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I assume PWR = some calculation of attack and strength.
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PWR is the portion of displayed ATK that relates to damage calculation after a hit has successfully landed. The other portion of displayed ATK is ACC which relates to your chance to hit. Yes, STR has an impact on PWR.
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Unsure how the minimum damage is 19
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If you look at live parses where high damage (15+) weapons are used, you'll see that:
MIN_HIT = DMG_BONUS + MAX(FLOOR((WPN_DMG+5)/10),1)
So for your poly axe, it's 15 + FLOOR((37 + 5)/10) or 15 + 4 = 19
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54 Paladin using Polyphenomenal Axe (37/48)
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All classes besides war/mnk/rog/rng still use the (STR + OFF) / 100 to calculate their max damage multiplier post-50.