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Having attempted to do some maths myself, and coming to a dead end, in an attempt to unify stat priorities for maximising damage on a Demon Hunter.

The main area of confusion lies in how to evaluate Sharpshooter, and its relationship with different types of weapons for Archery.

The furtherest I have gotten is a formula for Sharpshooter that doesn't account for the tapering off of crit and the 1 second crit linger after having crit, while ignoring Archery completely.

The question is:

Given a static amount of Dexterity, weapon DPS, attack speed, critical rate, critical damage, how should one prioritise the stats in order to maximise single target damage over a specific time period (t) as a Demon Hunter?

Related for damage calculation purposes: How do the damage calculations work in Diablo 3?

Some base assumptions:

  • Time is a reasonable value. There can be arguments made for maximising burst as well as maximising overall DPS.
  • Zero movement. I know this isn't realistic, but the model would get way way out of hand if one included movement (and consequentually, ramping up SS).
  • You are simply autoattacking the boss with a basic attack (no skills, 100% damage modifier).
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Given that fine-tuning builds and stats only really matters at higher difficulty levels, I'd say the "Zero movement" assertion isn't just unrealistic, it's deeply flawed, as is the "autoattack only" assertion. Diablo3's endgame doesn't revolve around boss-runs. In fact, boss loot generation has been deliberately kept below that of champs and elites... which, especially for a DH, will punish you hard if you try a stand'n'shoot approach. –  Catalept May 29 '12 at 3:41
    
@catalept the first part you can simulate with smokescreen + lingering fog + 12 max discpline gear. gives you about 9 seconds of raw dps time. With backup plan its an additional 30% to extend by 4.5 secs. Autoattack only because there is no focus on creating extra stress in the maths by worrying about multipliers - you can fill in yourself when the stat priority is sorted (as a 100% attack will have the same impact as a 200% attack, etc, relatively speaking) –  hkf May 29 '12 at 3:48
    
@hkf - the problem is now the actual time for SS is only 1sec.(1.5 with Lingering fog). And there's a 1 sec cold down after SS effect wears off. Which means there's no raw dps time anymore. SS is now only a last resort in terms of surviving. For DH, either dodge rate, mobility, healing rate, or Armor can help in inferno. Even with 40k health, a DH can only take 2-3 hits max from a normal mob. And with that kind of health points, dmg will be significantly lowered. I don't see how a DH can survive inferno with gears from hell difficulty. –  user26500 May 29 '12 at 6:05
    
@dannyip you haven't been past act1 I take it.. even with 40khp 400resall you will be oneshot (doesn't even count the bugged Lacuni Huntresses). –  hkf May 29 '12 at 6:31

1 Answer 1

up vote 9 down vote accepted

Archery vs Crit

http://i.imgur.com/UHAhI.png

I take no credit for the following, as I did not do the work. All credit goes to nxmehta#1150.

Calculation Summary

This is the equation to calculate your total DPS (two handed weapon ONLY):

DPS = (Weapon DPS) * (Attack Speed Bonus) * (Dexterity/100 + 1) * [(1 - Crit Chance/100) + (Crit Chance/100) * (Crit Damage/100 + 1)]

Weapon DPS = This is the number on your weapon. If the weapon already has increased attack speed, it's already calculated into this DPS. For example, my crossbow has 900 DPS.

Attack Speed Bonus = This is the sum of all your attack speed bonuses (again, weapon attack speed is already in your weapon DPS). For example, my ring and amulet both give 15% attack speed, so this number would be 1.30.

Dexterity = Self explanatory- mine is 1300.

Crit Chance = Self explanatory- mine 10%, so that would be 10 here. IF YOU HAVE THE SHARSHOOTER PASSIVE ACTIVATED THIS WILL BE SET TO 100. TURN IT OFF IF YOU WANT TO SEE YOUR REAL DPS.

Crit Damage = Self explanatory- mine is 100%, so that would be 100 here.

So for example, my DPS = (900) * (1.10) * (1300/100 + 1) * [(1 - 10/100) + (10/100) * (100/100 + 1)] = 15264.

Relating attack speed to dexterity

So how can you compare attack speed and dexterity? The simplest way is to calculate, for a given increase in dex, what is the equivalent increase in attack speed bonus that would yield the same DPS increase. Here's how you do that:

Equivalent attack speed bonus = (New Dex + 100) / (Old Dex + 100)

For example, lets say I increase my dex from 1300 to 1400 using some gloves. The equivalent attack speed bonus would be:

(1400 + 100) / (1300 + 100) = 1.071

Or roughly 7%. This means that with 1300 dex, a 100 dex glove is equivalent to a 7% increased attack speed glove, all other things about the glove being equal.

