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[intrinsic_parity]

Preface:
I'm making this thread to continue a discussion from https://fractalsoftworks.com/forum/index.php?topic=19094.0 without further derailing that thread.

I think maybe there is an argument for across the board dissipation buffs (or weapon flux cost reductions) to most ships (or weapons) to try and make heavy weaponry a bit more palatable without fully committing to max dissipation. Right now, weapons like the mjolnir/storm needler/heavy blaster feel like they are very difficult to fit on ships without, absolute max dissipation and a lot of empty slots, and I feel like ships generally need to max vents to use their slots effectively. Maybe alleviating that a bit with increased dissipation could solve some of these other problems. That's a lot of balance work though. Maybe worth a different thread.

Going down the rabbit hole a little...

It would be a balancing nightmare but I agree. However, I don't think all guns blazing 100% of the time is the goal, either. In a vacuum, I'd say most Vanilla weapons are balanced: efficiencies are about where they need to be, opportunity costs are real, etc. But it's telling that even a single Pulse Laser is more than a Wolf can really support even with max vents. Is that the fault of the Pulse Laser or the Wolf? Even if you bumped the Wolf's dissipation to 200 (33% increase), it still can't really handle a Pulse Laser without max vents.

To the degree that a lot of us are optimization wizards, if there's a maximum benefit, we'll find it and max vents is typically the best way to spend OP. Dissipation is just so vital in this game. Even if we raised dissipation 25-30% across the board, I'd still go max vents for the majority of my builds because many ships would still "need" it. (As a thought experiment, raising all dissipation would lead to more up-time for bigger guns, more DPS, and faster kill times. It'd speed the game up but is that what we want?)

I would argue that it's actually optimal to use as many vents as necessary to cover your weapon flux generation + shield flux generation. Anything beyond that is much less useful. My idea was that using less flux intensive weapons would let you save some additional OP on reduced vents (because you could meet weapon flux requirements without maxing vents) that could be spent on strong hullmods, while max vent loadouts could sustain heavier weapon setups, making for an interesting decision. I feel like right now, you have to really undergun stuff to get weapon flux below dissipation without maxing vents meaning there isn't much of a decision to be made. Hopefully it would still be possible to over-gun stuff as well, even with higher max dissipation. You might be right that it would just be optimal to use the heavy weapon setups always and still max vents.

Alternatively you could mess with vents to allow for higher dissipation without changing base stats. Some ideas that come to mind are a straight increase to the max number of vents (say 50% more vents can be equipped for all classes), or and increase in both dissipation per vent and OP cost per vent (15 dissipation and 2 OP per vent). The idea being that ships have the ability to get a higher max dissipation to mount the heavy weapons, but it costs more OP to specialize into using those weapons.

I also generally agree that the balance implications of these changes go really deep and aren't immediately obvious (or clearly good in all cases).

[Goumindong]

So... given an optimal AI people probably fit too many vents. And while I will explain that I should first explain why this matters. It matters because the reason that this is true is also probably a reason why it’s unfixable.

The reason is pretty simple at its heart but complicated in its construction. So let’s abstract. And then when we have a conclusion we can draw back the abstractions and see if specifics change our conclusions. Imagine two fleets which have perfect information about the other fleet(abstraction 1). Now imagine that the fleets don’t have ranges and ships don’t take up space, any ship can always shoot any other ship (abstraction 2). Now imagine that ships cannot retreat and will always take fire until they die (abstraction 3). Now the ability of how to win a fight is featured in two aspects one, each sides ability to determine an optimal target priority and two, the relative offense and defense of ships themselves.

The second aspect flows from the first aspect and there is an easy rule for the first aspect. That is. You shoot ships that have high dps relative to their defense first and ships with low dps relative to their defense second. This because for any fixed output dmg your incoming damage is minimized. Now we ask what we would do to fit ships in order to flummox that target priority. And the answer is again simple. We would take ships that are going to be targeted first and make them tankier and ships targeted last and make them more damaging. We have limits on how much we can change things because if we make a ship too damaging or too tanky enemy target priority will change. And as a result every ship should be as close to the same ratio of dps to defense and the product of the two should be maximized.

