Combat Formula Approximation
Damage per shot = tanh( attack*(random(0.6 to 1.666)) / (defense * 5) ) * damagecap
damagecap = 2.5 * npcrank ; for players, damagecap = 0.5 * decks in most cases.
The tanh() function is almost linear up to 0.40, therefore if your attack ~= npcdefense , you will do about 0.20 * 2.5 = 0.50 * npcrank (your rank in the case of matched npcs). If your attack > 2 * npcdefense , you will do about npcrank in damage.
To hit around the damagecap on npcs, you need around 10 * npcdefense (~96.4% of cap).
The "attack randomization" is not linear, but a large data sample indicates the lower multiplier is 0.6 and the upper is the inverse, 1/0.6 = 1.666, and most of that range is linear. The shape of the randomization appears to be a truncated arctanh() function. The average effective attack multiplier is about 1.10.

I'd also like to point out that it SEEMS that the damage equation for base combat is a derivative of that with a factor of 10x somewhere. Recently TU battled a base that had roughly the same att/def as my ship and it was consistently doing about 10x the damage to me that I was doing to it.

I'm thinking that it may be { DPS = tanh( attack * (random(0.6 to 1.666)) / (defense * 5) ) * ( damagecap / 10 ) } when attacking a base.

That's the long math-speak version. Short version is you (or they) need 5 points of additional attack to balance out 1 additional point of defense for most of the damage range. Due to the nature of the tanh function, the closer you get to hitting for damage cap, the higher the attack vs defense ratio needs to be.