@Seleuceia: In a word, I agree. With everything.

I'll add the bit about flak accuracy against fighters to the above post under the "rebalancing fighters" suggestion, with credit to you.

Likewise, I'll add a section on Phase Missiles vs. Advent to the section on phase missiles -- since, as you said, Advent (with their paper hulls) suffer more from an attack that ignores shield mitigation than a race with beefier hulls.

EDIT: I like the suggestion of providing a phase missile defense buff, either via research or straight up, to Iconus Guardians. It's a REALLY good solution.

A (relatively) recent update allowed PM blocking to be granted via technologies, as it previously was only a entity modifier allowed through abilities...

Before that update, the primary discussion was whether the domina subjugator or the iconus guardian should be the Advent ship granting PM blocking...

Many advocated buffing the domina's perseverance ability by giving it PM blocking...since the ship was one of the weakest support ships (down there with the cielo), many felt it was the most in need of a buff, and PM blocking seemed like a useful bonus...

Some advocated giving the guardian's shield projection the PM blocking...doing so would make PM blocking more accessible early on, and it also would help protect all ships instead of just a few as shield projection is an AoE ability...some however felt PM blocking was only needed late game...furthermore, many felt PMs were only a problem against capital ships and not against fleets, so having fleet wide PM blocking would be too powerful...

As I recall, most people favored buffing the domina...personally, I favored buffing shield projection (and even did so in Project Equilibrium)...my reasoning was mostly that the domina could be buffed in many other ways to make its abilities more useful...furthermore, I believed AoE PM blocking was essential since the Advent depended heavily on higher shield mitigation (granted through culture bonuses and their higher shield tech) and all their ships were disproportionately vulnerable to PMs, not just Advent capital ships....

But then the developers allowed PM blocking to be granted via technologies, and I think it's safe to say most people would prefer that mechanism over support ships providing the PM blocking...the only real controversy is whether it should be all shield techs, only Advent shield techs, or only the highest level Advent shield techs...

The problem with doing anything to PMs is that it is not an isolated issue at all...for example, what if bombers and LRFs were significantly nerfed against capital ships?  Well, then PMs might not be so much of a problem...furthermore, if the Advent receive some much needed economic buffs, they may end up being on par with Vasari and therefore the PM thing would no longer cause a heavily one-sided Vasari/Advent match up...

Giving shield techs some PM blocking is the simplest and most direct solution...it is viable, easy to implement, and gives the greatest help to the faction needing the most help...that being said, the problem with phase missiles goes much deeper than this and is interconnected with many other OP elements...

Sins as a whole is fairly "balanced", but mainly because 1) All three factions have access to the same OP units like LRFs, carrier caps, and bombers and 2) All three factions have severely overpowered and severely underpowered elements that come out to a wash, giving the illusion of balance...

Thanks. I'll note in the above post that adding PM block via shield research might be viable, as well the note about the Domina.  Personally, I think the Domina AND the Cielo need a buff, but I also think that's another thread.

I'm not sure I see the difference. In order to move like a fighter, fighters would HAVE to be able to decelerate, come around, and approach faster.

Yes. On the other hand, since they have short range, and capital ships are, in general, very slow, you can micro your LRMs.

I'm not trying to be elitist, but a classic example is Marines vs. Banelings in Starcraft 2. In this analogy, your Marines are your LRFs (a ranged glass cannon) and the Banelings are your capital ships w/ point defenses.

The Baneling is a little rolling ball of death, employed because it is (relatively) cheap and deals large amount of splash damage to light units like Marines.

Unfortunately, all the Baneling can do is roll toward the Marines, and Banelings are rather slow under most circumstances. Though this isn't too much of a problem if the Marines stand still (since Banelings tend to appear in large groups), Terran players can split their Marines into scattered small groups to avoid the splash damage of the Banelings.  Cost for cost, a split Marine group will almost always come out ahead.

My point is: if Starcraft 2 players can do it, so can Sinners!  Split your LRFs into small groups (three or so) and have individual groups fall back as the capital ship approaches -- other groups can continue firing with impunity.

I'm trying to account for as many situations as possible. 

Hence: I lack data, therefore I withhold judgment.

Noted.

