Hurray!
This is bugged. The shields seem to absorb sqrt(damage + 1) and let the rest of the damage pass through to armor and hitpoints. So an attack that does 1 damage, the shields will absorb 1.4. If the attack does 15 damage, the shields will absorb 4 and let 11 points through. This was meant as a buff, I think, but the bug makes shields much less useful.
If it wasn't bugged, I think this would be severely overpowered. Fairly early barriers already give 18 points of shield (accounting for bonuses) with a low mass, and can be stacked. If you keep this, a shield can become incredibly point-efficient against high-damage attacks, so shield values and ability to stack shields should be reduced correspondingly. It would also make both armor and shields relatively weak against weak attacks, which I don't think is a good balance.
As long as armor has proper degradation, you should be able to find a balance point for shields without sqrt scaling. A shield stops it's rating in damage flat out. A block of armour in the best case can be expected to absorb half it's rating in each hit, but degrades linearly, so if it never "overstops" the damage, it can be expected to stop 5 times it's rating (stopping half it's rating each hit, but rating decaying to zero over 20 hits). This is the best possible case, but against "too strong" attacks it can be expected to stop only half it's rating (i.e. it gets one roll and the pass through damage is enough to kill the ship underneath it) and against low-damage attacks it could be expected to stop as few as it's rating or 20 points, whichever is lower.
So if armor is basically expected to stop somewhere between half and 5x it's rating, I think armor could be "valued" at about 2x it's rating in hitpoints. If you manage to arrange things so your armour is only a bit above your opponent's per-hit damage and your ship has enough hitpoints to survive leaking, you can approach that 5x number, but a lot of the time you will be way below it. So aim for shield modules giving about twice as many shield points as corresponding armour modules and I think you would be reasonably balanced.
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Kinetic base accuracy reduced from 67% to 50%.
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Missile base accuracy increased from 50% to 67%.
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Kinetic cooldown increased from 1 to 2.
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Missile range increased from 5000 to 6000.
All this seems pretty reasonable.
I don't really like this concept and it's inconsistently applied. Barriers can be stacked, titanium armour can't. It just feels messy to start laying different layers of tech on your ship and having this implied non-linear penalty to larger ships that *should* be able to stack defences. It feels like an over-reaction to the bug with armor not degrading.