Now this implies that for every 1% increase in flux dissipation you should have a corresponding increase in flux capacity and the strongest fit is that which maximizes the product of dissipation and capacity. Given that these can rightly be called dps and defense and given that weapons have the same flux/dmg rations (abstraction 4)

Let’s back out some of our abstractions and see if they hold. There isn’t perfect information but it’s pretty close. And reducing information just introduces randomness it doesn’t mean that you’re going to miss the ships that clearly have more guns fit and can fire them. Abstraction 2 is a bit harder but if we consider each engagement in a fight as an individual fight on the same construction then the conclusion holds in each engagement and so the whole fight. Abstraction 3 is a bit harder as ships that win or lose minor engagements can retreat and come back... buut a ship with better proportioned defense/offense will do more damage in any given fight and have more of an ability to retreat (given the current trend is to overfit offense) and otherwise retreat ability is determined by hull choice and not vent selection and for the vast majority of ships their guns turn off when they take damage and so capacity is still the entirety of their effective tank. Abstraction 4 actually does break things. If the flux/dmg ratio changes based on the OP of weapons then the optimal fit may not have the highest product of capacity and dissipation. Unspoken abstraction 5 also breaks things different sized ships means bigger ones should tend to have more dmg since killing 5 ships with 1/5th dmg and HP of a bigger ship will mean the net sum is lower and so there exists an amount of extra dps the bigger ship could do before it would be optimal to target it. So bigger ships should prioritize dmg in a mixed fleet. And unspoken abstraction 6 does as well which is that all ships can attain the optimal ratios. And unspoken assumption 7 is broken the AI doesn’t even really do target selection (but this does not break the conclusions). Fortunately most of these tend to break to “more ships should be fit tankier” so we can still use the insight.

Anyway now that that is done how does this inform us about fitting. Well the reason it’s still generally better to slam vents is that it’s very hard to get the AI to optimally apportion weapon usage but it’s also important to have a selection of weapons that can be optimally apportioned because not all target ships are created equal. When this happens the AI will end up shooting its defense, which may or may not be optimal, but is always optimal to shoot less of its defense than more. You cannot fit weapons for fighters and weapons for cruisers and expect the AI to only shoot them at the right targets. You can try but there will always be plenty of situations where the cruiser weapons are shot at fighters and the fighter weapons at cruisers. And so you need spare dissipation in order to reduce the penalty for this happening....

Even then I bet people would be better off fitting more caps on their ships in general. Like, everyone loves hardened shields but caps are often just as if not more efficient in terms of total tank to OP.

[TaLaR]

But dissipation doesn't actually equal damage output, while flux capacity doesn't equal tankiness. These assumptions come anywhere close to being true only under sub-optimal AI piloting. Player can keep shields up for much smaller portion of time and use every little opportunity for short vents, at which point dissipation contributes more to both damage output and tankiness.

[Goumindong]

But dissipation doesn't actually equal damage output, while flux capacity doesn't equal tankiness. These assumptions come anywhere close to being true only under sub-optimal AI piloting. Player can keep shields up for much smaller portion of time and use every little opportunity for short vents, at which point dissipation contributes more to both damage output and tankiness.

But... Yea it does? And venting doesn't work like you think it does?

OK so lets assume for a weird reason that the player isn't being shot at (because the AI does prioritize shooting the player). They shoot over their dissipation and vent. While they're venting they're not shooting but are dissipating twice as much as normal. If we assume that they can shoot infinity over disspiation without overloading then DPS = Dmg/Flux * dissipation * 2 because they spend 100% of the time venting and you vent at dissipation*2. If we assume they shoot 0% over dissipation then DPS = dmg/flux x dissipation. For any amount over dissipation they can shoot we just have a different multiplier which is a function of the amount over dissipation they can shoot and the amount of capacity they have both of which increase the multiplier (because you're venting a higher proportion of the time)

We might note that because this is a flat multiplier its just like having more efficient weapons... which do not modify the fitting considerations because they do not modify the percentage amounts of dmg that adding flux or capacity add...

