Diablo® III

(Almost) Everything You Should Know about DPS

This thread explains how Diablo 3 calculates a weapon’s tooltip damage range, its tooltip DPS, and your character sheet DPS, which is also known as your “paper DPS.”

The tooltip damage range is based on six factors:
  • The weapon’s base damage range, which is visible on rare weapons before they are identified but unseen afterward if the item has a socketed ruby or any of the affixes listed below
  • The +X Minimum Damage affix
  • The +X Maximum Damage affix
  • The +X% Damage affix
  • The +X–Y Elemental Damage affix
  • Any socketed rubies

The affixes need to be on the weapon to show up in the tooltip damage range. (A +X Maximum Damage affix on a ring will not be included, but it will be included in your paper DPS.) Any fractions in the tooltip damage range are rounded to the nearest integer. As a result, this range is almost always* an approximation if the item has the +X% Damage affix; it is not the weapon’s real damage range.

Each weapon’s tooltip DPS is based on two factors:
  • The weapon’s average damage per hit, which is based on the weapon’s real damage range and almost always* differs from the tooltip damage range if the item has the +X% Damage affix
  • The weapon’s attack speed, which is based on the following factors:
    • The weapon’s base attack speed, which is visible on rare weapons before they are identified but unseen afterward if the item has has either or both of the affixes listed below
    • The +X Attack Speed affix
    • The Increases Attack Speed by X% affix

The character sheet DPS is based on these factors and many more, namely:
  • The +X Attack Speed affix on either weapon, which applies to both weapons when determining the character sheet DPS calculation but does not appear in the weapon tooltip of any weapon that doesn’t have the affix
  • The Enchantress’s Focused Mind skill
  • Numerous character skills, such as the Monk skill Breath of Heaven: Blazing Wrath
  • All +X Minimum Damage, +X Maximum Damage, and +X–Y Damage affixes on armor
  • The Adds X% to Elemental Damage affix on weapons, which applies to the weapon’s non-elemental damage and all +Damage affixes on armor
  • All Increases Attack Speed by X% affixes on armor
  • The 15% attack speed bonus for wielding two weapons (a.k.a. dual-wielding)
  • Your character’s Dexterity score
  • Your character’s total Critical Hit Chance percentage, which is compiled from all weapons and armor and displayed in the Details screen of your character sheet
  • Your character’s total Critical Hit Damage percentage, which is compiled and displayed like the Critical Hit Chance score

The initial calculations in this thread will not cover buffs from class skills such as Blazing Wrath. I will add them at a later date, but I haven’t researched them extensively because I don’t use those skills in my build. They’re straightforward, however, compared to the calculations I will examine in this thread, so I will incorporate them later. I have no plans to examine non-Monk skills because I am only playing a Monk at the moment, but I encourage those who play other classes to take this information and run with it.

WARNING: HERE THERE BE MATH. This thread is going to be very long and filled with examples and step-by-step calculations. If you’re looking for a TL;DR version, I can’t help you. My goal is to help players understand these mechanics so they can design better spreadsheets and calculators and make more informed AH purchases. I can’t accomplish these goals in a TL;DR format, but I’m going to break the steps into separate posts so people can digest it in chunks.

* I say “almost always” because an item with a particular range might not produce any fractions when combined with a particular +X% Damage figure. For example, if an item’s base damage range is 225–375, the +8% Damage affix will increase range to exactly 243–405.
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Tooltip Damage Range
As noted in the original post, the tooltip damage range is based on six factors: the weapon’s base damage range, the +X Minimum Damage affix, the +X Maximum Damage affix, the +X% Damage affix, the +X–Y Elemental Damage affix, and any socketed rubies. The affixes need to be on the weapon to show up in the tooltip damage range—a +X Maximum Damage affix on a ring will not be included, but it will be included in your paper DPS. Any fractions in the tooltip damage range are rounded to the nearest integer. As a result, this range is almost always* an approximation if the item has the +X% Damage affix; it is not the weapon’s real damage range.

