that is some high math, he he

I sugest that shield capacity to absorb missile damage is still sqrt value, and the missile damage reduces general shielding by the amount of damage absorbed AND sqrt value, so if ship have 16 shields, it have capacity to absorb 4 missile and 4 point defense damage, if it receives 5 missile damage, it absorbs 4, 1 damage goes to the hull and shield new capacity to absorb damage is 12 beam, 0 missile and 3 mass driver damage
one "quick" example (let just say that maximum values apply, for easier understanding):
defense: beam-missile-massdriver / missile-beam-massdriver / massdriver-beam-missile
Ship1 have defenses 16-4-4/16-4-4/16-4-4, 50HP
Ship2 have attack 3x9/3x9/3x9
beam A: 9 damage; beam defense reduced; new defense is 7-2-2/16-4-4/16-4-4
---notice that shield capacity is sqrt value---
beam B: 9 damage; beam defense destroyed; new defense is 0/16-4-4/16-4-4; 2 damage pass through shields, it is absorbed by missile defense, so defense is 0/14-2-3/16-4-4
---notice that missile defense is reduced by 2, missile capacity to absorb beams is reduced by 2, and missile defense capacity to absorb mass drivers is not reduced by 2, it is sqrt(14)=3---
beam C: 9 damage; as missile defense already absorbed 2 damage, it can only absorb 2 more damage, armor absorb 4 more damage, defense is 0/12-0-3/12-0-3 and 3 damage pass to the hull, HP reduced to 47...
--notice that missile defense is not capable to absorb any more beam damage, but it could absorb 12 missile damage or even sqrt(12)=3 mass driver damage!---
missile A: 9 damage; missile defense reduced; new defense is 0/3-0-1/12-0-3
missile B: 9 damage; missile defense destroyed, armor is reduced for 3 damage, and new defense is 0(0-0)/0(0-0)/9(0-0), defense is bypassed and 3 damage pass to the hull, HP reduced to 44
--notice that armor is penetrated to all beam and missile damage, but it still can absorb 9 mass driver damage!--
missile C: 9 damage; no defense so HP reduced to 35
mass driver A: 9 damage; armor is now destroyed, new defense 0/0/0
mass driver B: 9 damage; HP reduced to 26
mass driver C: 9 damage; HP reduced to 17
next round RELOAD and REPAIR, so ship2 receives 3 beam damage then 12 missile damage and first mass driver destroys the ship, two mass drivers left to attack the next one!

so, what do you say?