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Stats Affecting Attack Rating
Dexterity is the only stat point that affects attack rating. Increasing your dexterity using the five stat points you are awarded each time you gain a new level will increase your attack rating. Another way to increase your dexterity is to equip items that offer dexterity bonuses. You can also carry dexterity charms with you in your inventory.
Attack Rating for Amazons
Attack rating is important for amazons, since it does affect ranged attacks. It is also quite easily obtained since the amazons' primary stat point is dexterity, since it increases ranged attack damage for bowazons and chance to block for javazons that use a shield.
Attack Rating for Melee Characters
As a melee character, such as a smiter paladin, you want the highest attack rating possible to increase your chances of hitting your opponent. The highest your "chance to hit" (seen by hovering over the attack rating box on the character screen) is 95 percent. If you also use a shield, you want as many points in dexterity as possible since it raises both chance to hit and chance to block.
Attack Rating for Casters
Attack rating offers no benefit to magic casters, such as sorceresses, summoning druids, caster necromancers and singing barbarians. Attack rating doesn't affect the accuracy of spells, and since you don't physically attack (melee) as a caster, you don't need to worry about raising your attack rating.