So I'm just going to try to tl;dr this for people. Xbow is only better if you have > 33% crit chance, before that bow is better.
Am I correct in what you're saying?
Well, partly anyway. Bow beats Xbow below 35% crit chance or so no matter what. Above that, it depends on your crit damage bonus, but even a small amount of crit damage from items can pretty easily push you into bow territory.
So for most players, bows are probably better than 2H Xbows, at least as far as Archery is concerned. But Archery certainly isn't the only variable to consider in making a weapon choice, just part of it.
Wrong math.
1.15(baseDPS)( 1 + critChance * critDmg) = (baseDPS)( 1 + (critChance)(critDmg + .5))
Why 1 here?
From N attacks you do N * critChance - crit, and not 1, or N, but N * (1 - critChance) - non crit.
So if we calculate dmg for 100 attacks it be:
100 * (1 - critChance) + 100 * critChance * critDMG.
True equation is:
1.15(baseDPS)((1-critChance) + critChance * critDmg) = (baseDPS)((1-critChance) + (critChance)(critDmg + .5))
and final: y = (-0.15/x + 0.65) / 0.15
Here's a simulation:
100 shots, 100 damage per shot, 30% crit chance, 50% crit damage, non crit damage
baseDamage = 100*100 = 10,000
Total damage = 70 normal hits for 7000 damage, 30 crits for 4500 damage, total damage = 11500.
Your formula seems to be attempting to calculate normal hit damage and adding critical hit damage, just like I showed in the example simulation, but the formula doesn't work the way you've written it.
If you want to think about it that way, the formula should look like this:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))] ::: the key here is that the critical hits do 100% + bonus crit damage.
but when you simplify that you get:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))]
(baseDPS) [(1 - critChance) + (critChance * 1 + critChance * critDmg)]
(baseDPS) [1 - critChance + critChance + critChance * critDmg]
(baseDPS) [1 + critChance * critDmg]
I'm assuming this doesn't model any kind of an attack, right? The numbers tell me I should use a hand crossbow, (350% crit dmg, 30% crit) but honestly I have nothing to be gained from attacking faster for less damage. I use Cluster Arrow and Spike Traps as my damage dealers, which are solely dmg scaling based. So, switching to a hand-xbow with a considerably lower damage range and a faster attack speed might increase my hungering arrow damage, but it would ruin my frontloaded damage from these 2 big hitters as far as I know.
Yeah, it doesn't model anything beyond which weapon type would give you the greatest bonus to DPS from Archery. It's a much simpler comparison between 2h Xbows and Bows, since they can be used interchangably, but 1h Xbows have a lot more to consider, such as having a second Xbow for another potential 200% crit damage bonus. The chart most accurately compares using any of the weapons with a quiver, for the case where you have otherwise equal weapons of type.
Beyond that, there's other gearing considerations such as hatred efficiency and crit chance proc rates to consider when gearing your character, I just thought it was interesting to look at how the Archery bonuses stack up against each other.
Where is the legend? What do the axis represent? I'm not sure I get this
Sorry about that, I couldn't find a online graph program that would let me label anything. X-axis is your crit chance, y-axis is your crit damage. Original post updated.
One simple conclusion is that if you have more than 250% crit damage, you'll get a higher damage bonus from Archery with a bow over a 2H Xbow, even at 100% crit chance.
Here's the basic explanation:
Above the Red line, hand Xbows are best.
Below the Black line, Xbows are best.
In between Red and Black, Bows are best.
The blue line compares hand Xbows to Xbows, 1-hand above the line, 2-hand below the line.
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
I am not sure that you have modeled the damage calculations correctly. Think of it this way, if you have 100 dps before crit/dmg modifiers, 100% crit and 50% crit damage, the xbow bonus takes you from 150dps to 200 dps whereas the bow bonus takes you from 150 to 172.5. At 100 dps, 50% crit and 50% crit damage, the xbow takes you from 125 dps to 150 dps whereas the bow takes you from 125 to 143.5. Similarly, at 0% crit, you go from 100dps to 100dps with the xbow and from 100 dps to 115 dps with the bow bonus.
From these examples, we can see that crit% does indeed have an impact on the viability of bows vs xbows. The issue in your calculations is that you are multiplying non-crits by the crit damage modifier.
It should be more along the lines of:
1.15(baseDPS)(1 + critChance * critDmg) = (baseDPS)(1 + (critChance)(critDmg + .5))
1.15 + 1.15(critChance * critDmg) = 1 + .5critChance + critChance*critDmge
.15 + .15(critChance*critDmg) = .5critChance
So your break-even depends on your existing crit chance and crit damage modifier. Also, the crit chance you have is a bit harder to model due to sharpshooter.
Thank you! I knew I just needed someone else's eyes on it.
You're right, my original formula was wrong. Substituting y for crit damage and x for crit chance, your formula simplifies to:
Bows are better above the line, which means that for most players, bows still beat Xbows as far as Archery is concerned. Basically until you hit 35% crit, bows are better, and after that bows still win as long as you have enough crit damage from gear (which you probably should be stacking if you have 35% crit).
You're right that sharpshooter makes things a bit more complicated, but not by much, since at the crit levels required to make Xbows better, Sharpshooter resets pretty often.