Now lets assume the player is being shot at. Well then extra capacity lets them absorb more damage, dealing more damage before they have to vent. This increases the amount of time they are venting in proportion to not venting and so increases the final effective DPS by a flat multiplier... which... oh

[rokenx2]

personally ... and i may catch flack for this but just throwing it out there.... one on ones often feel a bit one sided where its like one ships constantly over fluxed the others just slowly pounding away till it melts.... and i think this is fixable by.....  splitting weapon flux and shield flux into two totally different bars many ways to do this but i think if done right it could make for very fun brutal slug fests where it feels less one sided

[MesoTroniK]

(because the AI does prioritize shooting the player).

I am pretty sure this is not the case, but not 100%. Hoping Alex can clarify.

[intrinsic_parity]

@ goumindong
The main assumption that the 'optimal strategy' is to target the enemy ship with the highest ratio of DPS/defense is just not true. In fact, it's easy to construct a strategy that will beat it. If you knew that the enemy would doggedly pursue whichever ship had the highest DPS/defense ratio, you simply find a ship that is very fast and give it the biggest guns it can fit, as well as the worst defenses it can fit (so that it is the priority target), and then have it distract the entire enemy fleet by hovering just out of their range while the rest of the fleet picks them off one by one. Of course that would never happen because the AI is smart enough to avoid that 'optimal' strategy.

In my experience, fast ships can dictate engagements, so it's usually best to target them first. Small ships might not individually do a lot of damage, but if several of them join a local engagement suddenly, they can swing it in their favor, so it's valuable to kill them first so that you can keep future engagements in your favor with your own maneuverability. Basically, I find it best to leave the slowest ships for last, since they can often be ignored safely (even just having you own ship that can't beat the enemy big slow ship, but can keep it engaged without dying is enough). If a ship is fast enough to dictate engagements against you and powerful enough that you can't keep it occupied without losing ships, then that ship becomes the priority, regardless of if it has a particular damage/defence ratio. Also, it's usually best to prioritize targeting isolated ships since you ensure that you can gain a local advantage by fighting away from the rest of the enemy fleet. Those factors that dictate targeting priorities are more about maneuverability than defense/damage.

I actually tried to analyze the value of adding a capacitor vs a vent a while ago and found that it was a very complicated and non-linear relationship. The value of a vent depended on how much capacity you had and vice versa. I'll type that up tomorrow because it's very late.

[Grievous69]

Yes, yes and a million times yes. Many ships have so little flux they can barely handle "budget" loadouts with low flux/sec weapons. It's ridiculous to me that you have a ship with let's say a large ballistic mount, and that you can't even dare to put a weapon of your choice there. You HAVE to go with the cheap option and then invest 60 points into vents. Sure you could do the opposite, no one's stopping you, but that ship will die horribly. I'm all for things that help with the mandatory OP taxes, it'll eventually lead to some more interesting builds.

But I can see how this would be incredibly tough to balance, with so many ships we have. Also I don't have a problem with overfluxed ships IF they're using high powered weapons.

[Goumindong]

@ goumindong
The main assumption that the 'optimal strategy' is to target the enemy ship with the highest ratio of DPS/defense is just not true. In fact, it's easy to construct a strategy that will beat it. If you knew that the enemy would doggedly pursue whichever ship had the highest DPS/defense ratio, you simply find a ship that is very fast and give it the biggest guns it can fit, as well as the worst defenses it can fit (so that it is the priority target), and then have it distract the entire enemy fleet by hovering just out of their range while the rest of the fleet picks them off one by one. Of course that would never happen because the AI is smart enough to avoid that 'optimal' strategy.

