two things

1. most ships dont have that kind of shield to hitpoint ratio (advent trends toward more shields than armor, making them prime targets for this weapon)

2. you did not factor in shield mitigation which with ordinary weapons can reduce the damage by 15% (that is base line) or more (up to 75% with a level 10 Advent Capital ship) were as the shield penetration bypasses completely

I have seen many a ship die by the hands of the Phase Missile while still have a good portion of its shields left (after all, shields just surround the ship, the armour/hitpoints are what hold it together)

Well when the missle bypasses shield it also bypasses the mitigation. That is the key.

well the game sets up kinda like that the TEC have many advantages over the Vasari, the Advent have many advantages over the TEC, and the Vasari have many advantages over the Advent

kind of like the rock/paper/scissors game only it runs TEC>Vasari>Advent>TEC

I dont think you are getting the phase missile damage vs shield mitigation factored right, phase missile damage bypasses or is not affected by shield mitigation
hence:

at 100 damage

regular damage verse shield mitigation of 60% will only apply 40 damage

phase damage verses shield mitigation of 60% will apply 40 damage plus 30 damage directly to hull

leading to

regular -116 hits to remove shields plus 101 hits to destroy armor/hitpoints (not factoring in shields being regenerated)

phase missile -116 hits to remove shields and do 3480 points of damage to vessel hull, leaving only 600 hitpoints which are struck for 70 damage total which will take only 9 more hits

so you have 217 hits for regular damage versus 125 hits with phase missiles, mind you armor and early setting of Shield mitigation will shift these numbers slightly (they may even cancel each other out in certain cases) but the overall effect is still in favor of phase missiles

hm so the pierced damage is extra?

i calculated

base 100  | 30% goes to 50% absorb armor | 70% stays on 60% absorb shield

15 armor-dam
28 shield-dam

when i understood you right you mean its

base 100 | 100% goes to 60% absorb shield | an "extra" 30% goes to 50% absorb armor

15 armor-dam
40 shield-dam

if that is correct (i will test this) then of course the phase missle is good because it's an "indirect" damagebonus as long as the target have shields (and better if shieldboosting is in the play)

edit: i just testet it and the piercing is not a damagebonus 30% of the shots goes direct to armor and do 100% of there damage there leaving the shield untouched, and the other 70% ot the shots goes 100% to the shield and got mitigated there leaving the armor untouched.

so it looks again not very good for our phasemissle friend

Phase missiles are, no questions asked, the best weapons upgrade in the game.  Anything with shield bypass properties is awesome.  In battles, mitigation usually hoovers around 60% reduction rate, which means ignoring mitigation means you deal 250% damage.  A 30% chance to deal 250% damage means a 75% overall dps increase.  The other factions get a paltry 30% damage increase, Vasari effectively get a 75% boost.

Most of the time, even with fully upgraded phase missiles, you will not kill a target with its shield points still intact.  The exception is if the enemy is using capital ships with shield regenration abilities, such as the Progenitor or Dunov.  In these cases it's actually extremely common to see ships with very high shields be destroyed. 

xSurrealx, I have always noticed exactly what you are talking about.  I almost always see ships die to my phase missles with 0 shields left on them.  The only time I can make a ship die with substantial shield remaining is if I use the "death egg" with the nano dissassembler a few times.  The nano bomb does direct damage to the hull and bypasses shields.  Once you use that weapon a few times you can finish a ship off with phase missles.  But is it worth so many expensive upgrades if you can really only use it in conjunction with the special ability of one capship?

Let's get some real numbers.  Throw the equations away and test this in reality with a friend.  One test with phase missle upgrades, and one without.  Tell us your results.

as i said i testet it against some ais and against a capital with nearly 1:1 armor-shield and 6 armorpoints it lost at around 90% of the times i tryed (saved befor the fight) all it shields befor it died.

Its all a bit lucky though 1 time i killed it with 1000 shield left so this was very nice result for the phasemissles.

But for the first test i think its save to asume that if the enemy has more armor then shield or very close to it and a higher armor-rating than 6 the phasemissles become pretty obsolete.

Overall i think i can say that phasemissles are good against low armor (absorb) ships with close to 1:1 armor-shield rating
the irony is that the 30% phasemissle upgrades takes a while and until you reached it the enemy will most likely have some armor techs up.

Against small ships as the light frigs or some drone carrier from advent it was also quit usless some time they died befor there shield went to zero but in a larger fleet this doesn't make it up to the ress invested because there are more missles on the way to the ship to kill it anyway.

When i have some more time i will test this in a "fake" 1v1 and build some caps(and level them up to 10) and other stuff to shoot at.
I think most peopel are more interested in the "end-game" balanceing which means phasemissles against full teched and lvl 6-10 caps and the rest of the fleet.

as you can read i tested it in a game and 90% of the time the units die with no shields left = no benefit from 30% chance to ignore the shield but i will test it against some hightech units and i am pretty sure it just get worse for the missle.

edit: to keep it simple a unit has 2000 armor 2000 shield and dies with no shield left = 4000 damage taken

same unit again 2000 armor 2000 shield dies with 1000 shield left = 3000 damage taken = 1000 damage less needed to kill it if that happens then the phasemissle "buff" is usefull but if the ship dies with 0 shield you still must do 4000 damage to kill it and that means you didn't have any use of the phasemissle.

Also, shield mitigation applies even if the shields are at 0, so the ratio of shields to hull is irrelevant as long as your target has at least some shields (and thus mitigation).

go for the test but I used yoiur equations and I got this set 241 hits with phase missiles and 288 hits without phase missiles so I dont see were you are coming from

no I did not, I used your equations, were you got your answers I have not been able to reproduce

Your missing the key point to all this....Phase missles bypass mitigation. That mean when they phase the hit for the full damage. And when they dont they are affected by the mitigation. And another key point is this.....