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I found some rings that add bonus physical damage. Once has +x-y Damage and the other has +x Minumum Damage +y Maximum Damage.

Here is a picture: enter image description here

Both are from post 1.0.3 and there is still y +x-y Damage attribute contradicting this question.

So my question is how do they differ and would they have the same effect if the value for x and y were the same for both rings (all other attributes ignored). So if the first had +10-12 Damage and the second had +10 Minimum Damage +12 Maximum Damage would they be equal?

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They're pretty similar.

So, the first thing you need to know is that flat +Minimum and +Maximum effects get applied first, and they do so in a way described in this answer. The short version is that the +Minimum gets applied first, then, if this causes your weapons Maximum damage to be lower than your Minimum damage, your +Maximum will be increased to Minimum+1, and then finally, the +Maximum is applied.

Effects that are described as a range work as expected, adding the first number to your weapons Minimum Damage, and the second number to your weapons Maximum Damage, simultaneously, so there should never be any concern about strange overlaps. Bonus Elemental Damage on a weapon works this way as well, and is also applied after flat +Min/+Max effects.

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