Looking at the formula- damage determines how high their attack would have to be to hit your damage cap. my limited understanding of tanh function is it produces a bell curve of damage. A middle you will often find- and outliers up and down you will hit less frequently.
Defence is 5x as important as attack in the formula- so basically it takes a crap load of attack to hit someones damage cap consistently instead of with a fluke shot
As an example- i have with a basic 10% buff (how i hunt on bt) approx 11.5k attack. i regularly hit ships with only two or three thousand defence- there are a lot of guys that think a big hull is all you need lol. These ships are easy to kill as i go close to damage cap on them- but i am nowhere near high enough attack to hit the damge cap consistently even on these ships with tin foil hulls- i could tell if i was hitting it because i would get same damage every hit- i do not.
Only ships i get damage cap consistently on is scouts
If i hit a ship with a lot of decks- (star destroyer or early galaxy destroyer classes) - and little defence and do over 1000 damage a hit- so their 5k shield and 15k hull is gone in 20 shots
Now if they instead installed more defence- and got their defence up to say 6000- or even 8000 or 10000- my damage would be a consistent average of 500 350 or 200 (these figures vary based on ship size- are just indicative). even if they dropped a lot of hull for this the level of effort to kill them is significantly higher. So assuming they gave up all their pretty scan and cloak for defence and still had 20k combined hull and shields. So instead i have to pay 40, 60 or 100 shots to kill them.
I am not sure i have answered your questions- not in the way you wanted- but i hope i have illustrated the practical ramifications of the formula from my very extensive real game experimentation.
Approx 3000 kills
Cheers
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Once Fabulon, now known as Thebloodynine
Most exasperated leader at Project Anarchy. Don't talk to me till the caffeine hit is in
Have given up caffeine- probably best just not to talk to me