Each weapon starts with a base damage range. The +X Minimum Damage and +X Maximum Damage modifiers are added to this base range, as are the bonuses from any rubies. (Note that a ruby with a listed modifier of +X–2X Damage actually adds +X to the weapon’s minimum damage and +X to the weapon’s maximum damage, which you will see as soon as you socket the gem. This means that a ruby adds two-thirds the amount of damage you’d expect it to add by examining a non-socketed ruby in your stash.) The new values are then multiplied by 1 plus the weapon’s +X% Damage affix. Finally, any elemental damage is added to this range, which is rounded for display in the weapon’s tooltip.

As an example, consider a Shenlong’s Fist of Legend with a tooltip damage range of 436–842 and the following affixes:

+282–484 Lightning Damage
+48% Damage

You can use these affixes to work backward from the tooltip damage range to identify the weapon’s unseen base damage range. To begin, subtract the elemental damage range (which is never modified by the weapon’s affixes) from the tooltip damage range, which produces a new range of 154–358. Next, divide each figure by 1.48 (1 plus 48% for the +48% Damage affix), which produces the following range that I’ve rounded to the nearest hundredth of a point:

104.05–241.89

This figure approximates the base damage range, which you can pinpoint by rounding each figure:

104–242

So the game actually determines the minimum damage as follows:

104 (minimum base damage)
x 1.48 (+48% modifier)
= 153.92
+ 282 (minimum elemental damage)
= 435.92

And it determines the maximum damage as follows:

242 (maximum base damage)
x 1.48 (+48% modifier)
= 358.16
+ 484 (maximum elemental damage)
= 842.16

These figures are rounded in the weapon’s tooltip as 436 and 842, but the real damage range of this weapon is 435.92–842.16. We’ll come back to this number later.
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Tooltip DPS
As noted in the original post, the tooltip DPS is based on two factors: the weapon’s real damage per hit and its attack speed. The second post demonstrates how to calculate the real damage range, so let’s examine the tooltip attack speed.

Tooltip Attack Speed
As noted earlier, the tooltip attack speed is based on three factors: the weapon’s base attack speed, the +X Attack Speed affix, and the Increases Attack Speed by X% affix. The tooltip attack speed is affected only by affixes on the weapon itself; affixes on your armor, the +X Attack Speed affix on the Echoing Fury in your other hand, the bonus granted by the Enchantress’s Focused Mind skill, etc., are not used to calculate the tooltip attack speed.

Each weapon starts with a base attack speed, which is determined by its type (sword, fist, spear, etc.) and is always a multiple of 0.05 (0.90, 0.95, 1.00, 1.10, etc.). This figure is multiplied by 1 plus the IAS bonus on the weapon itself; bonuses from the +X Attack Speed affix are added next, but only if the affix is on the weapon.* The tooltip attack speed is rounded to the nearest hundredth of an attack if it extends beyond two decimal points, but the game uses the real figure in all DPS calculations.

For example, consider a weapon with a tooltip attack speed of 1.52 and the affix Increases Attack Speed by 8%. We can divide the attack speed of 1.52 by 1.08 (1 plus 8%) to generate the weapon’s base attack speed, which is 1.40. If an Echoing Fury has a 1.42 tooltip attack speed and a +0.22 Attack Speed affix, its base attack speed is 1.20, and its real attack speed is 1.42. If a two-handed mace has a tooltip attack speed of 1.00 and the Increases Attack Speed by +11% affix, its base attack speed is 0.90 (1.00 divided by 1.11, rounded to the nearest tenth of a point), and its real attack speed is 0.90 times 1.11 (1 plus 11%), or 0.999. This number is rounded to 1.00 in the tooltip, but the real attack speed is 0.999, not 1.00.

* I have not yet used a weapon with the +X Attack Speed affix and the Increases Attack Speed by X% affix, so the order of operations here might be reversed. I made my best guess based on how the game handles the +X Attack Speed bonus from a second weapon on a weapon that has an IAS bonus on it.

Calculating the Tooltip DPS
To calculate the tooltip DPS, simply multiply the average of the weapon’s real damage range by its real attack speed.

Recall the real damage range of the Shenlong’s Fist we examined earlier:

435.92–842.16

The average damage per hit suggested by the game’s displayed damage range of 436–842 is 639, but the average damage per hit of the actual range is 639.04. If this weapon has a tooltip attack speed of 1.40 and no affixes that relate to attack speed, its tooltip DPS is 639.04 times 1.4, or 894.656, which Diablo 3 rounds to 894.7 for display purposes.

