Once the weapon's damage is determined, the attacker's defenses come into play.
Each ship has a shielding system from level 1 to 15. The player begins the game with Class 1 Shields known (but not automatically installed on all ships) and they can research shields with the classes of 2, 3, 4, 5, 6, 7, 9, 11, 13, and 15. These are in Roman Numerals, ie. XIII rather than 13.
The shielding level is not modifiable by anything other than one special type of weapon and subtracts directly from damage dealt to the ship.
If a weapon deals 1 to 4 damage and the defender has a Class IV shielding system it doesn't matter what the attacker rolls they will never do any damage.
If the attacker has a weapon that does 1 to 5 damage and is 50% likely to hit a result of 51 - 60 would do 1 damage, 61 - 70 would do 2 damage, 71 - 80 would do 3 damage, 81 - 90 would do 4 damage, and 91 to 100 would do 5 damage.
Thus if the defender had a level 1 shield, an attack roll of at least 61 would be required to do any damage at all, not 50. If the defender had a level 2 shield, the attacker would have to roll at least 71 to do any damage at all. If they had a level 3 shield, a roll of 81 would be required to do damage. If they had a lvl 4 shield a roll of 91 would be required to do any damage, and if they had a lvl 5 shield then no roll would do damage.
Note, in the above scenario, that if a roll of 91 to 100 were made, the damage would always be 1. Rather than having a range of 1 to 5, the range would be -4 to 1 or effectively 0,0,0,0,1 since negative damage cannot be dealt to anything.
Note also, it doesn't matter how likely they are to hit you if your shields are high enough level. All the enemy can do is research weapons that do more damage than your shields can handle and then equip them to ships and attack at a later time.
There is a special type of weapon that halves the values of the defender's shields (round down), referred to as "Armor Piercing". These weapons include the Neutron Pellet Gun (2 - 5 damage), the Mass Driver (5 - 8 damage), the Hard Beam (8 - 12 damage), the Gauss Autocannon (7 - 10 damage x 3 shots per weapon), and the Particle Beam (10 to 20 damage).
There is also a special equipment that makes all of your weapons (except missiles, torpedoes, and Bombs) count as armor piercing (doesn't stack if the weapon already has it). This is called the Oracle Interface and is a very high level technology in the Computers research field.