Also noted. Thanks for the analysis -- it basically confirms what I was thinking. Mad karma for you!

Question: are you for a GENERAL phase missile nerf (let's say 30% damage mitigation reduction 30% of the time, for a hypothetical nerf), a buff to Phase Missile Block research or abilities, or all of the above?

You could easily make a passive ability that has an AoE effect doing DPS only to SC...capital ships still have one extra ability slot so this solution is entirely viable and doesn't affect LRFs in the slightest...

I'm not saying it is a good idea...I'm just saying you can make capital ships shoot down SC without them being anti-LRF bastions...

Again...just make it an ability, and most of these problems go away

Could only agree if they got a damage buff vs bombers. As they are, flaks main job is anti fighter and damage sink. Yes some people use them to take down lrf/lf but thats not their primary/most effective functions. If you take away the damage sink side of things, then we should make them true Anti-SC and up the effectiveness vs bombers.

{Bumping this as I actually wrote a lot of this reply on February 12th, didn't get around to posting it sooner and was also hesitating about whether I needed to clarify anything, but then I can always clarify in later posts anyway, so here it is.
The order of information may jump about a little, so my apologies if that is the case. I've now added even more to it too.}

EDIT: Just a note, the post was a little wider than most, probably because of the charts, so just SCROLL to the right, from the bottom of the post. All that you miss out on by doing so is my [lack of an] avatar. "

"Basic probability (.3^32.6) tells us that the Kanrak has a roughly .000000000000000000899% chance of destroying the Cobalt without damaging its shields at all.
This means that most of the time you're gonna have to eat through the target's shields before you can destroy anything with Phase Missiles -- the shield bypass just makes things a LITTLE weaker in the hull department once you've gotten through the shields."

If that is what it calculates, that doesn't matter at all. The idea is not to hope that it ALWAYS destroys a target without ever touching their shields, it's that it destroys them before wiping out ALL of the shields.
If 99.5% of shields are knocked out by the time all of the hull disappears, you have still avoided the shots required to deal the remaining amount (0.5%) of damage to shields, which would also be mitigated of course, so you save more shots than if those extra shields did not mitigate (this is the difference between that extra life being shields that would otherwise mitigate damage and the extra life instead being armour that would not mitigate, not counting the lesser reductions from armour).
These calculations all suppose that whatever chance causes the effect to trigger precisely that amount of times.

Either way, as I understand it, there is no point in dealing any damage to the hull before removing the shields unless you can wipe out all of the hull before wiping out all of the shields, but, as I say, you don't NEED it to wipe out 0% of the shields to be useful. The one exception is with abilities like Disintegrate added into the equation, abilities that remove an amount from the hull directly as well, so that having first weakened more of the hull with Phase Missiles means that the ability destroys the ship before removing the last shields. Unless the ability is one like Nano-Disassembler, which only affects the hull, or any affect (I can't think of any) that deals damage to both shields and hull but MORE to the hull, however, a percentile chance of phase missiles hitting the hull would still need to be greater than the percentage of overall life that the target ship or structure has in HULL, otherwise, if it it equal, shields will still all be removed at the same time or (far more likely) before the hull. Obviously, if phase missiles just happen to kick in far more often than their percentile chance suggests it will, then the very occasional early kill (well, it's not alive, so destruction really) will occur from Phase Missiles, but then that's going to happen so rarely and if anything, are more likely to find PMs kicking in less often than their percentage suggests, according to the following:

Multiple chances of an event occurring at a given percentage have a lower percentage of occurring once than the number obtained from multiplying the decimal value by the number of chances.

For example, a coin has two sides. If we flip it twice, what is the chance that tails will occur even once?¹

Each side, assuming it doesn't land on an edge or something odd and unusual, has a 50% chance (supposedly ) of landing upright.
If you simply tried 0.5×2(1.0) from 2 chances, you'd be convinced there was a 100% chance, but we know that this is not the case.

The correct formula is 1-(1-x)^`
where x = the decimal value of the percentage, e.g. 0.25 for a 25% chance each time
and where ^` is "to the power of" whatever number of attempts are made.

For the coin flip (try it in your calculator): 1-(1-0.5)^2 =0.75.
2 Heads = failure
2 Tails = success
Tails first, Heads second = success
Heads first, Tails second = success
"Three out of four ain't bad!"