In my experience, fast ships can dictate engagements, so it's usually best to target them first. Small ships might not individually do a lot of damage, but if several of them join a local engagement suddenly, they can swing it in their favor, so it's valuable to kill them first so that you can keep future engagements in your favor with your own maneuverability. Basically, I find it best to leave the slowest ships for last, since they can often be ignored safely (even just having you own ship that can't beat the enemy big slow ship, but can keep it engaged without dying is enough). If a ship is fast enough to dictate engagements against you and powerful enough that you can't keep it occupied without losing ships, then that ship becomes the priority, regardless of if it has a particular damage/defence ratio. Also, it's usually best to prioritize targeting isolated ships since you ensure that you can gain a local advantage by fighting away from the rest of the enemy fleet. Those factors that dictate targeting priorities are more about maneuverability than defense/damage.

A ship that cannot be targeted has infinite defense and the targeting strategy would change to ignore that ship... You're either not respecting the abstractions that you do to make the math work nor understanding what they represent. And not respecting that the targeting decision isn't static as a fundamental assumption. You cannot make a ship "tankier and with less DPS" than any other ship and not have the enemy retarget.

Either way you're not understanding the exercise. Plus like... small fast ships tend to have high dmg/flux ratios... a lasher has 15 capacity per dissipation and an onslaught has 28... Even if you fit all caps and no vents a lasher would only have 29 cap per dissipation.  You shoot small ships first because they're the optimal targets to shoot first. Even if they had ratios similar to capitals the ability to take them out of a fighter faster and remove their DPS would make them ideal targets.

Does this mean that you should fit a lasher with all caps and no vents? Well no, because more caps or more vents is always better. But if you are constrained then it might.... because again there are other issues to consider. But if you take a default lasher and optimally allocate vents/caps you're likely to beat the default lasher on autopilot without that allocation.

edit: Does this mean that you should make your frigates and destroyers offensive powerhouses when you're in the cruiser and capital stage? Well maybe only if you have spare OP after slamming them caps.

I actually tried to analyze the value of adding a capacitor vs a vent a while ago and found that it was a very complicated and non-linear relationship. The value of a vent depended on how much capacity you had and vice versa. I'll type that up tomorrow because it's very late.

Its not linear but its not actually that complicated because its linear in logs. Let z = x*y . This is a non linear relationship. But if i wanted to maximize this in relation to a constraint x+y = k then i could make it simple by taking the log. Log z = Log (x*y) -> Log(x) + Log (y) and now it should be very simple to understand that the maximization happens when x=y. Even if you don't want to do the "actual math" to solve it. And we can do this to more or less any construction of this formula.

2xy? Log 2 + Log x + Log y -> x = y.

2(x^2)*y? Log 2 + 2 Log x + Log y -> x=2y *

Now it gets tricky in using the math to find exact answers for a fit because our formula will produce sums inside the logs. But if we ignore that and instead look at the total we find the easy relationship which we can test algorithmically rather than finding a closed solution. Which is probably faster all things considered.

Edit: it occurs to me I maybe did not describe the algorithm. I think I did but it is whichever produces the highest product of cap or vents, which is the same as whatever produces the highest percentage increase in whichever thing were increasing.

If we go back to the logs we find that this relationship falls out naturally. For log z = log x A percentage increase in x produces a similar percentage increase in z. For log z = 2 log x a percentage increase in x produces a 2% increase in z (continuous percentage). Adding another log term does not change the relationship because it’s linear in logs.

*pretty sure. didn't do the actual math but i checked close values and it looks to be a local maximum. Plus d/dx =2xy and d/dy = x^2 and so if x+y = k then y=k-x and d/dx = d/dy is a local maximum (as if one was larger we would progress on that path until you could make it larger by going on the other...) so we have 2xy=x^2 -> 2y=x and then replace the constraint so that 2y=k-y we find that y=1/3 k and therefore x = 2/3 k and therefore 2y=x and i guess i was right.

