Big Bad Dreadnought #1 tears apart one ship of the line with weapons giving 70% accuracy.
As it turns its guns on the next ship, the accuracy is up to 71% due to experience
The training value adds directly to/is subtracted from to-hit calculations does it not?
One way of dealing with AI 'incompetence' in this regard is to let them 'cheat' and mod them to use the psychic training (applies over a system not a sector) ability.