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¹An interesting story, to me at least , I always choose tails and, while it's different for each person and some people even swear by heads, I once predicted 7 coins in a row, choosing tails each time. The coin was not rigged and was part of the change my friend had from purchasing lunch at a café. He would sometimes swap the side the coin started on, sometimes he would choose to catch it, sometimes not, but 7 times in a row, I was right (calling it each time only directly before each flip). He was ready to flip it an eighth time, but I declined to bet.
He flipped it anyway.
Heads!
—————————————————————————————————————————

So, applying this to 5 phase missile shots at full upgrades without the additional aid of a Stilakus' Shield Disruption, for 30%...
1-(1-0.3)^5=0.83193.

5 chances of 30%, you might think about 1.5 should, on average, bypass shields, but there is only around an 83.2% chance of it happening once.

With only 10% shield bypass chance, after firing 10 shots,
1-(1-0.1)^10=0.651321559
there would only be a 65.13% chance of one bypassing shields.
If you instead were just reliably dealing 10% more damage, the 6 shots would deal a little more damage than you would from dealing 0.6513 of a shot (out of the ten) directly to the hull and the other 9.3487 shots normally distributed to the hull and shields (I did factor in mitigation and armour).

So, here's another example. If you look at plenty of TEC and Vasari ships, most of them have somewhere from 60-67% of their life as hull. Even amongst the Advent ships, they're either just under or exactly 50% hull (Disciple+Seeker+Destra, Illuminator) or over 55% hull (Purge, etc.), with the SINGLE exception of the Iconus Guardian, which regularly donates a lot of its shields to protecting the others anyway, so phase missiles only seem good at all when targeting either Iconus Guardians or ships that are benefiting greatly from the cuddle of an Iconus' shields.

If we consider that plenty of ships also have over 65%, I would like to take 64% as an average. It may be just a tad higher than the overall average, but then neutral ships are also TEC and they are scout/light/siege/flak/heavy, which have 72%/63.1%/64.1%/66.7%/66.7%/63.7% hull. The average of those is 66.05% too, so again, 64% as my average seems fair enough.

If said unlisted ship shoots 10 times with a 10% chance of going straight through to the hull each time and we take the realistic floating point number of PM shots that bypass shields as 0.6513 and we also suppose that the ship is 63% shields & 64% hull, with straight 50% shield mitigation when being fired and 2.5 armour, also supposing armour precisely divides damage by 1.x where x is .05 per armour, so that damage is multiplied by 0.5 versus shields and divided by 1.125 versus hull, then
~36% of 9.3487 shots go straight to the shields
~64% of 9.3487 shots go straight to the hull because the shields would have gone by now
All 0.6513 (pfffft) shots go straight to the hull regardless.

Comparing to the imagined damage if you saw total life, ignored Shield Mitigation and ignored Armour,
0.36×9.3487×0.5(shield mitigation) = damage value of "1.682766" shots
0.64×9.3487÷1.125(armour) = damage value of "5.31837" shots
0.6513÷1.125 (armour still applies to Phase Missiles that get through) = damage value of "0.57893" shots
1.682766+5.31837+0.57893=7.580066 shots worth of damage compared to damage from 10 shots against 0 defence.

A straight 10% damage bonus upgrade instead would deal
0.64×10×0.5×1.1 = damage value of "3.52" shots
0.36×10÷1.125×1.1 = damage value of "3.52" shots
(See why I was keen to choose 64%/36% and 2.5 armour exactly? )
3.52+3.52=7.04 shots worth of damage compared to damage from 10 shots against 0 defence

Random Minnesotan: "But 7.580066 is often recognized as being a larger number than 7.04, don't cha know?"
The Phase Missiles seem to be 7.67% better!
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Now let's try with 30%:

1-(1-0.3)^10=0.971752475
10-0.97175=9.02825
0.36×9.02825×0.5(shield mitigation) = damage value of "1.625085" shots
0.64×9.02825÷1.125(armour) = damage value of "5.13607" shots
0.97175÷1.125 (armour still applies to Phase Missiles that get through) = damage value of "0.86377" shots
1.625085+5.13607+0.86377=7.624925 shots worth of damage compared to damage from 10 shots against 0 defence.

