signature Radius and Signature Resolution
Turrets have a Signature Resolution, measured in meters. Ships have a Signature Radius, also measured in meters.
By having a smaller Signature Radius than the Signature Resolution of the attacking ship's turrets, turret accuracy is reduced. Similarly, having a larger Signature Resolution than the attacking ship's turrets will boost enemy turret accuracy.
However, this relationship is only a variable to Tracking Speed. If the ship being fired upon is stationary, Signature Radius and Signature Resolution will have no effect on turret accuracy.
Tracking Speed and Angular Velocity
Turrets have a Tracking Speed, measured in radians per second. When the imaginary line connecting two objects changes its angle, this generates Angular Velocity, also measured in radians per second. If you wish to observe this effect, you can leftclick on the target once to place the selection box on it, and observe the connected line that appears.
The speed, angle and distance between two objects will affect the radians per second generated. Steeper angles, faster speeds, and closer distances make the imaginary connecting line move faster, while the opposites will cause it to move slower.
Turret Tracking Speed is not simply "enough" or "not enough" to hit. If you have half the speed of the Angular Velocity, it will modify your tohit chance by reducing it by half. If you have double, then the hit chance is doubled.
Turrets in EVE are not "simulated". That means that the graphics representing your turrets on your ship are purely decoration. They do not have to turn in realtime. This means that if a ship were to somehow suddenly move very fast in across your bow for a moment, then start moving more slowly, the calculations would be based only on the speed, distance, and heading the ship currently possesses.
Signature Radius and Signature Resolution work in conjunction with these variables. Having a smaller Signature Radius on your ship versus the Signature Resolution of the enemy guns will cut down your accuracy by modifying the value first given out by the tracking and angular velocity relationship.
All of this taken together has the following consequences:
 A slow moving ship making very tight loops may be able to evade fire by the simple fact that it is close.
 The effects of having double the SigRad of an enemy gun SigRes (i.e. enemy lands more hits) is canceled out by the effects of having double the Angular Velocity of the enemy gun Tracking Speed (enemy lands less hits).
 If both ships are stationary, turret accuracy can only be affected by Falloff... and will otherwise be 100% with all turrets. Signature Radius/Resolution does not come into play at all unless one of the ships is moving.
 However, a ship moving slowly (say, 20 meters per second), but having an extremely favorable signature radius versus the enemy guns, will still generate high evasion.
 Orbiting a stationary ship will generate Angular Velocity, and may cause misses depending on how much.
 Two ships orbiting each other "consensually", causing an effect where each ship is moving in a circle at opposite ends, with one ship always to the others side... will generate Angular Velocity. A very high amount of it at that.
 To cancel out the angular effects of another ship, you must move in a direction and speed that causes the imaginary "angular line" to be pointing in precisely the same direction for as long as possible. This can be difficult if the enemy chooses "Orbit", as their ship will automatically adjust on the fly. In that case, you must skew the orbit by flying straight, then cut down and across to the outeredge of their orbit. You can take advantage of the fact that they must travel further around in a circle than you do in a straight line. Just don't expect them to sit there and do nothing about it  be ready to make course corrections.
It should be noted that this is a "twoway street". There is one Angular Velocity value generated for a pair of objects. This means that if you orbit a stationary target, Angular Velocity will still be generated and affect your turret accuracy.
There is an Angular Velocity indicator that can be turned on in the overview. It doesn't take into account Signature Radius or Resolution, so be certain to adjust it in your head accordingly.
Zero Meters Accuracy
You are now able to fire and hit targets at 0m as of the 1.5.1 Apocrypha patch.
Missiles
Explosion Velocity and Explosion Radius
Missiles have an Explosion Velocity and Explosion Radius.
If the missile's Explosion Velocity is equal to or greater than the ship's current velocity, the damage will be unmodified by this variable. If it is less than the ship's velocity, it will be reduced by an amount proportionate to the difference.
If the missile's Explosion Radius is less than or equal to the ship's Signature Radius, the damage will be unmodified by this variable. If it is greater than the ship's Signature Radius, it will be reduced by an amount proportionate to the difference.
The result is that a good Explosion Velocity cannot make up for a poor Explosion Radius, or viceversa. This is contrary to turrets, where a good Tracking could make up for bad Signature Resolution, all the way up to 100%.
Missile Velocity and Flight Time
Missiles fly at a certain speed through space, and can fly for so long. You can use these variables to gauge the maximum range of a missile, although this assumes a straight flight.
It is possible to fly fast enough that missiles can't even touch the ship. Usually you can only accomplish this by use of a MWD.
Bombs, Smartbombs, and Doomsday Devices
These 3 weapons have no modifiers to their damage, other than resistances or bonuses gained from ship abilities or equipment.