[DISCLAIMER: all suggested modifications to abilities and stats are meant as a proof of concept- the numbers aren't final and are only included to give a rough estimate of the changes- please focus any feedback on the ideas behind the changes rather then only on whether the current numbers are balanced(though numbers feedback is also useful)]

General Analysis of the Role of Battleships

It's well known that 2 of the games three battleships are rather sub-par.  Battleships as a whole have been designed to be "pure-combat" ships with less in the way of utility/late game fleet support then most other capitalships, but contribute more in the way of firepower then, for example a colony or support capitalship. 

This really should mean the battleships should excel in the early game, when the added firepower of one combat-focus ship to a small fleet makes a larger difference to your total fleet potency then fleet-support skills which scale better into the late game when most of a fleet's firepower comes from it's large complement of frigates.

The problem is of course that it's hard to justify battleships as a means of boltering early firepower when frankly for the advent & TEC carriers posses superior firepower at a greater range with more flexibility(fighters for anti-light damage, bombers for anti-module).  I will discuss the firepower of battleships relative to carriers more thoroughly in the next section.

Firepower of Battleships and Carriers Contrasted

The core of this problem lies in the fact that carriers start with 3 extra squads of strikecraft, and by level 10 have 6 more squads then a battleship.  By contrast the radiance's weapons exceed the DPS of the weapons of the Halcyon by about 20 DPS at level 1,  and somethign around  38-40 extra damage at level 10.

3/6 squads of fighters have roughly 12*3/12*6=36/72 DPS(=48/96 damage against light armor, 18/26 against most other armor types)  3/6 squads of bombers have about 17*3/17*16=51/102 DPS(which is 33/66 DPS against capitalships, 51/102 DPS against heavy cruisers, & 25/50 against most other ships).

There's something to be said about the battleship damage being dependable whereas strikecraft squads can be damaged and destroyed to be sure.  But IMO that is more then made up for by the fact that strikecraft have an enormous range advantage and can focus fire(whereas the battleships divide their DPS between banks targeting separate enemies).

The point is even before abilities come into play carriers have a firepower advantage on the battleship- this is not the only issue of course(radiance & Kol have ship specific issues as well unrelated to their battleship status).

Consequently I believe the less powerful battleships could be remedied by improving their firepower.  I think the best way to do so is by buffing seperate abilities to improve firepower in ways focused on different types of enemies- that way the player can specialize the firepower of their battleship to meet the situation much as a carrier can be loaded with fighters or bombers to meet the situation(though since skills learned are permanent and can't be swapped like strikecraft the skills shouldn't be too specifically focused).

So What Makes a Battleship "Work"?:

So far the two battleships which are actually viable are the kortul and the discord(we'll see when the vasari are in whether their new battleship is any good).  I'll focus mostly upon the Kortul as it fills a more traditional battleship role then the discord(which is as much a support debuff boat as a battleship despite the name).

So what traits do these ships have that the radiance & Kol lack? Well both despite being strong early game combatants with good offensive firepower abilities also have some degree of late game utility(jam weapons & AM draining attacks for kortul, Armor reduction & Lethargy for the Discord)- this is primarily an area which the Kol falls short(radiance has DA).  

That said, the biggest area the Kortul excels where the other battleships fail is in it's high sustained firepower and durability via Power Surge.  Power Surge allows the Kortul to match if not exceed the firepower of a carrier, and become fairly durable it's self making it a very potent addition to early game fleets which are small enough that capital-ship firepower is a large portion of total fleet firepower. 

Honestly I think the biggest problem with the radiance and Kol is just that- they can't compete with carriers in terms of early game firepower.  Specifically the radiance lacks the tools(only one basic ability deals damage and the damage isn't really the focus of that ability) and the Kol has the tools(Gauss Railgun can put out some serious damage if spammed) but lacks the AM to keep up with it's ability's AM demands.  That said, being that the biggest flaw in radiance specifically has always been early firepower(even in diplomacy) I can't understand why DA dmg/sec was heavily nerfed in rebellion.  Seriously it went from 16.67/26.67/33.33 DPS in diplomacy to 12/14.9/17.8/20.7 DPS in rebellion.

The last part of the equation is durability- the Kol has this in spades(it mostly lacks in the previous areas). The radiance however doesn't.  EAA is definitely the world of the 4 battleship "survival mechanism" even considering it is passive(this is in large part due to the fact that advent fleet synergy being what it is, by the time a capitalship is taking hull damage it's already in dire straights).  That said, personally I think any deficits in survivability are far less important then the lack of early game firepower.  