A More Complicated Single-Weapon Example
Let’s look at an Echoing Fury with a tooltip damage range of 622–836, a tooltip attack speed of 1.42, a tooltip DPS of 1,034.8, and the following relevant affixes:

+284 Minimum Damage
+152 Maximum Damage
+40% Damage
+0.22 Attack Speed

First, we need to determine the base damage range of this weapon. The min/max damage modifiers are subject to the +40% Damage affix, and the weapon does not have any elemental damage, so we begin by dividing the tooltip damage range by 1.40 to approximate the base damage range plus the min/max modifiers, which I’ve rounded to the nearest hundredths:

444.29–597.14

Next, we subtract the min/max modifiers to produce the approximate base damage range:

160.29–445.14

Finally, we round these values to determine the true base damage range:

160–445

So the game starts with this base damage range and then adds the min/max affixes to determine what many players refer to as its “black damage” (i.e., non-elemental damage or physical damage):

444–597

And multiplying both numbers by 1.4 (1 plus 40%) produces the weapon’s real damage range:

621.6–835.8

Diablo 3 rounds this figure to the tooltip damage range of 622–836.

The weapon’s base attack speed is easy to calculate: it’s 1.42 minus the +0.22 bonus, or 1.20. This figure isn’t very useful on its own, but it will be more important later when we dual-wield this Echoing Fury with a weapon that has the Increases Attack Speed by X% affix.

The real DPS of this weapon is thus the average of the real damage range times the real attack speed:

621.6 + 835.8 (real minimum/maximum values)
/ 2 (average)
= 728.7 (real average per hit)
x 1.42 (attack speed)
= 1,034.754 (real DPS)

Diablo 3 rounds this value to the nearest tenth for display purposes, so it shows a DPS of 1,034.8 in the tooltip. The game doesn’t actually use this value to calculate your character sheet DPS, however—it uses the “under the hood” value of 1,034.754.

Note: I don’t know whether the game generates random numbers for the base stat, adds modifiers, and then multiplies them by 1 plus the +X% Damage figure, or whether it treats the decimal ranges as the actual ranges and generates a random number that falls somewhere in that range. Because the two calculations are functionally equivalent, it doesn’t really matter. Given that the tooltip implies the range is larger than it would be without the +X% Damage affix, I assume that the fractional range is, in fact, correct.

Edit: Some weapons, like polearms, have attack speeds that are multiples of 0.05, not 0.10, so I changed that part of this post.
Edited by Vrkhyz#1472 on 11/10/2012 2:24 PM PST
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good read!!!
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Character Sheet DPS
As noted earlier, the character sheet DPS is based on several factors, including all those identified in the tooltip DPS post. To recap, the following factors also contribute to the character sheet DPS:
  • The +X Attack Speed affix on either weapon, which applies to both weapons when determining the character sheet DPS calculation but does not appear in the weapon tooltip of any weapon that doesn’t have the affix
  • The Enchantress’s Focused Mind skill, which is added to the weapon’s attack speed after the weapon’s IAS bonus has been applied but before any IAS bonuses on gear
  • Numerous character skills, such as the Monk skill Breath of Heaven: Blazing Wrath
  • All +X Minimum Damage, +X Maximum Damage, and +X–Y Damage affixes on armor
  • The Adds X% to Elemental Damage affix on weapons, which applies to all non-elemental damage on all weapons and all +Damage affixes on armor
  • All Increases Attack Speed by X% affixes on armor, which are added together
  • The 15% attack speed bonus for wielding two weapons (a.k.a. dual-wielding), which is added to the sum of the IAS bonuses on your gear
  • Your character’s Dexterity score
  • Your character’s total Critical Hit Chance percentage, which is added together from all weapons and armor and displayed in the Details screen of your character sheet
  • Your character’s total Critical Hit Damage percentage, which is added together and displayed like the Critical Hit Chance score

These factors are detailed below.

Recalculating the Weapon Damage per Hit
The weapon damage calculations presented earlier explain how the game calculates the tooltip damage range and the tooltip DPS, but these factors alone do not explain the DPS on your character sheet. If your gear has some combination of the +X Minimum Damage, +X Maximum Damage, and +X–Y Damage affixes, these modifiers are added to the real damage per hit calculated earlier.