[Megas]

Staying flux neutral, or close to it, is important because AI will kill themselves otherwise.  They cannot help from not firing weapons until they cannot anymore by driving flux too high.  Flux neutrality is also useful for me in case I want to swap ships in the middle of a battle.  I do not want to hand my flagship to the AI and watch them self-destruct because they cannot handle my flagship loadout of choice.  It is even more important if the ship also has a timed system that can end prematurely by venting.  No point giving Scarab multiple IR pulse lasers if it cannot use them for the full duration of a time shift.

That was a reason why Accelerated Ammo Feeder in earlier releases was bad when it did not have a flux discount (or enough of it).  AI Hammerhead or Lasher activated ammo feeder, fluxed itself out after a couple seconds (before the system timed out), then it died when the enemy sneezed on it.

Yes, yes and a million times yes. Many ships have so little flux they can barely handle "budget" loadouts with low flux/sec weapons. It's ridiculous to me that you have a ship with let's say a large ballistic mount, and that you can't even dare to put a weapon of your choice there. You HAVE to go with the cheap option and then invest 60 points into vents. Sure you could do the opposite, no one's stopping you, but that ship will die horribly. I'm all for things that help with the mandatory OP taxes, it'll eventually lead to some more interesting builds.

This is what I do not like about Onslaught, and Legion to a lesser extent.  If Conquest did not have Heavy Ballistics Integration, I would use more Heavy Needlers instead of a Mark IX for kinetics.  (I would use HAG or Mjolnir for anti-armor and anti-hull because medium HE is lacking.)

Then, there are others where if I want to have a good weapon or two, I need to leave the rest of the mounts empty and optimize dissipation and maybe capacity too if I cannot get dissipation low enough.

But I can see how this would be incredibly tough to balance, with so many ships we have. Also I don't have a problem with overfluxed ships IF they're using high powered weapons.

If only the AI could control themselves.  Since they cannot, high-powered weapons are often a liability except for some playership loadouts that the player cannot give to AI if player needs to swap ships.

[TaLaR]

But dissipation doesn't actually equal damage output, while flux capacity doesn't equal tankiness. These assumptions come anywhere close to being true only under sub-optimal AI piloting. Player can keep shields up for much smaller portion of time and use every little opportunity for short vents, at which point dissipation contributes more to both damage output and tankiness.

But... Yea it does? And venting doesn't work like you think it does?

OK so lets assume for a weird reason that the player isn't being shot at (because the AI does prioritize shooting the player). They shoot over their dissipation and vent. While they're venting they're not shooting but are dissipating twice as much as normal. If we assume that they can shoot infinity over disspiation without overloading then DPS = Dmg/Flux * dissipation * 2 because they spend 100% of the time venting and you vent at dissipation*2. If we assume they shoot 0% over dissipation then DPS = dmg/flux x dissipation. For any amount over dissipation they can shoot we just have a different multiplier which is a function of the amount over dissipation they can shoot and the amount of capacity they have both of which increase the multiplier (because you're venting a higher proportion of the time)

We might note that because this is a flat multiplier its just like having more efficient weapons... which do not modify the fitting considerations because they do not modify the percentage amounts of dmg that adding flux or capacity add...

Now lets assume the player is being shot at. Well then extra capacity lets them absorb more damage, dealing more damage before they have to vent. This increases the amount of time they are venting in proportion to not venting and so increases the final effective DPS by a flat multiplier... which... oh

Incoming fire is not evenly mixed stream in absolute majority of cases. There are usually small windows of opportunity enough to drop shield for a few seconds. You can also vent in short bursts, as long as you maintain low (10-30%) flux levels.
You also don't have to catch every projectile on shield. Selectively allowing kinetics through goes long way.
Then there is accuracy. Quite often a projectile would hit the shield, but not ship's hull - that's invitation for short shield drop as well.

