Azrak has deciphered my equation correctly. 

 EDIT:  To further clarify, the equation locks like this:

(1-bypass_percent)*damage_per_volley*mitigation + bypass_percent*damage_per_volley = pwned

So it's confirmed that phase missiles bypass mitigation, then?

Ah, jolly good. I kept hearing it as being "Probably bypasses mitigation", but no actual confirmation either way.

Yeah, but you included the nano-bomb.  What does that Advent equation look like when you have level 3 detonate AM?

Also, you're equations are extremely hard to follow with all the equal signs.  Also, you are comparing 2 different races.  You have to play to each one's advantage.  Also, note that the 1200 hp loss from nano-bomb comes from 40 seconds, it's not instant.

And another thing, the 4000hp is for a level 1 progen.  If you're doing late game fleets (i.e., 30% phase bypass), your progen is probably level 5 at least, so 7000hp is more reasonable.

You'll have to rework that equation, How, Halycon decreases weapon cooldown, that's far from a plain dps-% increase. E.g. 50% cooldown reduction result in 100% damage increase.

Sorry Ill try to make things easier to read from now on.Level 3 det does 33 dps.So you could just add 33.The actual 1200 hp instant loss is not from the nano but rather from the -6 armor and 30% shield bypass.If you calculate for 7000 hp then the hp loss goes up to 2100. It is my understanding that 1 armor is = to 5% hull.

I factored in the 30 dps from nano on top of the dps for the 20 kanracks(160+(egg30)=190 mitigated damage per sec).

I think advents main advantages are its cap ships and its shields.

Azrack is right. Each level from the haly adds 1 dps to an illum. Taking its max dps to 26.You can get 35 on the destra which is all great unless you have to keep the thing on the sideline.

Illums-30x26/2=390. The 3 sec volley =1170.So first shot is 995 and every shot after is 410.So I got 47 seconds to kill the cap ship.

Kanracks-With the 2100 hp factored in I get the cap lasting 19 sec.

I left the 30 nano dps and the am det 33 dps out of these.

Good point about the side beams killing things at the same time.It looks to me it would take 2-3 volleys(im unsure of the kanrack total hp).Lets say 2 which would be 6 sec.Since it is divided by 2 sides we have to cut that in half so every 12 seconds 2 kanracks would be destroyed.So by the time your cap is dead you killed 2 kanracks and his cap still has over 50% hull .Now that the haly is dead you probably lost more dps from its bonus then he did from the ships.Also the vas lost less than 1\3 the resources the advent player lost.The vas still has 28 sec to retreat his cap which is still more time than the advent player had by 9 sec.

Good point about damage multiplier.

lol. advent. mobility oriented?. and you can't compare detonate AM to nano-bomb. it doesn't affect your damage dealing ability except a stragith damage/second. it doesn't affect armor/shield mit. and everyone's assumptions are flawed until someone can prove that phase missiles bypass shield mitigation.

and go look at my post on illum's. the side beams each only do half the damage of the main beam.

crash we have the side beams factored in. we know that they do half

OK, math informs us as to what is possible, but does not equal gameplay.

An assailant without phase missile upgrades has the crappiest damage of all the LRF.  (LRM are much cheaper, so they supply DPS with numbers.)  Luckily phase missiles are good, so with a couple upgrades the assailant dps becomes "acceptable".  This is how it should be, because Assailants are tech level 1 while Illuminators are tech level 3.

The time counter to escape your cap ship does not start with the first volley hitting it.  It starts when you see a pack of LRF entering the gravwelll and heading for your position.  While Assailants have good range and strong focus fire, they stop moving to shoot.  Once you get a pack of Illuminators on you, you better be able to survive long enough to get out of the gravwell because they will be doing continuous damage as they chase your capital to the edge.  Assailants will only fire intermittently when chasing as they fall into and out of range.  They are also not as well positioned to chase the fleeing capital to the next gravwell because of their longer engagement distance.

Yes, a Vasari Egg with Assailants will get first kill on the Advent capital ship with equal Illuminator escort.  BUT:
A.  The Vasari Egg will then be killed by the Illuminators because it is too late to get away.
B.  The Illuminators would then clean up the Assailants resulting in a net victory for the Advent player.
C.  Assuming the Illuminators and Assailants had tech level 6 weapons upgrades, these wouldn't even be the fleet compositions!  I almost never even get the final Phase Missile upgrades before I have won most multiplayer games.
D.  No Vasari player worth his salt is going to suicide his treasured magical level 6+ Egg to take out some crappy level 6+ Advent capital; late game high level Advent capitals are much easier to get.
F.  This scenario is much more likely to occur in a real game with level 3-4 capitals and assailants with 10% phase penetration, and Illuminators that probably don't have weapons upgrades yet, but are still more dangerous than their Vasari counterparts.