How to add the damage is up to you. If you’ve already calculated the real damage per hit used to calculate the tooltip DPS, you simply need to add half the sum of your +X Minimum Damage affixes, half the sum of your +X Maximum Damage affixes, and the average of the summed upper and lower ranges of your +X–Y Damage affixes. For example, consider the real damage per hit (728.7) of the Echoing Fury used in the previous example. If you are wearing a ring with a +25 Minimum Damage affix, another ring with a +34 Minimum Damage affix, and an amulet with a +35–88 Damage affix, you can simply add 12.5, 17, and 61.5 to 728.7 to generate a gear-modified average per hit of 819.7. Or, if you’d like to calculate everything at once, you can use the affix-modified ranges to generate the gear-modified average without ever calculating the weapon-only average per hit:

160 + 445 (base damage minimum and maximum)
+ 284 (bonus minimum damage from weapon)
+ 152 (bonus maximum damage from weapon)
= 1,041
x 1.40 (+40% “black damage” bonus)
= 1,457.4
+ 25 + 34 + 35 + 88 (gear bonuses)
= 1,639.4
/ 2 (average)
= 819.7

No matter which method you use, the results are the same. If you’re calculating these figures by hand, use whatever method works best for you, depending on your familiarity with the mechanics; if you’re designing a spreadsheet or an application, use whichever method bests fits your inputs.

Recalculating the Attack Speed
The attack speed calculations presented earlier explain how the game calculates the tooltip attack speed and the tooltip DPS, but these factors alone do not explain the DPS on your character sheet. If you are dual-wielding weapons with the +X Attack Speed bonus, that bonus applies to both weapons. If you are using the Enchantress’s Focused Mind skill, that bonus also applies to both weapons. If you are wearing any gear that has the Increases Attack Speed by X% affix, these percentages are added together and apply to each weapon you’re wielding; if you’re dual-wielding, the 15% attack speed bonus is added to the IAS bonuses on your gear and applies to each weapon you’re wielding.

Here’s the full sequence for monks with one weapon, i.e., two-handers and sword-and-board setups:
  • Take the weapon’s base attack speed.
  • Multiply the result by 1 plus the weapon’s IAS bonus.
  • Add any bonus from the +X Attack Speed affix on the weapon itself.
  • If you are using the Enchantress’s Focused Mind skill, add +0.03. (The tooltip for this skill suggests that it grants a 3% IAS bonus, but this is not how the skill functions. I don’t know which one is supposed to be correct.)
  • Multiply the result by 1 plus all the IAS bonuses on your gear.

If you already calculated the weapon’s real tooltip attack speed to verify the tooltip DPS, you can skip the first three steps in this list and just skip to the Focused Mind modifier.

For dual-wielders, the steps are slightly more complicated because of affixes that carry over from one weapon to another, the 15% dual-wield attack speed bonus, and the fact that you can’t just average the two attack speeds to determine your real attack speed. Oh, and you have to calculate two attack speeds, of course. Here’s what you need to do for each weapon:
  • Take the weapon’s base attack speed.
  • Multiply this figure by 1 plus the weapon’s IAS bonus (just that weapon, not both).
  • Add any bonuses from the +X Attack Speed affix on either weapon.
  • If you are using the Enchantress’s Focused Mind skill, add +0.03. (The tooltip for this skill suggests that it grants a 3% IAS bonus, but this is not how the skill functions. I don’t know which one is supposed to be correct.)
  • Multiply the result by 1 plus all the IAS bonuses on your gear plus 15% for the dual-wield bonus.

Once you have both figures, you need to calculate the average attack speed. This isn’t as simple as just adding the attack speeds and dividing by two. You need to figure out how much time you need to make two attacks (one with each weapon; the game automatically alternates weapons as you attack) and then divide 2 by that number. For example, if you’re wielding a weapon with a 1.00 attack speed and another with a 1.50 attack speed, you need 1 second to make one attack with the first weapon and two-thirds of a second (0.6…) to make one attack with the second, so you need 1.6… seconds to make two attacks. This means that your average attack speed is 2 divided by (1.666… + 1), or 1.20. This is not the same as averaging 1.00 and 1.50, which produces a number that is higher than the actual attack speed.

