( Repost from my corp's forum on the Space RPG EvE-Online. Its designed for users already familiar with the game's ships and equipment, as well as its underlying concepts )
THE PASSIVE TANK:
Every ship in Eve has shields; this is rather well known. And over time, shields will gain health on their own without having dock. It is the objective of the passive tank to raise the rate at which shields recharge health for every second until it exceeds the damage per second the enemy can inflict on you. The goal in our inspection of passive tanking will be to reveal how absolutely high we can raise this health per second number. This unit is abbreviated as Hp/s.
CALCULATING HP/S:
Every ship's shields contain a finite value of Hp that can be destroyed before the shields failed and armor is exposed. Every ship also contains a Recharge Time gives the time required to recharge the shield's Hp from 0% to ~100%. Ingame, this value is identified as Recharge Rate, but despite its name, it is not a rate. The actual rate at which shields recharge is not linear, and varies depending on the current % of Hp in the shields. While the recharge function can and will be investigated further, for the sake of simple mathematical analysis we will opt, instead, to divide the total shield's Hp over the total Recharge Time in order evaluate an average recharge rate. So, the equation looks like this:
[#] Shield Hp / [#] Recharge time (s) = [#] Hp/s
It is clear that in order to increase this Hp/s value, we can either increase the shield's overall Hp or reduce its recharge time. There is equipment available ingame that does both, and we shall investigate the effectiveness of each.
Additionally, there is also the case of passive shield hardeners and active shield resistance field hardeners, which quite arguably do something to enhance the tanking capabilities of a ship, and should not be dismissed. In this evaluation, we shall imply that this equipment adds to the overall Hp of a ships shield with proportion to the Resistance Bonus of the shield hardener. So, if a Ferox has an Explosion Dampening Field I equipped, that has a 50% Explosive Dmg Resistance Bonus, we shall raise the Hp of the Ferox's shield by 50% (as we assume all damage dealt to said Ferox is explosive and the pilot can keep the field active throughout the engagement). The theoretical equation used for making these calculations is as follows:
( [#] Shield Hp + [#] Shield Hp * [%/100] Resistance Bonus) / [#] Recharge Rate = [#] Hp/s
SHIP EVALUATION:
Before we begin investigating the effectiveness of available ship equipment, let us first get a feel for the native Hp/s of ships without any equipment or skills:
Drake: 4.38 Hp/s
Ferox: 3.91 Hp/s
Myrmidon: 3.12 Hp/s
Hyperion: 3.00 Hp/s
Raven: 3.00 Hp/s
Apocalypse: 2.48 Hp/s
Dominix: 2.19 Hp/s
Kestrel: 0.63 Hp/s
These numbers are very relevant to our passive tanking build; every modifier we will investigate will be multiplied with the ship's native Hp/s.
While the Myrmidon's reputation as a superior passive tanking ship already seems to be tarnished, it is important to note that the Myrm has two more low slots and a greater powergrid then either the competing Ferox or Drake, but still the Ferox and Drake have the same or more medium slots, respectively, than the Myrm and a greater CPU. Which ship among these three offers the best passive tank can't be answered simply, and I feel you'll find that different circumstances and how much ship equipment a player chooses to invest in offensive weapons or utility will both significantly surpass ship's individual performance.