All LRF have enough firepower to take out a capital ship relatively quickly.  The real issue here is not about DPS, because Vasari DPS as a whole is the lowest -- Advent is the highest.  It is because phase missiles can take out Advent caps that are under the shield restore umbrella.  It is one of the weaknesses of shield restore, which is otherwise pretty godlike in its ease of use.  For the cost of Overseers it is much harder for Vasari to keep their capitals alive, only possible with intense micro or extreme investment in overseers.

OK, now that I have made all my unhelpful observations, let me make some comments about the math.

OK, first painful point.  Why do you want to include the Egg's armor debuff but not talk about the damage included by Nano or Det. Antimatter?  You know, Detonate Antimatter might be able to prevent the Egg from using Nano in the first place?  You know a high level Radiance might also fire off Cleansing Brilliance, not to mention it probably has a couple levels of armor enhancements.  The water gets pretty muddy when you try to assume for one set of abilities and not another.  If I was going to assume my Radiance was hit by a level 3 Nano, I would also want to assume I had level 3 Det. Antimatter, 2 levels of the armor upgrade, and get 1 shot of Cleansing Brilliance before my Radiance goes poof.

Second point, why talk about volleys when the damage is already normalized as "DPS" damage per second?  Just makes the math painful.  Ships actually hit much harder than their DPS numbers, but they all have different rates of fire.  All the math has been handled for you by the DPS number on a ships info card. 

On this note, a capital under focus fire jumps to full shield mitigation very quickly.  If anything could get a "pure unmitigated volley" it is an Illuminator, because they have instant beam damage.  Phase Missiles have travel time, and if you don't include this travel time, you are "front loading" in favor of the Assailants, of course the Assailants also engage from farther out.  Because the damage is not applied instantly, and ships rarely all fire at the same time due to moving into range, aiming, etc, I think you will not see these unmitigated volleys much in practice.  It is a lot easier to just talk about DPS vs a fully mitigated target, because the numbers will still be informative, but it will cause much less trauma to people such as myself who try and follow the math.

Illuminators that have no other targets and are purely focus firing and chasing a capital are often getting to bring one of their side betteries into play depending on whether their target is leaning left or right of center.  Illuminators that are in the thick of the fight are shredding other ships.  Yes, one side beam only does 1/4 damage.  But 30 sides beams on either side hurt, and assuming a skillful Advent player, he is already shredding Assailants while he is working on killing the Egg.

Third point, you can't just remove an extra 1050 shields from the Vasari target.  That has nothing to do with shield bypass.  You are already getting extra damage from unmitigated hits.  The way shield bypass works is you remove unmitigated hits from hull first and mitigated hits from shields first.  When the shields are gone, mitigated hits then also start to get removed from hull.  For the sake of argument, your "shield bypass" number is the number of shields left on your capital when it blows up because it has no hull left.  With low levels of phase penetration, like 10%, there will be no "shield bypass".  With 30%, there very well might be over 1K of shields left, because most of the damage is coming from unmitigated hits, considering that a late game Advent capital has significantly enhanced shields and shield mitigation tech upgrades.  It is not uncommon for Advent capitals under a Progen / Guardian shield umbrella to die with almost full shields.

For purposes

Illuminators
16.6 x 1.3 = 21.58 base damage x 30 Illuminators x 0.75 front & 1 side bank = 485 DPS
MITIGATED DPS against 65% mitigation = 170 (used against shields, then hull)
Against a 3500 shield, 3500 hull capital = 7000 / 170 = 41 seconds

If you assume only the front bank is firing at the enemy capital, you get 62 seconds to kill the capital, but you should be killing other ships with the side beam damage, which is a big advantage to winning the fight despite the earlier loss of capital ship.

Assailants
13 x 1.2 = 15.6 base damage x 30 Assailants = 468 DPS
Broken Down
UNMITIGATED DPS is 30% of 468 = 140  (used against hull)
MITIGATED DPS is 70% of 468 vs 70% mitigation = 98  (used first against shields, then hull)

Unmitigated DPS vs 3500 hull capital = 3500 /140 = 25 seconds
Mitigated DPS can be discarded in this simulation because it will not bypass the shield before the hull is dead.

This is like a rule of thumb  I was trying to keep it fairly simple.  Feel free to make it more complicated by adding Nano, Det. Antimatter, Cleansing Brilliance, loss of Assailant DPS due to Illuminator side beams, missile flight time, initial volley against unmitigated shields, armor mitigation, etc.

Can we have some tests under controlled circumstances?