A straight 30% damage bonus upgrade instead would deal
0.64×10×0.5×1.3 = damage value of "4.16" shots
0.36×10÷1.125×1.3 = damage value of "4.16" shots
4.16+4.16=8.32 shots worth of damage compared to damage from 10 shots against 0 defence

"Ha! 30% consistent damage is superior!"

Now these formulas are only taking into account the chance of bypassing shields ONCE in that many shots, so of course there is a chance that more will get through, but the problem with this idea is that the number is still less than 10, so if 10 shots were required to destroy the ship normally, we've dealt more damage NOW, but if we've determined we're very likely to still remove all of the shields before destroying the hull anyway, the remaining shots will deal less damage, obviously, seeing as we'll still have to go through whatever shields might be remaining and the phase missiles do nothing once the shields are gone anyway. A 10% bonus to damage will just continue to deal 10% more to either, regardless of type. After the calculated amount of shots have been fired, more shields will be left than without phase technology, so there are plenty of shields that still have to be depleted and much damage is yet to be mitigated. If you've dealt more to the shields already, future damage will be greater overall because less mitigation is left. Most often, phase technology swaps the order or some damage amounts, but that's about it.

The simple concept you have to understand is that if you cannot bypass shields often enough to remove ALL hull before ALL shields have been depleted, Phase Technology has done nothing for your ships.

Compare it to a straight 10% bonus and it's pathetic, because dealing more damage to a ship initially means nothing if it takes the same time to destroy it and if you remove all of the shields first despite some PMs going through, you're destroying it at 90.909..% (1÷1.1) of the speed that you would with a straight 10% damage bonus.

The higher the shield mitigation on the target, the more useful Phase Technology is at that point. The highest you would see it peak to in normal conditions (no late game 2% or 4% Advent bonuses) is 65%, not counting culture, which I think I've seen cause it rise to maybe 67 or even 69%, but only in very strong culture.

Is the base maximum 50%, but common amounts of culture raise it to around 65%, or is 65% the normal maximum and culture only boosts it that little bit? The exact detail evades my recollection at this point in time, so if someone could remind me, that would be nice.
Shield Mitigation only starts at 15% though and lower shield mitigation means that there's even less gain from bypassing a small amount of shields. During big battles, plenty of ships will be around 25-35%, so using 50% is probably generous.
Armour is often only 0 or 1, true, but it's a smaller difference and then, of course, the base armour is sometimes greater than 2.5 and ships can be upgraded to much higher amounts for a much greater benefit to the hull than the 2-4% to shield mitigation that only one race has. If the hull negates even more, again, it doesn't seem as beneficial to bypass a small amount of shields if destroying the whole lot of shields and hull would have been faster with normal upgrades.
Yes, you can get phase missile damage upgrades, but they come much later than normal 10% upgrades for other weapon types and you're paying a lot more for them.

Now it is time for some more examples. Due to the mixture of post editing dates, some of my points below might feature quite a bit repetition, so my apologies and you can just look at the examples and text directly relating to them below. I shan't apologise for an overall long post though, as complainers should "l2read" and plenty of people regularly read very long novels throughout the entirety of their lives anyway, so zip it and just pay attention!
If someone wishes to dispute some point I've made, I recommend you go over ALL of the text below first, to make sure you haven't just missed something I did state, just not in this first section.

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"Kanrak: 1.5x damage to medium armor"

Anti-medium (long range) damage vs medium (light assault) is 1.3333×, not 1.5×, it has been for quite some time, so my first examples will use the newer 1.3333×, but for consistency, I'll post the relevant 1.5× anyway, just after the first.

With only a fairly small chance of destroying hull first, the amount of shots fired required for enough phase missiles to go through(ignore/bypass) shields and destroy hull first is most often greater than the number required to just destroy it outright. By hitting hull earlier, you deal more damage early on, but so what? If you don't destory it all before depleting all of the shields, all you are doing is gradually destroying both instead of slowly going through shields and then tearing through hull. You chjange the order, but that is all. The only likely benefit in this situation would be if there were some abilities, likely Capital Ship abilities, which ignores shields (and thus both the damage mitigation and the large amount of remaining shields) and will swiftly wipe out whatever reamining hull there is OR abilities that deal damage to both at once, such as Disintegration, which would deal the same DPS to both shields and armour (damage to shields may or may not be mitigated, but it doesn't matter in this instance), possibly leaving many shields left but wiping out the far lower remaining amount of hull points.