If you don’t like that approach, you can calculate the time for each attack, add them together, take the average, and calculate the inverse (i.e., divide 1 by this figure) to determine the average attack speed. Either way brings you to the same figure:

1.00
+ 0.666…
= 1.666…
/ 2
= 0.83333…, which is 5/6

And the inverse of 5/6 is 6/5, or 1.20.

A Simple Example
For this example, I’m going to use the Shenlong’s Fist of Legend from the original post and a simple socketed dagger. The Shenlong’s Fist has a real damage range of 435.92–842.16 and an attack speed of 1.03; the dagger has the following tooltip stats:

482.8 DPS
199–397 Damage
1.62 Attacks per Second
Increases Attack Speed by 8%
+17 Minimum Damage (ruby)
+17 Maximum Damage (ruby)

I can use most of this data to generate the damage per hit because it’s all straightforward: the weapon’s base damage is 182–380, and its base attack speed is 1.50.

If I’m wearing one ring with a +25 Minimum Damage affix and an Increases Attack Speed by 7% affix and another with a +34 Maximum Damage affix, these are the damage per hit figures:
  • Shenlong’s Fist: 435.92 + 842.16 = 1,278.08 / 2 = 639.04 + 12.5 + 17 = 668.54
  • Dagger: 199 + 397 = 596 / 2 = 298 + 12.5 + 17 = 327.5
  • Average damage per hit: 668.54 + 327.5 = 996.04 / 2 = 498.02

And these are the attack speed figures:
  • Shenlong’s Fist: 1.40 + 0.03 (Focused Mind) = 1.43 x (1 + 0.07 + 0.15) = 1.7446 = 1 attack every 0.57320 seconds (rounded for simplicity but stored in full by Diablo 3)
  • Dagger: 1.50 x 1.08 (IAS bonus on weapon) + 0.03 (Focused Mind) = 1.65 x (1 + 0.07 + 0.15) = 2.013 = 1 attack every 0.49677 seconds (also rounded)
  • Average attack speed: 2 / (0.57320 + 0.49677) = 1.86921 (rounded here but tracked in full by Diablo 3)

Multiplying these figures provides my real base weapon damage:

498.02 x 1.86921 = 930.9040 (rounded)

The other factors are easy to incorporate:
  • Dexterity: Each point of DEX adds 1% damage, so DEX/100 + 1 is your dexterity modifier.
  • CHC and CHD: Multiply them and add 1 to determine your critical hit modifier.

In this example, if we have a DEX of 1,479, a CHC of 22.5%, and a CHD of +145%, here’s what happens:

930.9040 (base damage)
x 15.79 (1479/100 + 1)
=14,698.97416
x 1.32625 (1 + 0.225 x 1.45)
= 19,494.51

This doesn’t exactly match my character sheet DPS of 19,494.56, but that’s only because I’ve rounded the figures for the sake of this example. The spreadsheet I use to calculate these values produces the correct value, and it’s never been off by more than 0.01, which I attribute to working with a calculator and rounding numbers to the millionths or ten-millionths of a point before I transfer the information to the spreadsheet. Using a calculator to do the heavy math, like calculating the average dual-wielding attack speed with several modifiers in play, and then transferring the data to the spreadsheet is just easier than entering a formula in Excel to reverse-engineer a weapon’s base damage range, for example. Eventually, however, I’ll have this information coded, at which point I’ll simply enter some weapon and gear parameters into Excel and let it do all the hard work.
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The Red-Headed Stepchild: Adds X% to Elemental Damage
I left this affix out of the previous calculations because D3 treats the Adds X% to Elemental Damage affix much differently than it treats the +X% Damage affix. I had to do a lot of research to figure out what the game was doing, and I believe it deserves its own section. It was just too complicated to incorporate into the earlier sections, which are intensive enough without the anomalies.

Let’s consider Schaefer’s Hammer, which always rolls a boost to lightning damage. Here’s the version I keep in my stash:

Tooltip DPS: 1,081.4
Tooltip damage range: 875–1290
Tooltip attack speed: 1.00

+224–578 Lightning Damage
Adds 8% to Lightning Damage
Increases Attack Speed by 11%

Your gut might tell you that the Adds 8% to Lightning Damage affix is the elemental version of the +X% Damage and that you can simply work backward to determine the weapon’s base damage by modifying the method we used earlier.

