I want to answer more of your question then you wanted.
Bow damage is effected by your ATK rating, but the little detail here that makes it separate from other types of physical damage is that DEX has the formula in place of Strength (for melee) for bows. Keep in mind that just straight increasing your ATK rating is all you need to do to make bows hit harder though.
Now Dex also effects the rate at which you proc, and critically hit. Its a very small increase (and im not even sure how much per skill) until a number thats near 110, then it largely increases to a number close to 140 (so from around 100-150 is a huge jump), then its almost nothing past 140. You might ask, why don't I know, or why is it hard to calculate? Because 1) the numbers which have the largest percentage spikes are weird odd numbers not nice even ones like 120 or 130 etc, and 2) you have to parse a whole lot for each skill point you test with and that takes forever so not many people know
The bad news: Bows are dependant purely on dex for procs, damage, and everything - Its not the most powerful stat in the grand scheme of things.
The good news: Bows are dependant purely on dex for procs, damage, and everything - If you *really* wanted to be a better bow guy, you only need to worry about 1 Attribute (but also your ATK rating)
However, here's the big takeaway: bows aren't that great in this game overall. Don't focus on them. They are fun though and super powerful until around level 20 but they have a very flat damage curve throughout your characters life.
A cheap way to power level to 20 with a bow? Runed Oak Bow. Cheap. Powerful as hell.
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