Ship Specific Discussions:

The Kol:

The Kol's biggest problem is and always has been that it has 3 active abilities, two of which have short cooldowns and are primarily meant to just deal damage(which means to really boost Kol's sustained damage output they need to be spammed).  The Kol's AM simply can't keep up.  Flak burst is particularly an AM hog.

Another more specific issue is that Flak Burst is unreliable unlike other Anti-SC ablities doesn't "buy time".  If flak burst doesn't actually kill any squads(as it often won't in it's first shot) your ships are going to take the full brunt of the bomber attack even after using flak burst(which has a very high AM bost btw).  Moreover the effectiveness of Flak burst varies drastically based o who your opponent is- Vasari bombers have roughly twice the hull of advent bombers.  this makes the ability difficult to balance as balancing it against the advent means leaving it useless against the vasari and balancing it against the vasari will make it too hard of a counter to advent SC.  Flak burst needs something new- something that levels it's effect against all race's strikecraft so that it's effect can be balanced accounting for all races.

Because of these first two issues the first change I would propose is to make Flak Burst far stronger, but on a much longer cooldown(less of an AM burden & strong enough that the first casting has a quantifiable effect on the coming bomber swarm).

As many have suggested over the years, making Adaptive Forceshield Passive would help ease Kol's AM problems a bit(heck with it's duration it pretty much has 100% uptime already).

Gauss railgun I don't think needs any new effects, but could use a small AM cost reduction- It's post shield DPS is actually pretty comparable to that of the Jarrasul's Nano-dissembler(whic his IMO a good example of a sustained damage ability), but the AM cost per second of spamming Gauss railgun every 8 seconds is massively larger then keeping nano-disassembler running.  If they AM costs were similar the two might be pretty comparable(-50% speed>-3/4/5/6 armor but Nanon dissaembler may be maintained on up to 3 targets).  

SO I think my proposed changes would be something along the lines of:

Gauss Railgun: reduce AM costs by 5 or 10 at all ranks

[comments: nothing fancy here, just a modest AM cost reduction ]

Flak Burst:  Increase cooldown to 25 seconds.  Instead of dealing damage instantly destroys the 2/4/6/10 Nearest squads of enemy strikecraft  and deals damage to each other strikecraft in the area equal to 30/40/50/60% of it's maximum hull points(damage still reduced by armor).

[comments: After a great deal of thinking the only real way to make Flak burst equally useful against all types of strikecraft I really felt went with the theme of the ability was damage based on target health.  This also prevents later game strikecraft with hull upgrade research from becoming super resistant to flak burst.  The 2/4/6/10 squads instantly destroyed means flak burst WILL always reduce the impact of the approaching bomber swarm it is used to counter.  Moreover I think it's fair as even at max rank it essentially destroys a squad every 3 seconds on average- which isn't all that far off the rate carrier capitalships produce strikecraft for no AM.  Also for those leary of '% of max hull' damage, vasari bombers top out at what? 175*ish* health?  the ability would in that case cap out at 105 damage against the beefiest strikecraft(so about 1.5x current effect, less against frailer ships)]

Adaptive Forceshield(passive): Reduces all damage dealt to the Kol by 10/15/20/25% and grants it 14/21/28/35% phase missile block.

[comments: a little bit weaker then the current effect, but up 100% of the time with no AM cost.  it's WAY better then the radiance's EAA at the very least. ]

Altenative Adaptive Forceshield(passive): Increases shield mitigation by 4/6/8/10% and 4/21/28/35%

 [comments: This one would in general be slightly stronger then the first damage against damage that doesn't  bypass shield mitigation, but would be a bit vulnerable to effects that do(with the phase missile block this mainly means it would be weaker to abilities that bypass shields).  That said this one also has the advantage of being very simple. ]

Base Stats: Increase the damage of the kol's autocannons a bit- nothing huge, maybe a 10-15% boost

[comments: The greater spammability of Gauss should give the kol some anti-capital ship DPS, this change would give it a bit more anti-frigate firepower- they would also make the splash damage from it's ult a bit stronger]

These changes would IMO fix the Kol's problems.  It's AM supplies would actually be able to keep up with it's ability use, It would have more sustained firepower in general(possibly rivaling that of a carrier), and to top it all off it would actually have a strong and more importantly reliable anti-SC ability(actually probably the strongest early-mid game due the the relatively smaller numbers of strikecraft present)

The Radiance:

The Radiance is a bit more complicated.  It doesn't even really have the tools at present to compete with a carrier in offense.  It's clearly meant to be a pseudo-tank w/ animosity/EAA, but frankly no capitalship can really tank late game so past the early game the Radiance can't really perform this purpose.

