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.
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.
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.
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.