Drop your PvE ways for PvP and sooner or later you're going to hear the phrase "damage projection" or talk about a ship's ability to "project damage." And this is just a fancy of stating or asking, "How good is a ship at applying its DPS at range?" A railgun ship has lower-than-average DPS but has excellent damage projection. Whereas a blaster ship has fantastic DPS but very poor damage projection. Going back to Rote Kapelle's AT10 Finals match against Verge of Collapse, the major reason we lost that match was because the Verge Sleipnirs were able to project damage and our Vindicator and Kronoses were not (in that case, thanks to Verge e-war). As a result, Verge was doing full DPS and we were only doing partial DPS or no DPS.

Damage projection is a big deal.

But how does it work in practice? To demonstrate, I'll stick with PvE examples, but they apply more or less equally to PvP. Warning: scary math follows. For the purposes of this post I'll disregard tracking and resistances and mostly assume that all ships can apply DPS equally regardless of damage type. I'm ignoring implants. I'm also mostly assuming MWD-fit ships throughout with otherwise pretty typical fittings.

By doing so, by the way, I'm giving short-range weapons a significant advantage since most PvE ships -- particularly high-sec PvE ships -- fit afterburners, not MWDs. But let's stick with what we have.

Let's start with an example using blasters. Our first test case ship will be a Talos using Neutron Blaster Cannons using both Null and Void ammunition. With two Tracking Enhancers, the Void range is 9+10km. The Null range is 16+29km. The target will be a rat battleship at 50km initial range with 20k EHP. How long will it take the Talos to destroy the rat?

With Void ammo at 9km range, it will take the Talos only 16 seconds to destroy the rat, but from a standing start it will take the Talos 34 seconds to cross the 41km to get within 9km (trust me on this). The Talos can project one-half DPS at 16km range and one-quarter DPS at 19km range. But beyond 25km, the Talos will be doing little or no damage. So for the first 22 seconds, the rat takes almost no damage at all. Over the next eight seconds, it takes an average of about 600 DPS. The Talos reaches optimal range and 11 seconds later, the rat is dead. That's 41 seconds for the Talos to kill this rat using Void.(1)

If the Talos uses Null instead, it will take the Talos 23 seconds to destroy the rat at 16km range. But the one-half DPS point is about 38km and the one-quarter DPS point is about 48km. The rat will actually take a small amount of DPS even at 50km and the damage will rise quickly as the Talos accelerates. Over the first nine seconds, the rat will take about 250 DPS average. Over the next 12 seconds, it will take 550 DPS average. The Talos reaches optimal range a few seconds later and needs 13 more seconds to kill the rat. That's 34 seconds for the Talos to kill the rat using Null, seven seconds faster than the higher damage ammo.

In the first case, the Talos needed 29 seconds to reach its optimal range and its damage projection beyond that range was extremely poor. The rat was at about 80% EHP when the Talos reached optimal. In the second case, the Talos needed 26 seconds to reach optimal range but reduced the rat to about 45% EHP during the acceleration phase. Damage projection was much better in the second case.

I warned you this was scary math. ;-) But you don't really need to know the math in practice. You just need to have a feel for your ship's ability to project damage. Blaster Taloses using Null project damage very well even at long range assuming they can hit the target at all. That's the whole tracking topic.

Now that you understand damage projection, let's look at Retribution-era Drakes using both HMLs and HAMs. We'll stick with our 20k EHP rat at 50km range and we'll keep drones out of it.

Missiles greatly simplify the math, particularly if we ignore missile acceleration. Let's start with T1 missiles. Retribution-era HML Drakes will be doing 335 DPS at 63km. The Drake doesn't have to move though if it does it might save seven missiles by not launching a final futile volley. The rat dies in 62 seconds regardless.

If the Drake switches to Fury missiles, it will do 450 DPS at 29km. But it will take the Drake (at best) 22 seconds to get within that range, plus two more seconds for the first missiles to fly to and hit the target. During the first 24 seconds, the Drake does no DPS at all. Once the Drake's in range, it takes 44 seconds to kill the rat, or 68 seconds total.

