How does attack rating compare to damage in Diablo 2?

Solution 1:

According to http://www.lurkerlounge.com/spirea/Hirelings/Stats.shtml, the inherent attack rating (AR) of Act 1 mercenary is quite low: 796 on level 80.

Combined with the fact that the monsters in Hell difficulty have defense rating (DR) on the order of 1500 and the chance to hit formula (assuming equal levels of attacker and defender): toHit = AR / (AR + DR) , this makes her base chance to hit very low: 796 / (1500 + 796) = 0.35.

If we add 1000 to her AR, we'll get the chance to hit of 1796 / (1500 + 1796) = 0.54, which is 1.57 times higher!

So, if there were no other factors, I'd keep the AR bow even if it had 1.5 times less damage.

Note that other factors affecting the AR and Defense include Inner sight and Fire arrow.

Another thing to keep in mind is that the poison damage does not stack. If you have a weapon dealing 100 poison damage over 3 seconds and you hit once per second, the damage poison deals between hits will be mere 33.3, and then, when another hit lands, the old poison will be replaced with a new one, not added to it. On the other hand, poison stops the natural monster regeneration, which may be a big deal for really tough monsters.

Solution 2:

The attack rating determines your chance to hit (or miss) a target. The higher it is, the better. In late game, +1000 isn't all that much.
It doesn't directly influence your damage output; but high damage is useless if you can't land a hit.

Your to-hit chance will always be at least 5% and at most 95%. And it only pertains to physical attack (i.e. not to spells).

Edit: If I recall correctly, you can hover your mouse over the Attack rating number to see your chance to hit the last enemy you attacked.

Solution 3:

Attack rating controls chance to hit with physical attacks. It really depends how well she is hitting to begin with. If all or most of her attacks are hitting her targets, you should probably go with the higher damage bow. If she's having trouble hitting, go with the higher attack rating. Attack rating suffers from diminishing returns, so if she already has a good chance to hit, the increase in accuracy won't be near as much as it will be if she has trouble hitting targets.