Tuesday, April 21, 2009

Eve Master Class - Missiles

EDIT: I've been working on this one for a couple months here and there. If any mistakes are spotted please let me know ASAP so I can correct them.

EDIT 2: Corrected mistake in terminology and added comments from Karox Lominax right into the post, clarified lack of knowledge on tech II missiles in the damage formula, and fixed wide tables which I got from Google Docs where I wrote the article oringally.

Missiles are one of the major weapon types in Eve and every faction makes some use of them with Caldari ships being the largest users and Amarr Khanid ships being the second. This post will look in depth into missiles and their mechanics.

Types of Missiles

There are two broad categories.

Regular missiles is the largest and accounts for 99% of the missiles used in the game. They are simply missiles that require an active lock and will chase the target they are fired at until they run out of fuel or are destroyed.

Friend or Foe missiles are the second type and do not require target locks to fire and will sort-of-randomly attack nearby targets in range and see some usage by pilots expecting to be target jammed. There are also Defender missiles that are only used to target incoming missiles an an attempt to destroy them before impact. They are rarely if ever used due to the fact that incoming fire usually overwhelms any defender defence and using defenders takes away from your own offence.

More on Defenders from Karox Lominax:
It might be worthwhile explaining why defenders are rarely used - specifically that they all target the closest missile if multiple launchers are fired (although in some cases, i.e. torpedoes and their tech 2 counterparts or grouped missile launchers, you may need multiple defenders to do the job), and they need to be manually activated whilst there is an enemy missile physically in space, which makes them very tricky to get the timing right.

Missiles can be divided into four sub-categories determined by their size, and each sub-category (with one exception) has short ranged (aka unguided in Eve terminology) and longer ranged missile type (aka guided). (Karox Lominx: "Technically Citadel Torpedoes are Unguided as well, just because of the terminology that they aren't affected by the Guided Missile Precision skill.") The trade off for the short range - long range missiles is that shorter ranged do more DPS.

Size
Short Ranged Missiles
Long Ranged Missiles
Frigate / Destroyer
Rockets
Light Missiles
Cruiser / Battlecruiser
Heavy Assault Missiles
Heavy Missiles
Battleship
Torpedoes
Cruise Missiles
Capital

Citadel Torpedoes

Each missile type has its own launcher and cannot be used in any other launcher with the exception of the special Cruiser / Battlecruiser missile launcher called the Assault Launcher which fits Light Missiles. Its a weapon with a faster rate of fire and more capacity than the frigate classed Standard Launcher and allows cruisers and battlecruisers to engage frigates with size-appropriate weaponry than their own heavy and heavy assault missiles. This will make more sense when we discuss damage calculations.

Karox Lominax:
Also 'each missile type has its own launcher' except for Defender missiles, which can fit into any launcher type, but the main determining factor is capacity or rate of fire - generally its thought that a fast ROF of a rocket launcher is best even if you need to reload them a lot more often.
Base Damage
Some of the best advantages of missiles compared to turret based weapons is that they always hit (assuming range and target is not faster than missile) and every missile type comes in four versions, one for each damage type. The latter point means that missile ships can choose the damage type to use against particular targets.

Furthermore, with the exception of Citadel Torpedoes every missile has two tech II versions, one for greater precision and one for improved damage. For example, there are 12 different rockets you can load in your rocket launchers: four tech I versions, four Tech II precisions versions, and four Tech II improved damage versions.

Let's look at the base damage per missile:
Size
Short Ranged Missiles
Long Ranged Missiles
Frigate / Destroyer
Rockets = 25 HPs
Light Missiles = 75 HPs
Cruiser / Battlecruiser
Heavy Assault Missiles = 100 HPsHeavy Missiles = 150 HPs
Battleship
Torpedoes = 450 HPsCruise Missiles = 300 HPs
Capital

Citadel Torpedoes = 1800 HPs

You may at first be confused by the short ranged rockets and heavy assault missiles having less base damage than their longer ranged counterparts. However, each launcher has a rate of fire (Tech I versions for demonstrative purposes):
Size
Short Ranged Missiles
Long Ranged Missiles
Frigate / Destroyer
Rocket Launchers = 4 sec
Standard Launchers = 15 sec
Cruiser / Battlecruiser
Heavy Assault Launchers = 8 sec
Heavy Launchers = 15 sec
Battleship
Seige Launchers = 18 sec
Cruise Missiles = 22 sec
Capital

Citadel Torpedoes = 48 sec

Dividing the rate of fire into the base damage we get the base damage per second, aka DPS:
Size
Short Ranged Missiles
Long Ranged Missiles
Frigate / Destroyer
Rockets = 6.25 HPs/sec
Light Missiles = 5 HPs/sec
Cruiser / Battlecruiser
Heavy Assault Missiles = 12.5 HPs/secHeavy Missiles = 10 HPs/sec
Battleship
Torpedoes = 25 HPs/secCruise Missiles = 13.6 HPs/sec
Capital

Citadel Torpedoes = 37.5 HPs/sec

Thus you can see that short ranged missiles do more damage per second to their long ranged siblings.