From my calculations, Phase Missiles seem mostly useless and apart from Iconus Guardians, no target is really affected by them by any more than they would be if it were instead a consistent percentile increase in damage (and just hit shields first, like other weapon types) and a minimum of 41.5556% ((Disciple Vessels) phase mitigation is neceesary before phase missiles actually cause less shots to be needed to destroy a ship sooner (by destroying the hull before removing all shields) than they would without the phase effect.
In the case of Iconus Guardians, it's only about 19.8%, but Disciple Vessels, Seeker Vessels and Destra Crusaders are all around the 42% mark (~22% research of 30% required WITH Stilakus' Shield Disruption).
It only gets even less impressive in other cases, even for other Advent ships. Illuminators require 44%, while hull-heavy ships (Envoys, colony frigates, starbase builders) will be in the extremes and in general Vasari ships, or to a greater extent, TEC ships, with a greater percentage of hit points being made of hull points, require high phase percentages like 75.513514% for Cobalt Light Frigates (impossible in the game)!
These calculations are based on armour providing a ~5% decrease in damage (calculated by 1+x, where x=0.05×armour, so 2 armour divides damage by 1.1, rather than multiplying by 0.9) and shield mitigation being at a set 50%.
If mitigation is at the extremes of around 60% (I've seen above 60%, which confused me, but I expect it was to do with culture and it was a capital ship too, if that makes a difference), a little less phase chance will be required to actually make it destroy the ship sooner than it would by targetting shields first, but in a battle with many ships all naturally spreading damage over many targets, imagine only 15% shield mitigation. With shields being far less useful (actually less protection from damage than hull provides with 4 armour!), the gain from ignoring them occasionally will become even more negligible. If too many ships fire at one target, you boost their damage mitigation and instead of even only 'overkilling' them by wasting too many shots to actually destroy them, you also waste shots while weakening it; constant overkill, so again, using 50% shield mitigation is optimistic or generous, because it's not generally wise to manually lower your own ships' damage actual output.

With all this, imagine how much more useful percentile damage upgrades are! Shield mitigation mitigates the bonus damage, but only by exact amounts, not by percentage. What I mean is that a 15% increase will still (basically, but I'll address this) increase damage by 15% against shields, it'll just be a smaller bonus amount to damage than it is without the mitigation, of course. The exception is that shield mitigation increase is based on the exact amount of damage taken, so the last sentence isn't entirely accurate and a small dampening effect may be applied to the percentile damage increase. The change should be far, far too small to make phase missiles comparible in efficacy of hastening the destruction of enemy ships.

Some charts, indicating the number of hits for a Kanrak Assailant to destroy an Iconus, a Cobalt, a Disciple and an Illuminator, supposing 50% Shield Mitigation and 5% protection per armour.

The format:

The above is placed side by side four times, showing the results with 30%, 40%, 50% mitigation and then finally, from my calculations, the approximate minimum % mitigation required for Phase Missiles to destroy something more quickly than it would with a straight percentile damage increase instead of phasing.

It might be a little harder to follow outside of Excel, but do try! Note that extra spacing you may see before and after the chart below is so that I can easily edit this if necessary, as the post with trying to remove the charts using delete or backspace (chart highlighted or cursor in front/behind, it doesn't matter).

† Mitigation required to be destroyed faster by PMs than by normal with equivalent percentile damage upgrade.

‡ Mitigation required to be destroyed faster by PMs than normal.

The Iconus Guardian should typically be destroyed by PMs before it would have from straight damage at 30% SM, hence "Pha" in the "Killed by?" box.  "Shield Hits", "Hull Hits" and "Total Hits" show how many hits it would take to destroy the ship normally, Phase Hits shows the number of phase missiles that would have to be fired (with the phase% chance in "Phase %") to destroy the hull before wiping out all shields, i.e. the number of hits that must be fired for the given Phase % chance to be at all useful. You can see that it should take 384 Kanrak hits normally and 254 PMs to destroy the hull 675 Hull Points ÷ (13 damage ÷ 1.1 for armour × 0.75) = 76.1538, or 76.2.