[FooF]

@ OP

Absolutely, once you go above weapon dissipation+shield upkeep, you have quickly diminishing returns on invested OP on vents but the fact remains that if I have 20 OP to spend on vents or hull mods (and I'm still not at/near flux parity with weapons), using the 20 OP for more vents is almost a no-brainer. The question should be, "Why?" Is dissipation the God-stat? For High-Tech ships it definitely is. For most ships, I'd argue, it is. Clear flux advantages tend to result in superior battlefield presence, player-controlled or AI.

Back to the post you quoted of me: the problem with raising all dissipation levels or even increasing the amount of dissipation/vent is that it translates into more DPS. Even though I disagree with the conclusions that Goumindong came up with via abstraction, more flux available does ultimately translate into more DPS. (That translation is extremely diluted, though, because of weapon efficiencies, multipliers, range, positioning, etc. all play huge roles. Also, capacity doesn't directly translate into defense because many ships rely on armor, which is flux-free, for their damage mitigation. It's not nearly as one-to-one as dissipation is with DPS). If each ship has more DPS, either the speed of battle increases or we have to balance that out in another way.

Alex has said that AI use of heavy weapons will be "smarter" next patch. He did some tests against Fighters with flux hogs like the Heavy Blaster and demonstrated that even with such flux inefficient weapons, it was better for them to fire at fighters than not because the AI dialed the heavy weapons back as it approached high flux. Maybe, just maybe, autofire and AI loadouts won't be quite so hamstrung by high-dissipation builds.

Base Flux Stats

Just for kicks, I took a look at base flux stats across all Vanilla hulls (i.e. the ratio of dissipation:capacity). Considering you get 10 dissipation for every 200 capacity via investing OP in vents/capacitors, you'd think that most ships were in the .05 range for a ratio. Not including fighters, most ships were not. About 65% of all ships had a ratio greater than .05, which means that either the dissipation was higher than "average" or the capacity was lower than "average." In most cases, just looking at the numbers, it would appear dissipation is higher. Some Carriers have lower-than-average capacity and most Phase ships have very high dissipation but low relative capacity.

What stood out was that many Low-Tech ships were anemic in both categories. Not only does the Onslaught have half the dissipation of the Conquest, it has less overall capacity, too. The Eagle has 17% more dissipation but equal capacity with the Dominator. The Hammerhead has 50 more dissipation and 200 more capacity than an Enforcer.  I would imagine that low dissipation ships would be offset by a high capacity and vice versa but I don't see this. Most ships with high dissipation likewise have higher than average capacity.

The main point being: the ships that are flux-starved on the dissipation side are double-whammied by having lower-than-average capacity, to boot. My guess is that these Low-Tech ships are counting on flux-free armor to save them in a flux war but if that is the case, there is no reliable way of improving armor via OP except Heavy Armor (which has its drawbacks+OP costs) and Armored Weapon Mounts (also drawbacks+OP costs). Most of my complaints are about Low-Tech so perhaps we just need to adjust them up rather than re-balance the whole-thing?

[intrinsic_parity]

Once 'defense' includes factors other than capacity, then the conclusions you draw about capacity based on the assumption that defense=capacity don't hold anymore. This follows logically: if you can achieve sufficient defensive capability without shields (armor tanking and/or evasion), then you can place less value on capacity (I will show this in my next post). When you abstract away important elements of combat, you arbitrarily place additional emphasis on the remaining elements of combat.

It can be useful to consider a limited scenario to better understand short engagements (this is my approach as well), but claiming that conclusions from those very limited scenarios can be extended to optimal behavior in broad fleet contexts is not reasonable. Optimal behavior accounts for combat exactly, not some abstraction/approximation of combat. It should be easy to see that assuming dissipation=DPS/capacity=defense does not adequately represent combat as a whole. It's fine to do that to understand the flux war and gain an understanding of how ships perform, but it's not reasonable to devise outfitting strategies based on the assumption that the enemy AI will follow some optimal behavior that is entirely based on that limited approximation of combat.

Not to mention that the AI doesn't make decisions in that way, so even if it was theoretically 'optimal' for both sides to play in a certain way, your true optimal play would still be to abuse the AI's actual decision making process as much as possible, rather than to behave in the way that works best against optimal play.