EQUIPMENT EVALUATION:
Here we shall be comparing shield Hp and Recharge Time modifiers of equipment, by way of reducing every item to a basic % boost in shield recharge rate, and in the case of Shield Extenders, revealing % boosts for various fitted ships and number of modules already installed. This number is determined by applying equipment modifiers to the fraction 1/1. If we were to multiply a ship's Hp/s recharge rate by 1/1 it does not change, however if we multiply a ship's Hp/s recharge rate by 1/.8 (the result of a module that reduces shield recharge time by 20%), we've calculated the recharge rate of the ship's shield with that module equipped. The numbers given are the quotient of 1/.8 multiplied by a 100, in this case (1/.8)*100 or a 25% gain in recharge rate. The actual theoretical equation used for these calculations goes like this:
[ ( 1 * [%] Shield Hp Modifier ) / ( 1 * [%] Shield Recharge Time Modifier ) ] * 100 = [%] Change in shield Recharge Rate
And now for what you've been waiting for, the equipment listing:
Shield Recharger I - 11.1%
(CPU and minor pwr grid fitting, med slot)
Shield Recharger II - 17.6%
(CPU and minor pwr grid fitting, med slot)
Shield Flux Coil I - 13.3%
(CPU fitting, low slot)
Shield Flux Coil II - 41.7%
(CPU fitting, low slot)
Shield Power Relay I - 25.0%
(CPU fitting, low slot, -35% capacitor recharge rate)
Shield Power Relay II - 31.6%
(CPU fitting, low slot, -35% capacitor recharge rate)
[Dmg Type] Field I - 100%
(CPU and minor pwr grid fitting, med slot, specific only to described damage type, must be active)
[Dmg Type] Field II - 122%
(CPU and minor pwr grid fitting, med slot, specific only to described damage type, must be active)
Invulnerability Field I - 33.3%
(CPU and minor pwr grid fitting, med slot, persistent for all damage types, must be active)
Invulnerability Field II - 66.7%
(CPU and minor pwr grid fitting, med slot, persistent for all damage types, must be active)
[Dmg Type] Amplifier I - 48.1%
(CPU and minor pwr grid fitting, med slot, specific only to described damage type)
[Dmg Type] Amplifier II - 60.0%
(CPU and minor pwr grid fitting, med slot, specific only to described damage type)
Shield Extenders will now be described separately because they do not modify the existing shield Hp, but instead add to it. This means the % change in recharge rate that occours varies depending on your shield's Hp prior to equipping - including, of course, other equipped Shield Extenders. Their % change in shield recharge rate will be identified for up to 5 extenders in place for the Myrmidon, Ferox, and Drake. Values are derived from this equation:
( [#] Shield Hp + [#] Shield Extenders * [#] Shield Extender Hp bonus ) / ( [#] Shield Hp + [# - 1] Shield Extenders * [#] Shield Extender Hp bonus )
Now for the data:
Large Shield Extender I -
1st Module - 43.6% Myrmidon , 38.4% Ferox , 34.3% Drake
2nd Module - 30.4% Myrmidon , 27.7% Ferox , 25.5% Drake
3rd Module - 23.3% Myrmidon , 21.7% Ferox , 20.3% Drake
4th Module - 18.9% Myrmidon , 17.8% Ferox , 16.9% Drake
5th Module - 15.9% Myrmidon , 15.1% Ferox , 14.5% Drake
Large Shield Extender II -
1st Module - 61.1% Myrmidon , 53.8% Ferox , 48.0% Drake
2nd Module - 37.9% Myrmidon , 35.0% Ferox , 32.4% Drake
3rd Module - 27.5% Myrmidon , 25.9% Ferox , 24.5% Drake
4th Module - 21.6% Myrmidon , 20.6% Ferox , 19.7% Drake
5th Module - 17.7% Myrmidon , 17.1% Ferox , 16.4% Drake
Be aware this situation is entirely more sinister because all of the 25m Signature Radius boost given by all of the described modules. Signature Radius means faster locking by the enemy and greater damage dealt under certain circumstances, and the quantitative impact of an increased signature radius is very hard to identify. Experimental analysis revealed railguns to gain 7% damage with the addition of 25m of sig radius to a Ferox, and then 16.7% with the gain of 50m. If either the Ferox or the Drake equip one shield extender, they become fully susceptible to cruise missile damage (unlike their native 285m sig rad), while Mrymidons are already vulnerable to full cruise missile damage. All of these ship's damage taken from torpedoes will increase as Shield Extenders are equipped. Caution should be taken in employing shield boosters, and alternatives should be found wherever possible.
BUILDING YOUR TANK:
As you set up your own passive tank build in whatever ship you're flying, there is no one empirically proven build that will 'work best' for you. Whatever build you choose is you're own, and should be constructed based on your environment and needs. Every build will have a weakness (whether its a particular damage type, nosferatus, or guns), and players will choose different emphasizes in offensive weaponry; employing low slots for damage enhancing modules instead of more Shield Power Relays, or whate have you. The purpose of this guide is to help make you make that build and make it as an effective tank as is possible, through the backing of raw hard mathematics.
As you choose parts and design your build, the choice is yours - and epically if you do not fly one of the aforementioned ships, feel free to try different equipment combos and try calculating your avg Hp/s recharge rate yourself!
Thanks for reading,
Zeta Aece (aka mwace)
(Note: Numbers next to shield hardeners should be accurate, however the described method of calculating this pending updating. Also be advised shield hardener values do not account for resistance stacking penalties - these must be calculated individually.)
