Day 2 we skirmish, but with no casualties. She withdraws.
Day 3 her monitor and frigate avoid battle and get away.
Day 6 I catch her again and the battle results show that I 'won.' Yet, my losses were nearly 3 times hers even though her ships were crippled by previous battle damage, supply shortage, lack of a commander, and the minimum cohesion of one!!!

In the end, I sank the frigate, but the ironclad got away

My 2 ironclads were:
at full 80+ strength with maximum cohesion
well commanded
fully supplied
with a full magazine of ammunition
set to offensive posture to take advantage of the offensive 14 strength (rather than the defensive value of 10)
Her ironclad and frigate were(see screenshots of the USA turn file):
at 1 cohesion (zero combat power)
with no commander
with no supply
low on ammo with half magazine capacity
set to passive presumably yielding the passive penalty if combat ensues and a defensive strength of 10 from the ironclad and 5 from the frigate.
This should not have been a difficult battle.
If this were a rare occurrence, I would not worry. But, I keep losing on a fairly regular basis even with seemingly huge advantages. Am I just unlucky, or am I at fault and doing something wrong? If I'm losing 3 times the men and canon when I 'win' against a crippled enemy, then how can I expect to win overall in the many battles that are much more evenly matched, or I'm outnumbered? What is the advised superiority ratio of naval combat strength to ensure(or at least provide a good chance of) victory?...2 to 1?...3 to 1? 10 to 1?
Or, does Athena just ignore some of her penalties to make the game more 'interesting?'
(I guess that goddesses can do that)

background info:
Windows Vista
'vanilla' version 1.07 patched up to 1.15
default game/AI/system settings
turn 28 on my first full campaign(from April start date)