Again, despite higher damage ammo, the weapon with the best damage projection wins. Let's see what happens with HAMs.

With a 20km range, a HAM Drake with T1 missiles does 465 DPS maximum. But a maxed-out DPS HAM Drake is slow. I won't run you through the whole set of math; just trust me when I say that this case is comparable to the HML Fury Drake, only slower. It takes the T1 HAM Drake 72 seconds to kill the rat. Javelin HAMs do 334 DPS at 30km. Unlike the Talos above using long-range T2 Null which was clearly superior, this case is worse than using either using Fury HMLs or T1 HAMs. It takes 59 seconds to kill the rat

*after*you spend 22 seconds getting into range and waiting two seconds for the first volley to hit. That's 83 seconds.

Note to

**CCP Fozzie**: either Javelin range or damage should

*definitely*be increased a bit. Even with the ship velocity penalty removed, it seems clear there will be no reason to ever use them.

That leaves Rage HAMs. And this case is kind of interesting. Rage HAMs will be doing 625 DPS maximum at about 17km. That's 32 seconds to kill the rat. But again, a Drake fit this way is slow. It will take 36 seconds at best to reach firing range, meaning it will again take 68 seconds total to kill the rat. This is still worse than our HML Drake firing T1 missiles. Still, 36 seconds to kill a battleship rat with a Drake is pretty good.

Man, this is a long post. Stay with me.

Overall, I think it's very clear that even with the nerf, HML Drakes will still be superior at damage projection than their HAM counterparts and therefore will still have a niche in PvE. This niche will be broadened if the kinetic damage bonus is removed and a rate of fire bonus is given instead when BCs are rebalanced next year. Why are HAM Drakes superior in PvP, then? Because a PvP Drake will be using faction HAMs to boost DPS even further and over-heating to mitigate the HAM Drake's speed penalty, two things that aren't generally done in PvE.

So what happens with Tengus?

Our test case HML Tengu will be an afterburner-fit SSB-tank four-BCU model using faction BCUs and six launchers. This is expensive, but pretty typical of pure PvE Tengus. Once Retribution hits, this Tengu will be doing 500 DPS at 95km with Heavy Missiles. Our test rat dies in 40 seconds; the Tengu doesn't have to move. Switch to Fury HMLs and the Tengu does 675 DPS at 47km. The Tengu needs to move slightly but only needs five seconds to get into range. The rat dies in 36 seconds total.

HML Tengus are still clearly going to be the go-to PvE option, even post-Retribution with their damage reduced somewhat.

HAM Tengus, though, are about to become a slightly more interesting. To date, it hasn't really been possible to fit a good PvE HAM Tengu. There are a lot of niggling fitting issues that force you into an unacceptable compromise. You invariably run into a grid issue. The thing is... that grid issue is about to go away. Once Retribution hits, trade out HMLs for HAMs, trade out the AB for a dead-space MWD, and trade out one BCU for a PDS. And suddenly all of it fits just fine and is still cap stable.

And it's doing 590 DPS with T1 missiles and 800 with Rage HAMs. ...huh. Let's focus on the T2 ammo.

HAM range is only 27km but with a MWD, the Tengu is more than capable of closing range. The little-used Gravitational Capacitor subsystem provides the best base speed boost, making our Tengu capable of 1360m/s. The Tengu needs only 18 seconds to close range and with Rage HAMs, the rat is dead in 25 seconds. That's 43 seconds total, which is still worse than both T1 HMLs and Fury HMLs, of course.

Even for Tengus, HML Tengus are going to keep their PvE niche post-Retribution, no problem.

But suppose you have a cluster of three battleship rats in close proximity. Suddenly the math changes markedly. Our Fury HML Tengu spends 5 seconds getting into range, then 36 seconds three times killing the three rats. That's 113 seconds total. But the Rage HAM Tengu needs 18 seconds to get into range, then 25 seconds three times. That's 93 seconds total, 20 seconds faster. The same gap exists between Fury HML Drakes and Rage HAM Drakes, but it's (a) nowhere near as pronounced and (b) the Drake isn't even close to cap-stable in this configuration and the Tengu is.