I actually tried to analyze the value of adding a capacitor vs a vent a while ago and found that it was a very complicated and non-linear relationship. The value of a vent depended on how much capacity you had and vice versa. I'll type that up tomorrow because it's very late.

Its not linear but its not actually that complicated because its linear in logs. Let z = x*y . This is a non linear relationship. But if i wanted to maximize this in relation to a constraint x+y = k then i could make it simple by taking the log. Log z = Log (x*y) -> Log(x) + Log (y) and now it should be very simple to understand that the maximization happens when x=y. Even if you don't want to do the "actual math" to solve it. And we can do this to more or less any construction of this formula.

You've picked an arbitrary function of capacity and dissipation and claimed that maximizing it is optimal with no justification. You could just as easily pick J = (capacity + dissipation) or J = bessel function(capacity^2*co-tangent(dissipation)). There's no reason to believe that any of these represent meaningful functions to be optimized. There's no connection to combat, it's just an arbitrary function. (ok it satisfies the general relation 'increase in caps or vents --> increase in metric', but that doesn't mean it's optimum is significant in any way). 

A more principled approach is to select a meaningful metric of combat effectiveness that is a function of dissipation and capacity, and then analyze the sensitivity of that metric to changes in capacity/dissipation. I'm not claiming that this approach is the best/optimal, but it at least has some grounding in combat. I'll make another post shortly with some in depth analysis.

[intrinsic_parity]

Here is my attempt at analyzing the relative value of caps and vents:

Consider two ships engaging one another. We assume that the ships engage and fire until overload but we make no claim that this is a realistic model of combat, merely that it is useful for analyzing who is more capable of winning the engagement in a brawl.  One possible metric that approximates the degree to which ship 1 defeats ship 2 in the flux war is the relative time to overload. Increasing this value indicates improvement in performance for ship 1.The difference between the time to overload of two ships determines who will overload first. Time to overload for a single ship is generally:

TTO = total capacity/flux generation = total capacity/(shield upkeep + Incoming flux from damage + net weapon flux generation)

The terms are all generally functions of ship characteristics like shield efficiencies, weapons, skills and hull mods.

TTO has the general form
TTO = (A + B*#caps)/(C - D*#vents)
with
A = the base capacity,
B = 200
C = a sum of shield upkeep, flux generation due to enemy weapons, flux generation due to friendly weapons, minus base dissipation)
D = 10
(There's actually a bit more complexity here as if dissipation exceeds soft flux generation, there is no additional benefit. This is easy to simulate, but annoying to write down analytically so I've ignored it here, but it is simulated correctly)

Analytically, you could look at sensitivities like:
d(TTO)/d(caps) = B/(C - D*vents)
d(TTO)/d(vents) = (A + B*caps)*D/(C - D*vents)^2

You can draw some general conclusions:
- the value of adding caps or vents (in terms of how much you improve the overload time) depends on how many caps and vents you already have as well as on the specifics of the situation
- adding caps and vents is always good (naturally)
- adding vents benefits additional vents more than it benefits additional caps (the square in the denominator causes this)
- each additional cap has the same value, each additional vent has increasing value

The optimum TTO is generally going to depend on the values of A and C which are ship and situation specific so you really can't make any more general statements than that. I concluded from this that it's not feasible to analytically make strong statements about optimality without considering the specifics of the situation, so we turn to simulation.

i picked specific ships and loadouts. I plotted the value of the TTO differential (J = TTO_ship1 - TTO_ship2) as a contour over the space of vents and capacitors, and then I overlaid diagonal lines representing 'constant OP curves'. My reasoning is that all the points along these lines represent combinations of caps/vents with the same total OP cost, so the maximum of the contour along the constant OP curve is the best loadout at that OP cost with respect to the TTO differential. In the plots, the contours are 'rainbow colored' where brighter colors mean an advantage for ship 1.