Well, that’s reasonable—hey, that’s the first thing I tried, too—but it’s wrong. The Adds X% to Elemental Damage affix doesn’t have anything to do with elemental damage in that sense. It’s actually a super-charged “black damage” modifier. Unlike the weapon-specific +X% Damage affix, however, it is not used to calculate your tooltip damage range. The base damage range of the hammer in this example is just what you would expect if the Adds 8% to Lightning Damage wasn’t even there—it has a base damage of 651–712 and lightning damage of 224–578. The average damage per hit is (875 + 1,290) divided by 2, or 1,082.5. The weapon’s base attack speed is 0.90, which is then multiplied by 1.11 to account for the 11% IAS bonus. This produces a final attack speed of 0.999, which is then multiplied by the 1,082.5 damage per hit to produce a DPS of 1,081.4175 and a rounded tooltip DPS of 1,081.4, which matches what I see in the character sheet.

When calculating your character sheet DPS, however, D3 handles this weapon’s affixes (and your gear affixes) quite differently. For starters, the elemental damage bonus is applied to your base damage—the weapon’s “black damage”—which means that it applies only to the 651–712 portion of the weapon’s tooltip range, not the lightning damage like most (sensible) people would expect. This is similar to the +X% Damage affix in that it applies only to the weapon’s base damage, but it is different in that the +X% Damage affix, unlike the Adds X% to Elemental Damage affix, is included in your tooltip DPS.

Remember when I said that this affix is “super-charged”? Well, that’s because the elemental damage bonus is applied to any +X Minimum Damage, +X Maximum Damage, and +X–Y Damage affixes on your gear. This is very different from the way the game treats a weapon’s +X% Damage affix, which does not apply to your gear affixes.

Using these rules, I can correctly calculate my character sheet DPS of 25,032.60 with the following equipment:

Schaefer’s Hammer:
875–1290 tooltip damage range
1.00 tooltip APS (actually 0.90 with the +11% modifier applied)
+224–578 Lightning Damage
Adds 8% to Lightning Damage
Increases Attack Speed by 11%

Ring #1:
+25 Minimum Damage
Increases Attack Speed by 7%

Ring #2:
+34 Maximum Damage

Amulet:
+24–56 Damage
Increases Attack Speed by 9%

The real damage per hit, to use another calculation method, is the base damage (including rings) multiplied by 1.08 plus the lightning damage.
  • Base damage per hit: (651 + 712 + 25 + 34 + 24 + 56) * 1.08 / 2 = 811.08
  • Lightning damage: (224 + 578) / 2 = 401
  • Total damage per hit: 811.08 + 401 = 1,212.08

The weapon’s real attack speed, with the Enchantress’s Focused Mind skill active, is 1.19364:

0.90 (base AS)
x 1.11 (+11% IAS on weapon)
= 0.999
+ 0.03 (Enchantress buff)
= 1.029
x 1.16 (+7% IAS on ring #1 and +9% IAS on amulet)
= 1.19364

So the weapon’s real DPS is 1,212.08 damage per attack times 1.19364 attacks per second, or 1,446.7871712.

Next, we multiply this figure by 1 plus DEX divided by 100. My DEX is 1,337 with this weapon equipped, so:

1,446.7871712 DPS
x (1 + 1,337 / 100)
= 20,790.331650144

Finally, we need to account for my 26.5% CHC and my 77% CHD, which entails multiplying the 20K-ish figure by (1 + 0.265 x 0.77), or 1.20405.

20,790.331650144
x 1.20405
= 25,032.59882335588

D3 rounds this figure to the nearest hundredth, which accounts for the 25,032.60 I see in my character sheet with this setup.

Is this a bug? I don’t know. The game is consistently inconsistent, I’ll give it that much. All I know is that this is definitely how it works.
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And Now for Something Completely Different
My stash isn’t the world’s deepest, but I was able to pull out a wonky combo: an Echoing Fury and a Burning Axe of Sankis. These weapons, combined, have just about every affix I’ve mentioned so far. If one had a socket, they’d provide a near-perfect example. (If they both had sockets and both had the same cross-weapon affixes, this would really make your head explode.) When I equip both these weapons, my paper DPS is 27,067.70. Can I replicate that figure? Let’s find out!

