Fleet without defense defeats fleet with

The defenses seem to be calculated individually per ship. I tried to build a fleet with one ship having weapons plus defenses four others carrying only defenses - my attack capable ship was immediately destroyed then each defense ships took three or four rounds to get destroyed. The non specialized defense is still worth square root. Ability luck can increase practical (average) attack without being visible in the stats - apart from "real luck" (it is not X against Y but something random between 1 and X against something random between 0 (1?) and Y).

My understanding is that combat is assessed on ship by ship defense against fleet attack.

So if opposing fleet had a small number of larger ships and you had a large number of small ships, then enemy's combined attack would be targeted at a single ship of yours until it was destroyed, when your next ship would receive remaining attack and so on each round.  The same would be applied by your ships against him, but if his ships are large, you may not penetrate the target ship's defences so well.  So fleets of smaller ships tend to take much more losses than fleets of larger ships with the same aggregate stats. 

Furthermore, if most of your attack was in just a few ships with low defense, the algorithm automatically targets these as a priority, so your attack could drop sharply after the first round or so, making the damage you inflict in later rounds less effective (possibly no longer overcoming defence).

I noticed this, too. Having strong defence doesn't make your ships "survivable" as more as you would think. Defend values are rolled between 0 and shild max (calculated like mentioned above), so when your opponent has 12 attack and you have 4 defence value, you may get 10-12 damages several times, too.

Defences might be calculated in a different way to give it more significance.

It's difficult to determine how things happened in your above scenario without more information (specifically with regards to weapon/defense builds per ship).

However...

Defenses are depleted during the combat round and refreshed at the start of the next round-this means when they do get hit, they can't sustain as much in a given round as would be expected.

The targeting algorithm only chooses one target for each side, which means that all ships on each side will target the same ship until it dies.

This means that only when your defense is sufficient to absorb a majority of the opposing fleet's firepower is it actually going to make your ships anything close to invulnerable.

Since there comes a point where such a quantity of defense is actually impossible, defenses are not as valuable late game as they are early game.