For T1 HMLs versus T1 HAMs on a Tengu, the gap is zero. It's not worth doing.

*But*, I think this opens up some really interesting niche Rage HAM Tengu PvE possibilities.

*If*you're willing to use T2 ammo all the time and

*if*you're willing to spring for a dead-space MWD and

*if*you're mostly shooting at battleship rats and

*if*you're willing to do the extra work of motoring around from group to group...

...then I think a HAM Tengu is going to make quite a lot of sense. It'll be great for occasional battleship null-sec belt ratting for instance, or cherry-picking Sanctums or sites in null-sec regions that don't offer a lot of them. It might even make good sense in wormholes.

For everything else though, HMLs in PvE are still king, even after they get nerfed by Retribution. Wow, that was a long answer to a short question. ;-) Hope it was helpful!

(1) Remember how you told your math teacher that you'd never use higher math later in life? Most math in this post was done with differential calculus. It's what you have to do to calculate true acceleration and velocity, and changing DPS as an EVE Online ship closes range under acceleration. So "phhhbbbt" to what you told your math teacher.

I'm glad you broke it down for me. I've been worried about the PvE effects to my tengu missioner. However, I wonder about the other changes, in particular those affecting shooting frigs/spider drones. I fit 2 T2 Rigors, 1 T2 Flare. Can you work your mathemagical powers to evaluate how that will go? Thanks!

ReplyDeleteIf you're using T1 missiles today, nothing changes. Precision missile damage is being fairly substantially increased against extra-small targets, though. I'd try them out against Spiders and see if the 20 seconds you lose changing ammo there and back is worth the reduced time killing them.

DeleteAfter reading your post and the footnote regarding differential calculus, a scene from the move 40 year Old Virgin came to mind.

ReplyDeleteAt the 0:25 mark is where I think the footnote about differential calculus comes into play.

http://www.youtube.com/watch?v=DmYkt2RkhsI

While I am over 40 years old, I assure you that I am not a virgin.

DeleteLOL! No, it has to do with the remark of throwing out too many big words, and not understanding them, and since he didn't understand the words, they were taken as disrespect. Arguably the funniest scene in that movie.

Delete"If you can't explain it simply, you don't understand it well enough."

ReplyDeleteAlbert Einstein

Thanks for doing the math Jester!!

I assume you didn't mention it because it doesn't contribute much to the point you're trying to make but aren't you better off swapping ammo in several of these cases? For example a HML drake swapping to fury after 14 seconds should kill the rat in after 60 seconds total. In regards to the footnote can't you just use excel in place of the clac, assuming the small error gained will be negligible?

ReplyDeleteI'm a numbers guy on my worst day but for this topic I decided to be as precise as possible to settle the question.

DeleteAnd yeah, I considered running additional numbers for ammo switching and if this was about hybrid ammo, I would have. But for the 10 second missile reload time, the gains from switching ammo can be lost by a second or two of lost reaction time.

"Note to CCP Fozzie: either Javelin range or damage should definitely be increased a bit. Even with the ship velocity penalty removed, it seems clear there will be no reason to ever use them."

ReplyDeleteAll of your examples assume that long range ammo is used to begin putting out damage earlier as you gradually close range. That's never been the reason that Javelin was (and is) used though, the same as people generally don't use barrage while they go flying towards something. In PVP at least, it's used either when you want to kite (but didn't set out with the intention of always kiting, else you'd have fit HMLs) or when you're being kited yourself. In either scenario the extra 50% range is really handy - even with the penalties, I already carry them for both rockets and torps (I only don't use them for HAMs because I simply have no reason to use HAMs in the first place)!

Yeah, that's why Javelin Rockets are used, but I am having a hard time imagining a situation where Javelin HAMs will be used like that. Sac, maybe, possibly? The rebalanced Catalyst? A Drake using Javelins certainly ain't gonna kite anything and a Sac probably wouldn't do it much better.