First, the Echoing Fury:

1,034.8 tooltip DPS
622–836 tooltip damage range
1.42 tooltip Attacks per Second
+284 Minimum Damage
+152 Maximum Damage
+40% Damage
+0.22 Attacks per Second

Next, the Burning Axe:

836.3 tooltip DPS
459–827 tooltip damage range
1.30 tooltip Attacks per Second
+9 Maximum Damage
+280–484 Fire Damage
Adds 6% to Fire Damage
+39% Damage

Here’s a list of my relevant stats and equipment:
  • 1,389 DEX
  • Ring #1: +25 Minimum Damage, Increases Attack Speed by 7%
  • Ring #2: +34 Maximum Damage
  • Amulet: +24–56 Damage, Increases Attack Speed by 9%
  • CHC: 22.50%
  • CHD: +77%

Average damage per hit for the Echoing Fury:

622–836 (tooltip damage range)
/ 1.40 (+40% Damage)
= 444.29–597.14 (approximate damage range)
= 444–597 (actual damage range)
- 284–152 (min. and max. modifiers)
= 160–445 (base damage range)

160 + 445 + 284 + 152
= 1,041
x 1.40
= 1,457.4
/ 2
= 728.7 damage per hit
+ 12.5 + 17 + 12 + 28 (50% of min. and max. modifiers from gear bonuses)
= 798.2
x 1.06 (fire damage bonus from Burning Axe, applies to all this damage)
= 846.092

Average damage per hit for the Burning Axe:

459–827 (tooltip damage range)
- 280–484 (Fire Damage affix)
= 179–343
/ 1.39 (+39% Damage)
= 128.78–246.76 (approximate damage range)
= 129–247 (actual damage range)
- 0–9 (maximum damage modifier)
= 129–238 (base damage range)

129 + 238 + 9
= 376
x 1.39
= 522.64
x 1.06 (fire damage modifier)
= 553.9984
+ 280 + 484
= 1,317.9984
/ 2
= 658.9992
+ (12.5 + 17 + 12 + 28) * 1.06 (gear mods plus 6% fire damage bonus)
= 732.6692 damage per hit

Average damage per hit, both weapons:

(846.092 + 732.6692) / 2 = 789.3806

Attack speed: The attack speed for the Echoing Fury is 1.20 for the base speed plus 0.22 (weapon modifier) plus 0.03 (Focused Mind), or 1.45. This figure is multiplied by 1.31 (7% and 9% IAS bonuses on gear, plus the 15% dual-wielding bonus) to produce a final attack speed of 1.8995, or one attack every 0.52645 seconds. The attack speed for the Burning Axe is 1.30 (base speed) plus 0.22 (from the Echoing Fury) plus 0.03 (Focused Mind), or 1.55. This figure is multiplied by 1.31 to produce a final attack speed of 2.0305, or one attack every 0.49249 seconds. The average time per attack is thus 0.52645 plus 0.49249 divided by 2, or 0.50947, so the average attack speed is 1 divided by 0.50947, or 1.96281666…

The final paper DPS is thus:

789.3806 (damage per hit)
x 1.96281666 (average attacks per second)
= 1,549.4094
x 14.89 (1389 DEX)
= 23,070.705858
x 1.17325 (1 + 0.225 CHC x 0.77 CHD)
= 27,067.7056

This rounds to 27,067.71, which is different from my in-game paper DPS of 27,067.70 by 0.01. Sue me.
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bookmarking to read later
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Dammit, Ruru, you broke up my narrative! ;-)
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11/08/2012 08:38 PMPosted by Vrkhyz
Dammit, Ruru, you broke up my narrative! ;-)

LOL. that's why you block off all of your necessary posts before you start posting your content. I had to block off 9 pages for my guide. I know... kinda nuts.
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thats why i use DPS calculator my brain cant take this kind of $hit
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I knew I should've named this thread "WTS WKL" or "Help My Monk" if I wanted to keep it on the front page ;-)
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I titled mine "Don't read me yet!" until I was ready :P

Impressive job though, can't wait to fully read through it.
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I am a wizard but created a spreadsheet based on all of this information. It does end up working out more or less.

The one thing that wasnt called out nor shown in the calculations is that the base stats come into play (i.e. no gear at your level, e.g. 60). The pertinent ones are 5% CHC, 50% CHD, and INT 187...for some reason I have 243 INT above my gear rather than 187 so not sure why that is but thats what my character details screen shows vs. my gear totals.