Now, let's say I had 1500 dex instead of 1300, and I add that 100 dex glove again. The equivalent attack speed bonus would be:

(1600 + 100) / (1500 + 100) = 1.062

Or roughly 6%. So here, adding a 7% increased attack speed glove would be better than adding a 100 dex glove.

This is why it's important to know what your dex is and making this calculation before deciding which gear to get. The higher your dex is, the more diminishing returns you get from adding a fixed amount of dex. The lower your dex is, the more valuable it is to add that same amount of dex.

Here's a quick table that might help you decide if you should go for attack speed or dexterity in items, depending on your base dex and the dex of the item you are adding. (ID = Item Dexterity)

Table 1: Attack speed vs Dexterity

Equivalent Attack Speed as a function of Base and Item Dex                      
ID  20    40    60    80   100   120   140   160
---------------------------------------------------- 
BaseDex
200  6.7% 13.3% 20.0% 26.7% 33.3% 40.0% 46.7% 53.3% 
300  5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% 
400  4.0%  8.0% 12.0% 16.0% 20.0% 24.0% 28.0% 32.0% 
500  3.3%  6.7% 10.0% 13.3% 16.7% 20.0% 23.3% 26.7% 
600  2.9%  5.7%  8.6% 11.4% 14.3% 17.1% 20.0% 22.9% 
700  2.5%  5.0%  7.5% 10.0% 12.5% 15.0% 17.5% 20.0% 
800  2.2%  4.4%  6.7%  8.9% 11.1% 13.3% 15.6% 17.8% 
900  2.0%  4.0%  6.0%  8.0% 10.0% 12.0% 14.0% 16.0%
1000  1.8%  3.6%  5.5%  7.3%  9.1% 10.9% 12.7% 14.5%
1100  1.7%  3.3%  5.0%  6.7%  8.3% 10.0% 11.7% 13.3%
1200  1.5%  3.1%  4.6%  6.2%  7.7%  9.2% 10.8% 12.3%
1300  1.4%  2.9%  4.3%  5.7%  7.1%  8.6% 10.0% 11.4%
1400  1.3%  2.7%  4.0%  5.3%  6.7%  8.0%  9.3% 10.7%
1500  1.2%  2.5%  3.8%  5.0%  6.2%  7.5%  8.7% 10.0%
1600  1.2%  2.4%  3.5%  4.7%  5.9%  7.1%  8.2%  9.4%
1700  1.1%  2.2%  3.3%  4.4%  5.6%  6.7%  7.8%  8.9%
1800  1.1%  2.1%  3.2%  4.2%  5.3%  6.3%  7.4%  8.4%
1900  1.0%  2.0%  3.0%  4.0%  5.0%  6.0%  7.0%  8.0%
2000  1.0%  1.9%  2.9%  3.8%  4.8%  5.7%  6.7%  7.6%

Say you have a base dex of 1300 and comparing something like a 100 dex glove with 10% attack speed vs a 130 dex glove with 8% attack speed? Which is better? Well, we know that 10% is better than 8%. But will 30 points of dex make up for the 2% difference in attack speed? Look at this table to find out.

Table 2: Base dex vs attack speed

Base Dex          Dex Equal to 1% Attack Speed
--------          ----------------------------   
200                    3   
300                    4   
400                    5   
500                    6   
600                    7   
700                    8   
800                    9   
900                   10  
1000                   11  
1100                   12  
1200                   13  
1300                   14  
1400                   15  
1500                   16  
1600                   17  
1700                   18  
1800                   19  
1900                   20  
2000                   21

Here we can see that at 1300 base dex, 14 points of dex is equivalent to 1% attack speed. So the 2% difference in attack speed is equal to 2 * 14 = 28 points of dex. So that 2% difference is only worth 28 dex, which isn't as good as the +30 dex gloves. Those are the better ones, even though they are slower.

Notice that this changes if you have a higher dex, say 1500. Here, 16 points of dex are equivalent to 1% attack speed. So 2% attack speed is equal to 32 points of dex. Here, you would want the faster, lower dex gloves.

The below table illustrates how to go from crit chance and damage to an equivalent attack speed bonus. So for instance, an item with 50% crit damage and a 10% crit chance is equivalent to a 5% attack speed bonus.