Base Range
When you look at a missile's statistics you do not see range as an attribute. Instead you see attributes for Max Flight Time and Max Velocity. The maximum straight line range of a missile is calculated by multiplying those two values.
Size
Short Ranged Missiles
Long Ranged Missiles
Frigate / Destroyer
Rockets = 4.5 km
Light Missiles = 18.75 km
Cruiser / Battlecruiser
Heavy Assault Missiles = 9 km
Heavy Missiles = 37.5 km
Battleship
Torpedoes = 9 km
Cruise Missiles = 75 km
Capital

Citadel Torpedoes = 67.5 km

Once more, Karox Lominax:
On base range its important to note that the range never quite reaches the full calculated amount due to the fact that the missiles need to accelerate when they leave the launcher, they dont leave at max speed, which cuts about half a second from the overall flight time. In addition to that, because missiles need to 'chase' their target, the range between you and your opponent can vary during the missiles flight time, possibly overextending the range.


Skills
All of the above numbers were done with Tech I basic equipment. I reality, there are a lot of factors that improve on those base values:
- Tech II equipment with better starting statistics
- Ship bonuses
- Ship modules and rigs
- Implants and boosters
- Player Skill Levels

I will quickly review the skill set that can improve missile performance.
Skill(s)
Effect
Rockets,
Standard Missiles,
Heavy Assault Missiles,
Heavy Missiles,
Torpedoes,
Cruise Missiles,
Citadel Torpedoes
The basic skill for operation of the weapons, each one adds 5% damage per level to their respective missile type.
Rocket Specialization
Standard Missile Specialization
Heavy Assault Missile Specialization
Heavy Missiles Specialization
Torpedo Specialization
Cruise Missile Specialization
The skill required for the Tech II launchers and missiles, each one adds 2% bonus to rate of fire of the respective Tech II launcher type.
Guided Missile Precision
5% per level decreased factor of target signature radius for damage calculation (next section). Affects only Light, Heavy, and Cruise missiles.
Missile Bombardment
10% per level bonus to maximum flight time.
Missile Launcher Operation
2% per level bonus to rate of fire.
Missile Projection
10% per level bonus to maximum velocity.
Rapid Launch
3% per level bonus to rate of fire.
Target Navigation Prediction
10% per level decreased factor of target velocity for damage calculation (next section).
Warhead Upgrades
2% per level bonus to missile damage.

Missile Damage Formula

Essentially the missile damage you will inflict on an enemy ship is the base damage of the missile increased by relevant skill levels you have, and then decreased by factors such as their signature size and velocity compared to the missile's explosion radius and explosion velocity (which I have not listed in this article) as affected by the skills Guided Missile Precision and Target navigation Prediction.

I've done some searching for the exact Quantum Rise era formula and this post by Stafen from Nov 2008 Eve Online forums appears to be the most accurate. If someone knows of a place listing a more accurate current formula, please contact me!

Damage = Base_Damage * MIN( MIN( sig/Er, 1) , (Ev/Er * sig/vel)^c )

where:
Base_Damage is the base damage of the missile as modified by your relevant skills
sig is the signature of the target
Er is the explosion radius of the missile as modified by your levels of the Guided Missile Precision skill, i.e. Er = base explosion radius * (1 - (level of GMP) * 0.05)
Ev is the explosion velocity of the missile as modified by your levels of Target navigation prediction skill, i.e. Ev = base explosion velocity * (1 + (level of TNP) * 0.1)
vel is the velocity of the target
c is a constant value depending on the missile type, i.e. c = 0.586 * ln(drf) where ln means natural logarithm and drf is damage reduction factor of:
- 2.8 for light missiles
- 3.0 for rockets
- 3.2 for heavy missiles
- 4.5 for heavy assault missiles and cruise missiles
- 5.0 for torpedoes

(Note: I have not found any indication that these numbers are the same or different for Tech II versions. If anyone knows, please let me know so I can update the post.)

In non mathematical terms, it means that your raw damage is reduced by either the effect of your target's signature being far smaller then the explosion radius of the missile OR the effect of the ratio of the target's signature to velocity multiplied by the ratio of the missile's explosion velocity to its explosion radius multiplied by a missile size factor, whichever is smaller.

