Master of Orion combat damage calculations are governed by random "attack" rolls.
Generally, a random number is generated between 1 and 100 and then modified by the attacker's targeting computer and reduced by the defender's maneuverability level (1 through 13, 9 max for engines and 4 max for special equipment). Targeting computer's are researched under the Computers research field and range from Class I to Class XI. Ship engines govern maneuverability and are researched under the Propulsion research field.
Ship engines have warp ratings from 1 to 9. This is how far they can move on the galaxy map. The warp level of the engine is also a cap on the maximum combat maneuverability of the ship. A ship with a warp 4 engine cannot have a combat maneuverability from the engine that is greater than 4, but it can be any number less than 4.
Note: It can be good to move fast on the galaxy map and slow in combat. Increasing combat maneuverability decreases the space usable for other things, such as weapons, so it is not always best to choose the highest maneuverability possible for the engine.
The special equipment Inertial Stabilizers and Inertial Nullifiers add to the maneuverability rating of the ship, if they are researched and built into the ship design. Inertial Stabilizers increase maneuverability by 2 and Inertial Nullifiers increase it by 4. Both cannot be on a ship at the same time, so the max maneuverability is 13. This is 9 maximum for Warp 9 engines and 4 from Inertial Nullifier.
Note: It is generally better to use special equipment ONLY if you are already at the maximum standard maneuverability for the engine. E.g. Maneuverability 9 is better than Maneuverability 7 + Inertial Stabilizer or Maneuverability 5 + Inertial Nullifier. There is no difference in combat between these settings, because they all add to 9, but the space used for movement will be greater with the special equipment than if specials are not used and only standard maneuverability is used, essentially wasting space for nothing.
The base roll is a random number between 1 and 100.
If the attacker and defender both have the same modifiers, the hit chance is 50%. E.g. if the attacker has a Mark V targeting system and the defender has combat maneuverability of 5, then each weapon is 50% likely to hit. Each weapon on each ship gets its own roll. If a ship has 10 lasers there are 10 individual rolls. If there are 100 ships each with 99 lasers there are 9,900 individual rolls.
If the defender's maneuverability is greater than the attacker's targeting, the percent chance to hit is generally reduced by 10% for each level the defender is superior. E.g. Mark 3 targeting computer vs Maneuverability 5 defender, the chance to hit is 30% (50% base - 2 x 10% = 30%.
If the attacker has the advantage, the attacker generally gains 10% for each level they are advantaged. However, there is always at least a 5% likelihood to miss regardless of how much advantage the attacker has. If the attacker's advantage is 5 or more the chance to hit will always be 95%.
Some things can modify this.
Wide beam weapons add + 3 to the effective targeting computer level for that specific weapon attack.
The Mrrshan race ships act as if their targeting computers are 4 levels higher than they actually are (mark 4 for no computer installed to mark 15 installed with Mark XI targeting computer).
The Alkari race gets a + 3 racial bonus to its maneuverability calculations to avoid damage.
A special equipment item, the Displacement Device, makes all hits 1/3 likely to miss. This is an additional roll that occurs if a weapon would roll a hit, a second roll happens and 33% likely it turns the hit into a miss.
The Battle Scanner special equipment gives an effective + 1 bonus to the attacker's targeting computer.
The Technology Nullifier special equipment can be fired at a ship, if it hits, the defender's targeting computer is randomly reduced in level between 2 and 6 per hit.
Missiles have an additional level of targeting computer dependent on the type of missile. A given type of missile always has the same increase in targeting level. If missiles are used, the defender's ECM system is activated (electronic counter measures). The ECM will attempt to jam the missile's targeting computer. The formula to determine advantage is then (attacker) Ship targeting + missile targeting vs (defender) maneuverability + ECM level for missile attacks. Torpedo weapons follow the rules for Missiles.
Note: ECM computers can be quite expensive. This can be used strategically to benefit the attacker. If the player finds out the opponents are using no or low level ECMs, they can load up on missiles and be almost guaranteed to hit with everything. If the player finds the opponents are using high level ECMs, the attacker can leave missiles off his or her ships and use that space for additional weaponry, causing the opponent to have space wasted on their ships for nothing. This can be determined through the use of the Battle Scanner special equipment.
The Cloaking Device special adds 5 to the defender's maneuverability when it is activated. It must be turned off in order to attack, though. As soon as the ship attacks the cloaking device will de-cloak and the ship will not re-cloak until the ship ends a turn without firing any weapons.