Table 3: Critical chance vs critical damage

Equivalent Attack Speed as a function of Crit Chance and Damage
Crit                          Crit Damage
Chance  10    20    30    40    50    60    70    80    90   100
----------------------------------------------------------------  
0%  0.0%  0.0%  0.0%  0.0%  0.0%  0.0%  0.0%  0.0%  0.0%  0.0%  
1%  0.1%  0.2%  0.3%  0.4%  0.5%  0.6%  0.7%  0.8%  0.9%  1.0%  
2%  0.2%  0.4%  0.6%  0.8%  1.0%  1.2%  1.4%  1.6%  1.8%  2.0%  
3%  0.3%  0.6%  0.9%  1.2%  1.5%  1.8%  2.1%  2.4%  2.7%  3.0%  
4%  0.4%  0.8%  1.2%  1.6%  2.0%  2.4%  2.8%  3.2%  3.6%  4.0%  
5%  0.5%  1.0%  1.5%  2.0%  2.5%  3.0%  3.5%  4.0%  4.5%  5.0%  
6%  0.6%  1.2%  1.8%  2.4%  3.0%  3.6%  4.2%  4.8%  5.4%  6.0%  
7%  0.7%  1.4%  2.1%  2.8%  3.5%  4.2%  4.9%  5.6%  6.3%  7.0%  
8%  0.8%  1.6%  2.4%  3.2%  4.0%  4.8%  5.6%  6.4%  7.2%  8.0%  
9%  0.9%  1.8%  2.7%  3.6%  4.5%  5.4%  6.3%  7.2%  8.1%  9.0% 
10%  1.0%  2.0%  3.0%  4.0%  5.0%  6.0%  7.0%  8.0%  9.0% 10.0% 
11%  1.1%  2.2%  3.3%  4.4%  5.5%  6.6%  7.7%  8.8%  9.9% 11.0% 
12%  1.2%  2.4%  3.6%  4.8%  6.0%  7.2%  8.4%  9.6% 10.8% 12.0% 
13%  1.3%  2.6%  3.9%  5.2%  6.5%  7.8%  9.1% 10.4% 11.7% 13.0% 
14%  1.4%  2.8%  4.2%  5.6%  7.0%  8.4%  9.8% 11.2% 12.6% 14.0% 
15%  1.5%  3.0%  4.5%  6.0%  7.5%  9.0% 10.5% 12.0% 13.5% 15.0% 
16%  1.6%  3.2%  4.8%  6.4%  8.0%  9.6% 11.2% 12.8% 14.4% 16.0% 
17%  1.7%  3.4%  5.1%  6.8%  8.5% 10.2% 11.9% 13.6% 15.3% 17.0% 
18%  1.8%  3.6%  5.4%  7.2%  9.0% 10.8% 12.6% 14.4% 16.2% 18.0% 
19%  1.9%  3.8%  5.7%  7.6%  9.5% 11.4% 13.3% 15.2% 17.1% 19.0% 
20%  2.0%  4.0%  6.0%  8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 
21%  2.1%  4.2%  6.3%  8.4% 10.5% 12.6% 14.7% 16.8% 18.9% 21.0% 
22%  2.2%  4.4%  6.6%  8.8% 11.0% 13.2% 15.4% 17.6% 19.8% 22.0% 
23%  2.3%  4.6%  6.9%  9.2% 11.5% 13.8% 16.1% 18.4% 20.7% 23.0% 
24%  2.4%  4.8%  7.2%  9.6% 12.0% 14.4% 16.8% 19.2% 21.6% 24.0% 
25%  2.5%  5.0%  7.5% 10.0% 12.5% 15.0% 17.5% 20.0% 22.5% 25.0%
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Would you please update this very helpful table? Because they nerfed the attackspeed by adding some variables within the damage calculation. Not clue how to figure this out, maybe you do. Thank you. –  user28033 Jun 23 '12 at 11:23
    
The table is exactly the same as attack speed itself did not receive a nerf and only the values. –  hkf Jun 24 '12 at 6:03
    
The problem with the graphic is it assumes that weapon DPS is the same, which is a false assumption. Top bows cannot reach the same DPS values as top crossbows. There will always be a 100-200 DPS difference. For example you will get a 1100 crossbow with socket for about 5m, but only a 1000 bow with socket for the same gold. This is not only because of the given demand, but because of the base values for both weapons. –  ayckoster Jul 8 '12 at 19:38
    
Graph is for comparing EQUAL DPS weapons. –  hkf Jul 8 '12 at 23:36

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