EDIT: idlewild found my error, the correct math and graph updated
Chart:
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
His test showed that devouring is NOT multiplicative. Whether it adds 70% weapon damage each time (115, 185, 255, etc), or just adds 70% of base damage each time (115, 195.5, 276, etc) is tougher, since it's so close and damage ranges overlap. In any case, it's pretty close to puncturing. I use puncturing because even though the damage is a bit lower, it's less prone to overkill and since it has higher average number of pierces, offers more opportunities for on hit effects to occur.
I was surprised to see that Unique-Equipped was a thing in DIII. I dual wielded plenty of legendaries in DII.
Anyway, I suspect the reason for it is because of the mythology of the items. There's really only supposed to be one of each, so how would your character have two?
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Well, partly anyway. Bow beats Xbow below 35% crit chance or so no matter what. Above that, it depends on your crit damage bonus, but even a small amount of crit damage from items can pretty easily push you into bow territory.
So for most players, bows are probably better than 2H Xbows, at least as far as Archery is concerned. But Archery certainly isn't the only variable to consider in making a weapon choice, just part of it.
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Here's a simulation:
100 shots, 100 damage per shot, 30% crit chance, 50% crit damage, non crit damage
baseDamage = 100*100 = 10,000
Total damage = 70 normal hits for 7000 damage, 30 crits for 4500 damage, total damage = 11500.
My formula: 10,000 * (1 + (0.3)(.5)) = 10,000 * 1.15 = 11,500
Your formula: 10,000 * ((1 - 0.3) + 0.3 * 0.5) = 10,000 * (0.7 + 0.15) = 8,500
Your formula seems to be attempting to calculate normal hit damage and adding critical hit damage, just like I showed in the example simulation, but the formula doesn't work the way you've written it.
If you want to think about it that way, the formula should look like this:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))] ::: the key here is that the critical hits do 100% + bonus crit damage.
but when you simplify that you get:
(baseDPS) [(1-critChance) + (critChance * (1 + critDmg))]
(baseDPS) [(1 - critChance) + (critChance * 1 + critChance * critDmg)]
(baseDPS) [1 - critChance + critChance + critChance * critDmg]
(baseDPS) [1 + critChance * critDmg]
Which is what my formula is.
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Yeah, it doesn't model anything beyond which weapon type would give you the greatest bonus to DPS from Archery. It's a much simpler comparison between 2h Xbows and Bows, since they can be used interchangably, but 1h Xbows have a lot more to consider, such as having a second Xbow for another potential 200% crit damage bonus. The chart most accurately compares using any of the weapons with a quiver, for the case where you have otherwise equal weapons of type.
Beyond that, there's other gearing considerations such as hatred efficiency and crit chance proc rates to consider when gearing your character, I just thought it was interesting to look at how the Archery bonuses stack up against each other.
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Sorry about that, I couldn't find a online graph program that would let me label anything. X-axis is your crit chance, y-axis is your crit damage. Original post updated.
One simple conclusion is that if you have more than 250% crit damage, you'll get a higher damage bonus from Archery with a bow over a 2H Xbow, even at 100% crit chance.
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Here's the chart! http://fooplot.com/plot/asrikurc1t
Here's the basic explanation:
Above the Red line, hand Xbows are best.
Below the Black line, Xbows are best.
In between Red and Black, Bows are best.
The blue line compares hand Xbows to Xbows, 1-hand above the line, 2-hand below the line.
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
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Thank you! I knew I just needed someone else's eyes on it.
You're right, my original formula was wrong. Substituting y for crit damage and x for crit chance, your formula simplifies to:
y = ((-.15/x)+ .5)/.15
Which I've graphed here: http://fooplot.com/plot/k87can8y8r
Bows are better above the line, which means that for most players, bows still beat Xbows as far as Archery is concerned. Basically until you hit 35% crit, bows are better, and after that bows still win as long as you have enough crit damage from gear (which you probably should be stacking if you have 35% crit).
You're right that sharpshooter makes things a bit more complicated, but not by much, since at the crit levels required to make Xbows better, Sharpshooter resets pretty often.
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Chart:
Now obviously Archery isn't the only factor in determining which weapon type is best for your build and playstyle, but if you were wondering (like me) which weapon would give you the best DPS at a certain gear point, now you know.
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Freeze is found on Belts
Immobilize is found on Boots
Stun is found on Gloves
Fear is found on Helms
Any of them can be on a quiver or weapon.
I got destroyed by a Vortex / Shielding / Reflect Damage pack though.
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You can roll an item with 200 Dex, you can't roll an item with 200 Crit damage. So, 1% crit damage isn't really directly comparable to 1 Dex.
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Yes you do, but you also get a bonus 15% for equipping a quiver.
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On the last page, there was some testing to figure out how devouring arrow works exactly. That entry is here (reply #68):
http://www.diablofans.com/topic/37730-n-depth-look-at-hungering-arrow/page__st__60#entry887621
His test showed that devouring is NOT multiplicative. Whether it adds 70% weapon damage each time (115, 185, 255, etc), or just adds 70% of base damage each time (115, 195.5, 276, etc) is tougher, since it's so close and damage ranges overlap. In any case, it's pretty close to puncturing. I use puncturing because even though the damage is a bit lower, it's less prone to overkill and since it has higher average number of pierces, offers more opportunities for on hit effects to occur.
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If you care about actual dps, look for attack speed, crit chance, and crit damage on top of dex.
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Anyway, I suspect the reason for it is because of the mythology of the items. There's really only supposed to be one of each, so how would your character have two?
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