Hit ratio

[Alneyan]

There is a penalty linked to range: for every square between two ships, odds to hit the target are reduced by -10%. So, the base chance to hit a vessel right next to you is 90% (range 1), and it falls to 20% at range 8.

The only way to improve accuracy is to use offence bonuses: among those are Combat Sensors (available under Sensors after Physics 1), Ship/Fleet Training (under Advanced Military Science, once Military Science has been fully researched), and increasing aggresiveness when creating an Empire (and/or picking a culture like Berserkers).

Alternatively, you could use the Religious trait when setting up an Empire: it would give you the dreaded Talisman, a device making all weapons on a vessel hit their target all the time (accuracy of 100%). There are also some attacks that never miss: boarding, ramming or firing a missile at a vessel always work, though you will still have to overcome the defences of the vessel (security stations or self-destruct devices for boarding, point defence weaponry for missiles).

[capnq]

If you are using Tactical Combat, there is a toggle under Options that displays each weapon's chance to hit when you point at a target.

[Kamog]

In addition, some weapons have a built-in bonus to hit. For example, incinerator beams have +10%, high-energy magnifiers (a crystal tech weapon) has +30%, wave motions guns also have +30%, and so on. Seekers, I believe, never miss a target.