ROFLkets

Okay, the supposedly rocket-proof glass hadn't stood up, when it came to it, to an actual rocket, but then that had been a rocket that had been fired at very short range from inside, which probably wasn't what the engineers who designed it had had in mind.

--Douglas Adams

Last week I mentioned Rockets vs. Turrets on the Vengeance and promised a more in depth look at them in a future post.  Well, look at that.  It's the future.  And here's that post.

Back when I very first started playing EVE Online, and I'm talking week 1 here, I started looking through all the different ships available to fly.  Knowing almost nothing about the ships themselves, one thing struck me above all else.  Khanid ships were sexy.  Sleek Amarr designs coupled with black glossy paint jobs just oozed cool.  As I began researching those Khanid ships that I could fly the soonest, the frigate line, one response from other EVE players was more common than any other, "ROFLkets are terrible."

To understand why Rockets were terrible, we need to understand a few things about Missile Launchers in general.  Rockets suffer from the same drawback of all missile systems, namely that they do less damage the smaller and faster your target is.  That's sort of a broad statement, since Turrets suffer from exactly the same thing, so let me clarify.  Turret's use Tracking to hit their target, and due to the added attribute of Signature Resolution do less damage to smaller targets.  So a small target takes less damage and a suitably fast target has the potential to take no damage at all.

Missiles have similar attributes, of note that the attribute is actually part of the ammunition and not the Launcher this time, called Explosion Velocity and Explosion Radius.  Whereas Turrets care about the Angular Velocity relative to the ship they're firing from, Explosion Velocity cares only about the speed the target ship is moving when it's hit.  Explosion Radius and Signature Resolution are practically interchangeable in concept, however.

Similar in the way that Turrets of each type come in two flavors, short range and long range, Missile Launchers also come in two varieties for each size category.  On the one hand, you have short range yet faster firing Unguided Missiles such as  Rockets,  Heavy Assault Missiles and Torpedoes on the other long range slow firing Guided Missiles such as the Light Missiles, Heavy Missiles and Cruise Missiles.  Throwing all this slightly out of balance are the Assault Missile Launchers, which are a Cruiser-sized Launcher with Light Missiles designed to shoot at Frigates.

The problem was that Rockets hadn't been scaled well.  Rockets being the smallest of the Missile Launchers they were designed to be used by Frigates, and against other Frigates they were practically useless.  Here's where Guided versus Unguided missiles finally comes into play.  The Unguided variety don't receive a bonus from the Guided Missile Precision skill.  While greater damage to small targets would be great in a larger ship, when you're flying a small target yourself, you need to be able to damage other ships your own size.  As a point of reference, Rockets used to see reduced damage anytime their target was going more than 5.5 times faster than their Signature Radius in m/s.  In other words, a frigate going faster than 200m/s saw reduced damage from ROFLkets.  Having all this explained to me, I began to weep for my shattered dreams of flying Khanid Frigates.

As though they had heard my sobs, CCP stepped down from their mighty Citadel In the Clouds (What do you mean CCP doesn't live on Mt. Olympus?  Lies!  Lies I say!) to announce that the Incursion expansion would bring with it a "Rocket Buff".  My dreams renewed, I began training once again for my Khanid frigates sure that no one would ever laugh at my hopes of using ROFLkets again.

Once I had adequately trained to use Rockets, the Rocket Buff came and I again went to older more experienced players to ask about their use and this time I got a different response, "They used to suck, but I haven't tried them since the Rocket Buff."  It seemed that this was one question that couldn't be answered by experience, since no one had experienced Rockets v2.0 for themselves.

So I began to dig into exactly how Rockets did their damage.  My completely naive understanding of Missiles had led me to believe that they were popular in PvE because they were "simple" when compared to the Range/Falloff and Tracking calculations needed for Turrets.  I couldn't have been more wrong.  The formula for calculating Missile damage follows...warning, Maths Ahead!

Damage = Base_Damage * MIN((MIN(sig/Er,1),(Ev/Er * sig/vel)^(log(drf)/log(5.5))

What.  Yeah, that was pretty much my first reaction too.  Let's start by breaking this thing down a bit.  First up, a key of sorts.

Base_Damage = The Damage value found when you Show Info on the Charge.

MIN = A database function used to find the minimum value.

sig = The Signature Radius of the Target after Guided Missile Projection is applied. (Doesn't affect unguided missiles)

Er = The Explosion Radius of the Charge.

Ev = The Explosion Velocity of the Charge.

vel = The Velocity of the Target after Target Navigation Prediction is applied.

log = The natural logorithm, also expressed as LN.

drf = The Damage Reduction Factor found when you Show Info on the Charge.

5.5 = oaeDamageReductionSensitivity which can be found in the database, or through EVEMon.

Now, the first thing you'll notice is that the formula uses the MIN Function to grab the smaller of sig/Er or 1, and the smaller of that or the rest of the formula.  In practical application, this prevents you from getting a multiplier to damage if the Signature Radius of your target is larger than the Explosion Radius of your Charge, while still giving you a penalty to damage if the reverse is true.

