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I have two bows for my companion, one having higher damage (100, but in poison, so it takes effect slowly) and 5% life steal (with other stuff) and another with lower damage and 7% life steal (with other stuff) AND +attack rating based on the character, which currently is more than +1000.

Now I don't really know how attack rating works and if there is a cap or the +1000 is going to waste or not, but somehow that number is so big, it makes me want to keep the lower-damage-higher-rating bow for my companion.

Can somebody explain to me how attack rating is valued against damage? Am I doing a good thing by choosing the higher rating one?

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attack rating is MORE important than damage IMO –  user38944 Dec 27 '12 at 11:43
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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.

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Great answer thanks! Now I understand how it works. I had seen she doesn't have problem hitting with either bow, but now I know that in the future she would! While we're at it, do you think it's worth giving up the 7% life steal for Passion rune word? The attack rating would be slightly more, and the damage definitely more. –  Shahbaz Dec 16 '11 at 13:28
    
@Shahbaz, I personally don't think act 1 mercenary really needs that life steal. She is not usually the one taking damage, so there is nothing to heal, and if she is taking damage, she doesn't usually last long anyway, with life leach or without. You will need to heal her with potions. So I'd choose the higher damage bow. Also, Passion is a great weapon! And I think Harmony is even better. Vigor aura is nice to have! –  Rotsor Dec 16 '11 at 19:17
    
Indeed Harmony looks awesome! But unfortunately, I realized I didn't choose my character as ladder when I was about level 30 and didn't feel like starting all over. And, I am a druid myself (specialized in windy spells), so I myself am also not in the battle. Indeed, my companion has higher armor and life, so I let her get the beatings! :D I thought about getting a melee companion, but I decided since they so mindlessly charge to battle, they are even more likely to just die. –  Shahbaz Dec 16 '11 at 21:37
    
@Shahbaz, maybe it's time to reconsider the choice of the mercenary before you invest too much into her equipment. Not having any tank is not good for you and act 2 mercenaries are very popular for a reason -- they are very strong. Alternatively, you can adopt a bear pet. :) –  Rotsor Dec 16 '11 at 22:25
    
Nah, I think I'd stick with my magic. But I would try getting an Act 2 guy. The thing with the amazon is that I can go back and forth with the enemies, preventing her getting killed, also confusing the enemy. With the act 2 one, I'd have to test see how he fares. –  Shahbaz Dec 17 '11 at 14:40
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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.

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You can hover over the "attack rating" value in your character sheet to see your chance to hit an equally matched opponent. –  Resorath Dec 15 '11 at 22:16
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Nope; see my updated post. –  ver Dec 15 '11 at 22:35
    
oh really? I recall it always being a enemy equal to your level but there ya go. –  Resorath Dec 15 '11 at 22:36
    
@ver, Doesn't matter, I want it for my companion not me –  Shahbaz Dec 15 '11 at 23:04
    
Same roll-over tooltip applies for defence to see what the last enemy's chance to hit you is. –  Marty Dec 15 '11 at 23:42
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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.

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Wups. Thought I changed that to "physical damage". –  SaintWacko Dec 16 '11 at 18:48
    
That's not exact either. Some attacks, like Paladin's Smite, or Necromancer's Corpse Explosion can deal physical damage without performing the to-hit test. You can just say "normal attacks" instead. :) –  Rotsor Dec 16 '11 at 19:26
    
Ah, I suppose that's true. Hadn't thought about that. The wiki said "physical attacks". Guess it's not quite the same thing. –  SaintWacko Dec 16 '11 at 19:29
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