DeleteI think the base damage or range of Javelin HAMs should be increased slightly.

I don't know, Drakes are better at kiting than you'd think. With the powergrid reduction on HAMs, it should be possible to fit a PODLA-style nano drake with them.

DeleteI absolutely wouldn't say no to more range or damage, but I think they'll see plenty of use either way.

Sorry, why compare large weapons with mediums? Maybe a fairer comparison would be more interesting to use a Brutix instead of Talos?

ReplyDeleteMT

The idea of the first third of the post was to explain damage projection. Blasters are the best for that, and the bigger the blasters are, the easier it is to understand.

DeleteGood point about math. Often it's good enough to have "a feel" for some thing or situation. Where math becomes useful is in separating the wheat from the chaff. Often times people will have "a feel" for something that's complete bollox. Math provides an objective means for proving that some people who seem to be morons, actually are. Math is the referee of the IQ test.

ReplyDeleteDid you use Matlab or MathCAD for the simulation, or just some spreadsheet?

ReplyDeleteNicely written, Jester.

ReplyDeleteDamage projection is something that isn't understood by most players - they tend to just look at DPS.

One additional point to make is that damage projection greatly affects your ability to tank in PVE, as well. Whereas most PVP fights are short and brutal, most PVE fights are long and kiting, requiring an active tank and a stable cap. The further you are from the swarms of NPC rats, the less aggregate damage you take. This is a large part why the low alpha, long range weapons, such as rails, still have a place in the game, despite being relatively useless for PVP.

Just a side note: There are currently already people using HAMs on their Tengus for missions, and they seem to agree that it is already worth against groups of targets.

ReplyDeleteYou may start firing later, but you kill groups much quicker already.

Short range weapons shine against groups of targets because your damage projection increase against them dramatically, as shown in your third section of your post.

I was one of the ones asking you to clarify your post about PVE being king. I see now that it will actually be better to use T1 missiles again, which is what I was missing. I typically only use T2 missiles in wspace, but with the upcoming nerf it will be better to use T1. Strange times.

ReplyDeleteits the travel time involved to get into range that is doing it to you. If you are warping in range, or damn close to it, then other missiles will kill faster.

DeleteNow when you calculated the average damage from falloff to optimal, it got me thinking. This is what I came up with. I’m interested in seeing what you did. =)

ReplyDeleteNow lets assume some things. Chance To Hit = 0.5^((distance from target – optimal)/fallout)^2 .

Now, the distance to the target is going to be decreasing linearly as we fly closer to the target. Thus why we put in a substitution into the above equation distance Distance from target = Distance from target – Velocity* Time. Where time is the variable.

Assumptions:

Distance from target = 45000m – Velocity* Time(to close with and destroy the enemy) (meters)

Velocity = 500(m/s)

Time = (Distance from target – optimal) / Velocity

Using the specs from 800mm repeating artillery II

Falloff = 19020 m

Optimal = 4800 m

Time = 0 -> 90.2 seconds

Integral from 0 to 90.2 0.5^((50000-x*500-4800)/19020)^2 dx

Comes out to 40.2841 (b) chance to hit… over time

Now that’s cool, but what does that mean? Really at the point I venture a guess that,

(Chance to hit over time * DPS) / time = DPS (from engaging to optimal over time)

I’m guessing

Which if the DPS is 500 the average DPS from engaging to optimal is ~222.84 which sounds off.

(a) http://wiki.eveonline.com/en/wiki/Turret_damage

(b) http://www.wolframalpha.com/input/?i=integral%280%2C90.4%29+of+0.5%5E%28%2850000-x*500+-+4800%29%2F19020%29%5E2+dx

Great article.

ReplyDeleteThough I would add that there really isnt anything here that a little Y = MX+B wouldnt solve.

arent the equations for damage done based off a linear equation?

optimal + fall off = 50%

and optimal + falloff = 0%

The best equation I could get for this is (see link http://wiki.eveonline.com/en/wiki/Turret_damage )

DeleteSo its not linear at all... although it would help.