In case you wondered, I did test and they require the approximate mitigation to be destroyed faster by PMs:
Ico.G - 19.83%
Cob.L - 48.558%
Dis.V - 34.1865%
Illum -35.49%
You can see that in the ‡ column.

In the † column before it, you can see that for Phase Technology to be more useful than just having the equivalent level damage upgrade, those ships need the following phase chances:
Ico.G - 19.80%
Cob.L - 75.5135135% - NEVER!
Dis.V - 41.5556%
Illum - 44.00%
All other frigates/cruisers - over the 41.5556% of Disciple Vessels. Advent capital ships start with more armour than frigates and more hull than shields, so you should need notably more than 42% for them, although less once they get to very high levels, as they end up with more shields than hull. Hard to say with a 10th level Revelation with 14 armour (8 base + 6 ability armour)!

~~~

Just for the OP, this chart shows what it would be (for the two ships it applies to) if Anti-Medium damage was 1.5×:

You can see that while the actual number of hits changes, it changes in both cases by the same percentile amounts so that the same phase missile percentages are required for both † and ‡.

The percentages are based on the target ship only, it seems, regardless of the exact base damage dealt by the ship firing with phase missiles, or of damage multipliers.

~~~

It's a pretty weak ability if, with maximum upgrades, phase missiles won't be of any use against Disciple Vessels unless you have a Stilakus for it too.

It is possible that there is some detail I've missed, or that I may have used an incorrect formula at some point, but I'm 99.999999999999% sure that's not the case. Feel free to politely point out any mistake you think you have found though.

Discuss!

HERE ENDETH THE SECTION OF THE POST RELATING TO PHASE MISSILES.

Just touching on the topic Fighters and Bombers, if you make it too much easier for Fighters to stay alive by weakening the damage, accuracy, damage bonus of Anti-Strikecraft vs Fighters (1.33333 currently), they have full reign of the skies and no adversaries if you have enough to negate the AS threat.
The danger of weakening Anti-Strikecraft vessels is that neither fighters nor bombers are very good at taking down assault vessels quickly as both (probably fairly) deal only 50% damage to Medium armour, while assault types deal 50% more vs carriers (Heavy armour). If you make it so that strikecraft are not taken down as easily (even just bombers), players will generally require more Anti-Strikecraft vessels, which allows a player with carriers to get more fairly cheap light assault units to directly engage the AS.
Fighters being stronger will FORCE more AS, which allows the carrier player to lamely pre-emptively counter by already having a good (appropriate) portion of their army composed of assault types.
Currently, I believe you only need around half the cost in AS to deal with Fighters (per squadron, based on half carrier costs/third of Aeria DH costs), so I wouldn't rule out making AS a little weaker or more expensive for their purpose, but you must keep in mind how screwed someone will be if there are simply not enough AS units. It's the same as having no anti-air in a mostly ground based game or having absolutely no detection when invisible units arrive. Seeing as carrier class capitals are available from game start in Quick Start and almost immediately without Quick Start, it would be pretty bloody lame if anti-strikecraft were not available quickly enough to defend against the rush even when scouted (never mind lame, actually, that would just be a case of imbalance ). You need either AS, some sort of static defence that can handle it or to have enough ships/more than one capital ship to be able to destroy the charging enemy carrier capital before the superior number of fighters/bombers (and their capital ship) destroy too much of your fleet for you to be able to ever destroy the capital. Carrier capitals need to not be so strong that they and their supporting fleet beat another capital and its SUPERIOR fleet in the early game, we really need it to only be an issue once people can actually REACH Anti-Strikecraft and only then, if the opponent doesn't have enough, should Strikecraft prove so powerful, punishing the opponent for not making enough AS/Fighters.

Part of the strength of Strikecraft comes from them FORCING the opponent to get a decent amount of Anti-Strikecraft vessels, but obviously that's no much of a strength if AS actually are so efficient that you are only forced to invest significantly LESS in AS than the opponent has already invested in SC.