The 3 x 200 attack would get 3 x (100 - 120) = 0 because damage can't be negative.

Actually, the expected value would be -60 so the attacker would have to roll 61 points better than average to get 1 point of damage.

Clearly, against a ship that has all three defenses a ship with multiple weapons *always* does worse on average.

The thing is that your 600 points of attack fire only once. If it's a single weapon it's just the single fire of 600 against all of the defense, If it's 2 x 300 then it's 300 against all of the defense then another 300 against all of the defense. With three weapons the defender fires his defense three times. This is clearly an advantage for the defender that doesn't exist if the attacker has only a single weapon.

The net effect of this is that the only case where multiple weapon types on a ship buys you anything is when the defending ship has defense against the single ships weapon but doesn't have defenses against all of the multiple ships weapons.

But my point for wanting a multiple attack ship was to have a generic ship that didn't need to be redesigned and upgraded dependent on your opponents tech. If you have to worry about what type of ship that your facing you may as well just have the single weapon that you change dependent on your opponents defense.

Now none of this has to do with having different attack types in the same fleet. If you really feel the need for multiple attack types you should implement different weapons on different ships. I've never cared much for this because I like to build a single ship type at all my planets so I don't have to worry about forming fleets with the proper composition, they're all interchangeable.

Anyway, I hope this explains it sufficiently.

Now what is it you want to prove about multiple defenses?