So once I figured out those values needed to be added in, my calculations with elemental damage (i.e. triumvitrate offhand @ 18%) and all other IAS, CHC, CHD, INT, & Addional physical damage matched my character screen total dps (in my case ~133k).

i'm not sure how you used only the gear/weapon info above to get the matching figures on your character DPS, because I did not get that without first adding in the base character stats (on top of my gear bonuses). My character screen shows 133,625k DPS and I calculated via method above + base stats a 133,634k dps (off by 9, but I think thats because there is ~+8dps base state too)

Not sure how to share my spreadsheet but let me know and I'd be happy to email it to you or something.
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Oh - and thank you for all this great work! the dps mechanics are a little squirrely especially with the + elemental damage on gear and this cleared it all up for me!
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Great read. You sir deserve an "A" for effort.
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The one thing that wasnt called out nor shown in the calculations is that the base stats come into play (i.e. no gear at your level, e.g. 60). The pertinent ones are 5% CHC, 50% CHD, and INT 187...for some reason I have 243 INT above my gear rather than 187 so not sure why that is but thats what my character details screen shows vs. my gear totals.

i'm not sure how you used only the gear/weapon info above to get the matching figures on your character DPS, because I did not get that without first adding in the base character stats (on top of my gear bonuses). My character screen shows 133,625k DPS and I calculated via method above + base stats a 133,634k dps (off by 9, but I think thats because there is ~+8dps base state too)

Not sure how to share my spreadsheet but let me know and I'd be happy to email it to you or something.


Sorry if I wasn't clear, but the CHC, CHD, and DEX stats in my examples were from my character sheet. They already include the DEX gained by levels and paragon levels, the 5% CHC base, and the +50% CHD base. I didn't just sum the data from my gear.

I think you can share the spreadsheet via Google Docs. I have posted a few screenshots of mine to imgur.com, which is easy to use. If you want to send a file directly to me, you can reach me at tutenkharnage-at-gmail-dot-com. I'd love to see what people can do with this information.

@McSwagger and hlo: Thanks! Glad you enjoyed it. I put it together in Word over the course of three days (bracketed code included) and finally figured it was ready to post. Good thing, too, as I'm ready to move back to my spreadsheet and happy to stop testing these mechanics for a while :)
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Remember when I said that this affix is “super-charged”? Well, that’s because the elemental damage bonus is applied to any +X Minimum Damage, +X Maximum Damage, and +X–Y Damage affixes on your gear.

I must thank you so much Vrkhyz! My spreadsheet has forever been off by 1% and I just couldn't figure it out. I didn't worry about it as I guessed it got the relative comparisons correct for new gear (though I can see now this wasn't the case for the jewelry), but it bugged me nonetheless. This issue was it, the +dmg on my jewelry. So now finally my spreadsheet aligns with the character toolsheet precisely.

Again, my deep appreciation!
Edited by crushkyle#1915 on 11/9/2012 6:50 PM PST
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You're very welcome, crushkyle. Regarding spreadsheets, I took a few minutes today at work to put together a weapon worksheet that takes the tooltip stats and affixes and correctly strips them down to their base components. Bare-bones snapshot here:

http://i.imgur.com/KjJu4.png

The weapon used in this example is the Shenlong's Fist I use in some of the other examples. As you can say, the spreadsheet correctly determines the real damage range. Only took a few minutes, a ROUND function, and an MROUND function.

Eventually, it'll look a little better than this, given that I get asked to do stuff like this and Adobe forms around the office. Just working on getting the pieces in place before I go crazy with the glitter :)
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* I have not yet used a weapon with the +X Attack Speed affix and the Increases Attack Speed by X% affix, so the order of operations here might be reversed. I made my best guess based on how the game handles the +X Attack Speed bonus from a second weapon on a weapon that has an IAS bonus on it.


i was a wizard before being a monk and a chantodo's has both x% as and +x as.
a chantodo's wand has 1.4 as and it can roll max 10% as and +0.25 as. the max as this wand can have is 1.79.
the game first multiplies 1.1 to 1.4 which results in 1.54 as. then 0.25 as is added to make the max as 1.79 for a chantodo's will.
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