Diablo® III

Breakdown of Archery Passive (Math included)

Demon Hunter's Archery Passive
15% Damage to Bows
50% Crit Damage to Xbows
10% Crit Chance to Hand Xbow (main hand only)

Calculations are spread over 20 hits
1) Base stats – 1 damage, 5% crit, 50% crit damage
No Specialization – 19 hits at 1 damage, 1 crit at 1.5 damage = 19 + 1.5 = 20.5
Bows – 19 hits at 1.15 damage + 1 Crit at 1.725 = 19*1.15 + 1.725 = 23.575
Xbow – 19 hits at 1 damage + 1 Crit at 2 = 19 + 2 = 21
Hand Xbow – 17 hits at 1 damage + 3 Crits at 1.5 = 17 + 3*1.5 = 21.5
Bows – 23.575 / 20.5 – 15% damage increase
Xbows –21 / 20.5 – 2.5% damage increase
Hand Xbows – 21.5 / 20.5 – 5% damage increase

2) High crit chance – 1 damage, 20% crit, 50% crit damage
No Specialization – 16 hits at 1 damage, 4 crit at 1.5 damage = 16 + 4*1.5 = 22
Bows – 16 hits at 1.15 damage + 4 Crit at 1.725 = 16*1.15 + 4*1.725 = 25.3
Xbow – 16 hits at 1 damage + 4 Crit at 2 = 16 + 4*2 = 24
Hand Xbow – 14 hits at 1 damage + 6 Crits at 1.5 = 14 + 6*1.5 = 23
Bows – 25.3 / 22 – 15% damage increase
Xbows –24 / 22 – 9% damage increase
Hand Xbows – 23 / 22 – 5% damage increase

3) High Crit Damage – 1 damage, 5% crit, 100% crit damage
No Specialization – 19 hits at 1 damage, 1 crit at 2 damage = 19 + 2 = 21
Bows – 19 hits at 1.15 damage + 1 Crit at 2.3 = 19*1.15 + 2.3 = 24.15
Xbow – 19 hits at 1 damage + 1 Crit at 2.5 = 19 + 2.5 = 21.5
Hand Xbow – 17 hits at 1 damage + 3 Crits at 2 = 17 + 3*2 = 23
Bows – 24.15 / 21 – 15% damage increase
Xbows – 21.5 / 21 – 2.5% damage increase
Hand Xbows – 23 / 21 – 10% damage increase

As you can see from this data Bows maintain a 15% damage increase on all scenario's, while increasing crit chance increases the effect of Xbows and increasing crit damage increases the effects of Hand Xbows

4) Really High Crit Chance – 1 damage, 50% crit, 50% crit damage
No Specialization – 10 hits at 1 damage, 10 crits at 1.5 damage = 10 + 1.5*10 = 25
Bows – 10 hits at 1.15 damage + 10 Crits at 1.725 = 10*1.15 + 10*1.725 = 28.75
Xbow – 10 hits at 1 damage + 10 Crit at 2 = 19 + 2.5 = 30
Hand Xbow – 8 hits at 1 damage + 12 Crits at 1.5 = 8 + 12*1.5 = 26
Bows – 28.75 / 25 – 15% damage increase
Xbows – 30 / 25 – 20% damage increase
Hand Xbows – 26 / 25 – 6% damage increase
Values for 45% crit – Base = 24.5, Bows = 28.175, Xbows = 29
Values for 40% crit – Base = 24, Bows = 27.6, Xbows = 28 (40% crit is about when Xbows > Bows)

5) Really High Crit Damage – 1 damage, 5% crit, 200% crit damage
No Specialization – 19 hits at 1 damage, 1 crit at 3 damage = 19 + 3 = 22
Bows – 19 hits at 1.15 damage + 1 Crit at 3.45 = 19*1.15 + 3.45 = 25.3
Xbow – 19 hits at 1 damage + 1 Crit at 3.5 = 19 + 3.5 = 22.5
Hand Xbow – 17 hits at 1 damage + 3 Crits at 3 = 17 + 3*3 = 26
Bows – 25.3 / 22 – 15% damage increase
Xbows – 22.5 / 22 – 2% damage increase
Hand Xbows – 26 / 22 – 18% damage increase
Values for 400% crit damage – Base = 24, Bow = 27.6, Hand Xbows = 32, 33% damage buff