That said Radiance can already be useful late game just via DA & cleansing brilliance, so I will focus primarily on buffing the radiance's early game.

First off, boost DA damage.  There was no reason this should have been nerfed in rebellion(Radiance was already UP because of lack of earlygame firepower in diplomacy, so why nerf the damage of it's highest priority skill to level up?).  That said I would primarily like to buff the lower ranks of it's damage output to target the early game, so perhaps have the dmg/sec be constant at all ranks(after all the total damage per cast already scales up with rank via the duration increasing and getting closer to the cooldown).

 I know many people's reaction may be "DA is already great, why buff it?" simple, DA is good enough that it will generally be skilled first meaning any buffs to other skills past rank1-2 don't really see play in the early game...you can only really buff the early game by buffing abilities people actually have points in early game.  Buffing DA is practical for this reason(and frankly it's mostly just rolling back an unnecessary nerf to an already UP ship)

Honestly buffing DA's damage could probably give the radiance plenty of anti-capital ship firepower, so next I will focus upon giving it some anti-frigate firepower.  The best candidate for this feels like animosity as that ability is already tailored toward wading into a mass of frigates.  So perhaps add a secondary effect that improves Radiance's ability to engage multiple enemies.

Granting a bit of extra survivability to EAA may be nice as well(for the taunting battleship it's a bit odd that radiance is by far the squishiest battleship), but is less important then other changes.

Anyway without more ado my propositions would be:

Detonate Antimatter:  increase dmg/sec to 25 at all ranks.

[comments: total damage per 20 seconds in trinity: 200/400/600  With my changes total damage per 20 seconds would be: 300/390/480/570 .  Still slightly lower at rank 4 then trinity rank 3, but stronger at lower ranks(not to mention it's still better overall at rank 4 as it has an extra 3 seconds of duration compared to trinity rank 3).  I think this would be a reasonable way to give the Radiance much needed single target firepower(and frankly being that the damage didn't overpower radiance in trinity this should be fine as well).  ]

Animosity: additionally for the duration of animosity Radiance's weapons banks may attack one additional enemy and have their rate of fire increased by -15/0/15/30%

[comments: I know this sounds big: consider the following though: Kortul's 'Power Surge' essentially improves weapons damage output by 25/50/75% and is up  67/71/75% of the time(I don't know the rebellion values).  Meaning it cast every cooldown it is roughly a 16.3/35.5/56.2%.  By contrast Animosity is up at most 20/35=about 57.1% of the time. With my proposition animosity would constitute a 33.5/57.1/80.7/104.2% increase in weapons damage, but divided among twice as many targets(and dependant on having that many targets to reach it's full potential). The slightly higher damage boost is compensated by the reduced focusfire.  As for the other effects: considering Power surge has a better uptime compared to it's cooldown I think it's shield regen is about as useful as animosity's default effect.   Also this would make animosity into a great visual lightshow in large battles   .  Also I realize the rank 1 reduces weapon fire rate seems weird.  I initially had it at +0/10/20/30%, but wasn't satisfied with the distribution of bonuses as compared with 'Power Surge']

Base Stats: Shift some of Radiance's base shield points and shield points per level into hull and hull per level so that a larger percentage of it's health is in the form of hull. 

[comments: Making more of radiance's health come from hull instead of shields relative to the other advent capitalships would be an easy way to buff EAA without adding anything more complicated to that ability.  Moreover Advent capitalships are renowned for squishyness due to their low hull points- having their capitalship that is intended to serve as a pseudo tank eb the only exception to this rule would make the ship very unique in the Advent arsenal(possibly a good choice for combating vasari Evacuators/phase missiles? ]

Conclusion:

Well a discussion of battleships, what makes a battleship "good" and what can be done for the ships of this class which are subpar has been bouncing around in my head for the last few weeks.  Sorry if it is a bit of a rant, I tried to structure my thoughts as best I could at a moments notice(though I'll likely be editing this post over the course of the night).

Anyway any discussion on battleships, the general problems with the radiance/Kol, feedback to my proposed changes, or ideas of your own are welcome.  Honestly I think the first step towards balancing the underpowered battleships is figuring out exactly what role battleships as an archtype should play in game strategy.  I'm sure there's some controversy on the specifics of these issues, so let's hear some opinions!