Npc's? Anyway, according to title, I presume u are talking about pve. It helps plunder anyway, but not sure about damage...
My experience suggests it counts towards damage done, % chance of winning, and plunder calculations on attacks. However, it appears that it does not affect how much you make on steals, or taxes associated with spy actions, though it still counts for damage.
Damage you do is effected by your stats (based on your buildings and troop level) To that number add any reset bonuses and Propack bonuses Then add the small amount from your banner Then add the bonuses you get from allies Then add the bonus you get from attack potions. The plunder you earn is wholly on your target with the exception of your base stats, troop levels, and ally hire value (up until plunder capping). Ally Stats, Propacks, Reset Bonuses, Banners, and attack potions have no effect on plunder earned.
That is because the allies increase your strength. If your stats are too high compared of the stats of your opponent, you will start getting less money.
To affect, verb meaning to have an influence on something. The effect, noun meaning the end result of that influence.
What wrath said, if you plan on just PW'ing and T 1,2,3 EB's then an old trick is volleying up a 0 stat Allie for maximum plunder. ( Also reduces chance of a coincidental strip). Needless to say if you're planning on real war'ing or if you're a hansel and wanting to hit bigger EB's without pots then you want the highest BFA as possible ^_^.