Since I'm just looking at Rockets in this discussion, we can further simplify the formula by plugging in some of the values for Rockets with level V skills.  Tech I, Faction, and Javelin Rockets all have an Explosion Velocity of 225 with an Explosion Radius of 20 giving us 11.25 when one is divided by the other.  Tech I and Faction Rockets both have a Damage Reduction Factor of 3, the log of 3 being 0.4771ish so when divided by the log of 5.5 we get 0.6444ish.  Javelin Rockets have a DRF of 3.2, the log of which is .5051ish and 0.6823ish when divided by the log of 5.5.  Lastly, Rage Rockets have a DRF of 4.5 the log of which is .6532ish and 0.8823ish when divided by the log of 5.5, but Rage also have an Ev of 210 and an Er of 30.  This causes Rage to be affected by speed to a lesser extent than the others due to the exponent being closer to 1, but their lower Ev to Er ratio causing it to happen at slower speeds of the Target.  The only thing left unknown is the sig/vel of our theoretical target.

Since we already know that we're limited to a maximum value of 1, the only time the sig/vel matters is when that ratio exceeds the Ev/Er ratio, or 11.25 for Tech I/Faction/Javelin and 7.0 for Rage.  Looking at the Rifter as an example target, Rage rockets only do 29% of their potential damage against a speed fit AB Rifter at an effective velocity of 1000m/s after Target Navigation Prediction is applied.  Caldari Navy Rockets against the same target still do 55% of their potential.  Slap a web on it, and we're looking at 58% and 92%.  Caldari Navy is now doing practically max damage with every hit, keeping in mind that the Rifter will be turning and not always at full speed upon impact.  Reaching speeds of this nature requires a pretty dedicated fit on the Rifter, with speed rigs and mods in the lowslots.  With the TNP skill at V, when looking for quick reference on how much damage you'll be doing you could estimate max damage when your target is going less than 22.5 and 14 times its signature radius for Faction and Rage respectively.  

Which brings me to my next point, when Rockets actually hit their targets.  Unfortunately for the Rocket user, that amazing 10km Range that you're always hitting within is a lie.  Three factors converge to limit the overall range of any missiles, but due to their comparatively short 3 second flight time, they are particularly limiting to Rockets.

First up is acceleration time.  Missiles do not leave your launchers at full speed.  They accelerate to that speed within the first tick (around 1 second) after they're launched.  Since Rockets are only in motion for 3 seconds, losing out on a full second can severely limit their range.

Speaking of ticks, all missiles only adjust their course once every tick.  Again, due to the Rockets short flight time, this can lead to Rockets missing a frigate sized target as they only get at most three course corrections before they disappear.

Finally, all missiles launch out the front of your ship.  Similarly to Bombs launched from a Bomb Launcher, a missile's initial trajectory is determined by the direction your ship is facing when they're fired.  In a dogfight between two Frigates in which they're both orbiting, rarely is your ship actually pointing in the direction of your opponent.  

All this can mean your three second flight time is eaten up by 1 second of the Rocket flying out of the front of your ship in the wrong direction and about half a second as it backtracks in the right direction.  Giving it only about 1.5 seconds actually moving towards your target, giving realistic ranges closer to 5km.  All missiles see this slight reduction in maximum flight times, but Rockets suffer so dramatically since 5km is half of their total.

What does all this really mean?  Well, Rockets aren't awful anymore, but they're also not Press F1=Win.  I'd say they're pretty well balanced as weapon systems go, just don't use them without a web against a Frigate. Rage will actually perform better against a Frigate doing less than around 600m/s, due to its increased base damage.  Against anything larger than that, you'll be doing just fine even with Rage and no Web.  Against anything smaller, ie Drones, just don't use Rage since that initial sig/Er operation will be decreasing your max damage by 1/6 before speed is even taken into account.

Regarrrds,

FNG

PS  I should probably just go ahead and say that there are a couple of assumptions being made during this post.  The biggest being that the formula presented here is correct.  Well, it's not.  CCP has actually stated post Rocket Buff that this formula is incorrect, but has not given the actual formula for missile damage.  They've also stated the formula is close, and gets the relationship of Er/Ev/Sig/Vel right.  It's assumed that they're not using Log for the calculation, since a computer would handle Exponential calculations much slower than even very complex Addition/Subtraction/Multiplication/Division.  So while the formula is (relatively) easy for a human with only eight operations, a computer would handle it slower than something with many more operations but no exponents.  

The other thing to mention is that these calculations and EFT disagree.  Since the author of EFT doesn't release his code, I can't say for certain how the EFT damage graphs calculate missile damage, but I will say that they're incorrect.  The easiest way to demonstrate this is to just look at the ranges given, which are a flat Velocity x Flight Time.  This isn't how it works out in the actual game.  After some very short testing on my own, I found at most a 2% margin for error between this formula and Sisi.  Most likely, that large of an error was due to rounding more than anything as other people have found it to be much more precise.  So while common advice for this sort of thing is to not bother doing it yourself and just run DPS Graphs in EFT, I've not found EFT to be accurate when it comes to missile damage.