Some scenarios:
Two unskilled eagles

Spoiler

Two unskilled eagles, both with 2x Heavy needler, 1x Heavy mortar and 3x graviton. The opposing eagle has max caps and vents 36/36.

Interestingly, it appears that slamming caps is best in this scenario for all OP values since moving along the constant OP contours towards 'more caps' always improves the TTO.

[close]

Skilled eagle vs unskilled eagle

Spoiler

Two eagles, both with 2x Heavy needler, 1x Heavy mortar and 3x graviton. The opposing eagle has max caps and vents 36/36. The friendly eagle has defensive systems 2.

In this case, loadouts with high available OP (50+) should max vents and fill caps, while loadout with only a few spare OP should max caps. There's also a neutral region ~45 OP where it doesn't matter which way you go, performance is generally the same.

[close]

Skiled Eagle vs Sim Eagle

Spoiler

Friendly eagle with 2x Heavy needler, 1x Heavy mortar and 3x graviton. The opposing eagle has 3x heavy mortar and 3x graviton, max caps and vents 36/36. The friendly eagle has defensive systems 2.

Here it's better to max vents first in all cases.

[close]

Because the contour was locally very close to linear, you could mostly compare the slops of the contour to the slope of the red lines to analyze performance. Generally, it seems like either slamming vents or slamming caps is always best, but which way to go depends on the specifics of the situations. It seemed like anything that decreased flux generation (increased shield efficiency, reduced incoming damage, reduce shield upkeep) made vents more valuable. That includes evasion and armor tanking, so the utilization of those strategies does increase the value of vents, as far as I can tell.

Other considerations:
- It's not clear that maximizing the TTO diff is always desirable. You can overkill, or be so far behind that is doesn't matter(diminishing returns)
- Vents have the additional benefit of reducing vent time while caps increase it, which isn't accounted for at all.

This is purely a measure of how well a ship can brawl/win the flux war.

[SCC]

To me, the question of "are caps or vents better?" is reduced to a simple... I don't know what's the term. Equation? Situation? Anyhow, it's reduced to a simple reasoning: capacity allows you to dish more damage out within a certain time, whereas dissipation allows you to deal more damage over infinite time. Since capacity typically sets the time limit to a maximum of about a dozen seconds (assuming equal or stronger opponents, which is what I care the most about), which is rather short and most often wholly insufficient to end an engagement between ships (unless you use missiles, where you don't care about flux much anyway), a better approach is to perform better over infinite time. It's different only for ships that have top notch mobility (phase ships, hyperion), which are almost certain to be able to disengage from the enemy and vent safely (which can't be said for other ships), where it's more valuable that they go heavy on capacity and are able to operate behind enemy lines for longer.

Maybe I should address the original topic, too.
For specific examples posted in the OP, I'd say that Wolf is just rubbish, mjolnir is fine, storm needler's range is too specific for the "the only kinetic weapon you need on that ship" role it set for itself. Medium energy weapons were addressed a bunch of times in various places already, so I think it's fine for me to leave it alone now.
The reasoning for preferring vents to caps I already laid out above.
Should all ships have a viable (even if not very efficient) loadout that makes use of all its mounts? Not necessarily, if other loadouts, in total, do make use of all mounts. It is very true that some mounts are way more important than other. It's something of a repeat of a previous suggestion thread, about mounts being left empty in most cases, but I can only repeat that to change that either all the ships would have to have sufficient flux that weapon flux is never a concern, or making weapons which are sufficiently cheap in OPs and flux that they are preferable to leaving mounts empty. Though, since medium energy weapons already have heavy "almost a large weapon" blaster, maybe adding a flux efficient, but mount inefficient would work for them. Though there's those pesky midline ships to keep in mind with those balance changes...

(because the AI does prioritize shooting the player).

I am pretty sure this is not the case, but not 100%. Hoping Alex can clarify.

I recall Alex saying that it doesn't do that by default, but the player attracts attention to himself by acting unlike AI, typically more aggressively.