Got that? No? Ok, try this:

To reduce damage as much as possible, a target should try and go as fast as possible with the smallest signature radius possible. Conversely, to try an get the most damage out of his launchers as possible at small targets an attacker should use missiles with a smaller explosion radius and faster explosion velocity. This is why cruise missiles are no good against regular frigates: the frigates have small signatures and the cruise missiles have large explosion radii.

For example, a Merlin with signature of 40m being hit with a cruise missile that has an explosion radius of 300m sees a damage reduction on the base damage of 87% rounded even when sitting still, which means about 39 damage per missile. However, hit that stationary Merlin with a light missile with explosion radius of 50m and the damage reduction is only 20% which means about 60 damage per missile (ignoringskills for damage and bonuses to explosion radius).

One final note: target painters and webbers help with missiles because the former increases the apparent signature of the target while the latter decreases its velocity. Micro Warp Drives may vastly increase velocity but since they increase the signature by the same amount it has no beneficial effect other than simply outrunning missiles for a while.

16 comments:

  1. Just so you know, it looks as if your tables are being hidden off to the right side. So we're only seeing like 2/3rds of the table. This looks to be because you have the width of the table set to 1139 pixels. Amazingly wide. :)

    Great blog btw.

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  2. This is excellent work!

    Good job.

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  3. You have a mixup of terminology. Guided and Unguided missiles (as determined by what is affected by guided missile precision skill) are what you have classed as long range and short range missiles, i.e. Long Range should be labelled 'Guided' and short range should be labeled 'Unguided'

    Going on to nit picking issues: It might be worthwhile explaining why defenders are rarely used - specifically that they all target the closest missile if multiple launchers are fired (although in some cases, i.e. torpedoes and their tech 2 counterparts or grouped missile launchers, you may need multiple defenders to do the job), and they need to be manually activated whilst there is an enemy missile physically in space, which makes them very tricky to get the timing right.

    Also 'each missile type has its own launcher' except for Defender missiles, which can fit into any launcher type, but the main determining factor is capacity or rate of fire - generally its thought that a fast ROF of a rocket launcher is best even if you need to reload them a lot more often.

    On base range its important to note that the range never quite reaches the full calculated amount due to the fact that the missiles need to accelerate when they leave the launcher, they dont leave at max speed, which cuts about half a second from the overall flight time. In addition to that, because missiles need to 'chase' their target, the range between you and your opponent can vary during the missiles flight time, possibly overextending the range.

    Finally, its been mentioned, but the right side of the post is hidden as well.

    ReplyDelete
  4. Oh yeah sorry, one more thing to add, technically Citadel Torpedoes are Unguided as well, just because of the terminology that they aren't affected by the Guided Missile Precision skill.

    ReplyDelete
  5. Yes, the right end of the sentences is cut off. I've dragged my window about as wide as I can. I'm using Firefox.

    ReplyDelete
  6. Question about the DRF: at one point I found info that showed tech II missiles had different DRFs than their tech I counterparts. Do you know if this has changed now? Sorry I can't find the source of my original info, but I think it's older than Stafen's post.

    Luccul

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  7. You can read the whole text via the RSS feed, nothing was cut off for me in there.

    I've always been hesitant to try missiles because of one confusing fact. Like all other weapons there's two types, generally separated by range band. The two types of missiles are, confusingly, missiles and rockets. I've always wondered if various boosts to, for example, 'missile damage' applies to all missiles(rockets and sub-type missiles) or just sub-type missiles.

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  8. @All: fixed the width issue. I wrote the doc in Google Docs and copy and pasted into blogger. I didn't notice in my quick look that it went off the side. I put it at 100% instead of 1139 pixels.

    @Karox: unguided versus guided - what the heck? Totally unintuitive naming convention LOL. Oh well, learn something new every day. Fixed the post and added your comments on defenders.

    More info on missiles can be found here:
    http://wiki.eveonline.com/wiki/Missiles

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  9. Very nice work mate!!!

    ReplyDelete
  10. This is fantastic. Really nice job Kirith.

    ReplyDelete
  11. Nice one Kirith, clear up alot of things for me, thx

    ReplyDelete
  12. Okay all is great stuff!

    One question I don't get from all ammo/missiles.

    What is base shield/armor damage? It is listed on the bottoms under attributes.

    What the heck does that mean?

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  13. As far as I know, they are meaningless legacy numbers.

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  14. Thanks for the explanation of FoF missiles, was looking for it.

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  15. Hi Kirith,
    the DRF numbers you are looking for for the T2 ammo?

    They can be found ingame by showing info on the charge, and they are a little different.
    Taking standard missiles as an example
    DRF
    std: 2.8
    Prec: 2.6
    Fury: 3.2
    As I understand it this means that the precision charges lose less to speed/size compared to std while the furys lose more than normal.

    P.S apologies for the grave dig I needed a introduction to base a missile info post on our forums on so I linked your post.

    ReplyDelete

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