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Ever fight against an Archer who was using a 40% SSI Heavy X-Bow and has high Stamina? With all 70's suit, each shot is doing around 30s damage to you, disrupting your bandages every time. The higher swing rate of the Ornate Axe really doesn't matter when you can't keep close enough to your opponent to use it, plus your losing a good chunk of stamina per hit, when that opponent is able to hit you for 30s damage while at a range, and fire them off while running as well. With Lightning on the Heavy X-Bow, you can expect to be hit for 40 damage in one shot.
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My statement was on the premiss of all other things being equal(SSI, Stam, Hit Spell, exct..). I simply displayed the numbers. I'm sure it was made slower, and a lower DPS, because of the the range. OP wanted to know why the Heavy hit harder, and it is because it is slower. If the user of the Ornate axe doesn't have the ability to stay within range then their DPS might be lower, it's on them. I'm sure some have the ability to the ability to stay within range of their target. In those cases an Ornate axe would easily out damage a Heavy crossbow.