From this data we can make several conclusions:
First, you need approx +150% crit damage bonus for the benefit to Hand Xbows to outwiegh the benefit to Bows.
Second, you need approx +35% crit chance for the bonus to Xbows to outwiegh the bonus to Bows.
Third, we can conclude that 150% crit damage is = 15% crit chance (by looking at 2 and 5, increasing by by 15% crit improves base damage by ~7% and increasing by 150% crit damage does the same).
From these three we find that Hand Xbows scale the best with increasing stats. +150% crit damage is = 15% crit chance, but Xbows need 35% crit chance to be better than bows.
Example, we found that +35% crit = +350% crit damage, at 40% crit (5% base + 35% bonus) Xbows do just over 15% damage increase, and at 400% crit damage (50% base, +350% bonus) Hand Xbows result in a 33% damage increase.

So as long as Blizz has itemized correctly and made 10% bonus crit damage = 1% crit chance on item drops stacking crit damage and rolling out the Hand Xbows would result in a higher damage increase if a Hand Xbow did the same damage as a 2h Bow. (Unfortunately this isn't the case, because dual wielding for DH's is quite useless at the moment).

TL;DR -> Read it, it's math that is necessary to understand what I'm saying, but if you want to take it on faith, Xbows > 2H Bows with better gear (and with Sharpshooter Passive)
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Attack speed is irrelevant, otherwise you'd have to include different damage levels for different attacks.

Attack Speed doesnt effect crit chance or crit damage, or damage. The math here is based on percentages, and percentages dont change if you do 150 hits over 10 sec doing 150 damage total, or 15 hits over 10 sec doing 150 damage total.
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06/03/2012 04:17 PMPosted by Ghost
Attack Speed doesnt effect crit chance


lol
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06/03/2012 04:23 PMPosted by armannd
Attack Speed doesnt effect crit chance


lol


I assume what you mean is with more attack speed you crit more often since you attack more often, which is true, but crit chance is unaffected. GJ
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Well you also forget practical considerations..

If you dual wield hand xbows, it's likely for you to have a socket in each one = 50% crit damage advantage (at the least, since hand xbows can have inherent +crit damage, but quivers can't)

so you get into situations where it's going to be very hard to beat dual wielding, in a true "best case" situation


That's true, so maybe there is hope for dual wielding hand xbows.
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DW being useless isn't so much the reason but rather that 1hand weapons just have lower dps than 2h. If hand xbow had same dps as 2hand I'd be willing to bet that hand xbow + quiver would be better than DW.
It is good to see that if hand xbow has same dps as 2hands that in high end gear archery would be better with the hand xbow.
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True the extra socket might be make it so even if the weapons dps is lower by 100-200 it might still be better.. The extra attask speed from DW is kind of irrelevant though because Quivers can get 20% AS while DW only gives 15% so each weapon would actually have to have 5% AS to be equal. Basically forgetting the passives for hand xbow because you can get those passives with a quiver offhand rather than DW. The weapon socket is only advantage DW has over using a quiver.
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How can you possibly say atk speed is irrelevant when comparing the 3 types of bows??? If a hand crossbow can get in 10 hits while the 2h'rs get only 9 hits in, that's significant.
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85 Tauren Druid
3735
your base stats of "1" damage is inaccurate because it uses a normalized value for weapon DPS; they are not similar at all
also the modifiers are not just %, there are static bonuses +x "of death" can be + 286 to 667 damage.
those obviously factor different considering base APS to skew DPS in lesser proportions for slow cross bows

you will need to use some baselines such as

Revenant bows are 380 dps
Exorcists are 263 dps
Hellions are 514 dps

factor their APS * a pair of good mods + off_weapon damage from jewelery = a final DPS
then use those numbers

the bonus from Bow + archery is additive with steady aim, you should include a static buff in your evaluation such as cull of the weak or Mark of death

those combinations are going to skew results; you will need to include them to see scale in practice for a more realistic picture.

as a bit of *
lateral utility is time based; crits per second has invaluable qualities, you just can't equate this as damage similarly to explaining the value of r/w speed%

06/03/2012 05:35 PMPosted by MarineRogue
How can you possibly say atk speed is irrelevant when comparing the 3 types of bows???
it is because he is just modeling % effects using 1 DPS on all the examples.
however 1 cannot be used for an accurate evaluation.
Edited by zoid#1554 on 6/3/2012 6:03 PM PDT
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06/03/2012 05:35 PMPosted by MarineRogue
How can you possibly say atk speed is irrelevant when comparing the 3 types of bows??? If a hand crossbow can get in 10 hits while the 2h'rs get only 9 hits in, that's significant.


Except that Damage over time is (supposedly) more or less equal. So if a hand xbow would attack 2 times as fast then instead of doing 1 damage, it would do .5, but have 40 attacks (2x as many crits) and the damage would end up the same.

This is comparing percentages of damage, not real damage per attack. So a xbow that does 20 damage over 20 sec would be compared to a 2h bow that does 20 damage over 20 sec. the faster wep does more crits, but each of lower magnitude because the higher attack speed means lower damage per hit.

Overall attack speed does not affect these calculations as percentages are unaffected by attack speed.
Reply Quote
your base stats of "1" damage is inaccurate because it uses a normalized value for weapon DPS; they are not similar at all
also the modifiers are not just %, there are static bonuses +x "of death" can be + 286 to 667 damage.
those obviously factor different considering base APS to skew DPS in lesser proportions for slow cross bows

you will need to use some baselines such as

Revenant bows are 380 dps
Exorcists are 263 dps
Hellions are 514 dps

factor their APS * a pair of good mods + off_weapon damage from jewelery = a final DPS
then use those numbers

the bonus from Bow + archery is additive with steady aim, you should include a static buff in your evaluation such as cull of the weak or Mark of death

those combinations are going to skew results; you will need to include them to see scale in practice for a more realistic picture.

as a bit of *
lateral utility is time based; crits per second has invaluable qualities, you just can't equate this as damage similarly to explaining the value of r/w speed%

How can you possibly say atk speed is irrelevant when comparing the 3 types of bows???
it is because he is just modeling % effects using 1 DPS on all the examples.
however 1 cannot be used for an accurate evaluation.


I think what you mean is 1 cannot be used for COMPLETELY accurate data, however this is meant as a guideline, it shows the general trends of the effects of Archery based on differing stats, real data will of course differ because of the damage range on weps, but the general trend (10% crit damage = 1% crit chance, higher crit chance makes subsequent crit damage better etc) will remain the same.
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Hand crossbows have other advantages.

Higher passive crit means more discipline from nightstalker if you go that route. Dual wielding hand crossbows gives you an extra +discipline slot. You can get higher +life on it from hand crossbows.
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85 Tauren Druid
3735
06/03/2012 06:10 PMPosted by KonradKurze
1 cannot be used for COMPLETELY accurate data,

a more accurate piece of work is what I am suggesting, yes.
the peer-review I gave explains what is missing

Bows maintain a 15% damage increase on all scenario's,

it's just not correct in practice due to it being additive with steady aim
archery with a bow is a 12.5% multiplicative effect when using steady aim <shrug> i'd say at least half of all dh's use steady aim?
Edited by zoid#1554 on 6/3/2012 6:29 PM PDT
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It does seem like 2 very well itemized hand crossbows both with sockets will out damage any Bow or Xbox...The main problem IMO is have you seen the prices on those Hand Xbows lol? 50 mil a piece for a very good one.
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06/03/2012 06:29 PMPosted by DanteMustDie
It does seem like 2 very well itemized hand crossbows both with sockets will out damage any Bow or Xbox...The main problem IMO is have you seen the prices on those Hand Xbows lol? 50 mil a piece for a very good one.


this.

you dont need math to realize that dual wielding 1h xbows would be ideal.

the problem is that the dps equivalent 1h xbow costs at least 100x as much - and you need TWO of them!

edit: maybe 100x is an exaggeration - its still a lot
Edited by w00dberry#1617 on 6/3/2012 6:46 PM PDT
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