Diablo® III

(Almost) Everything You Should Know about DPS

Thanks for the information, Gosu. That's how D3 handles IAS on one weapon and +AS on the other (like an Echoing Fury), so this makes sense.
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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.

...

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)


I believe a level-1 character starts with 10 points in the class's primary stat and gains 3 per level, including paragon level. If that's the case, here's how your wizard's INT breaks down:

10 base
+ 59 x 3 (regular levels through 60)
+ 20 x 3 (20 paragon levels because you have to earn p-1)
+ 1947 (from gear)
= 2194

There's no +8 DPS base stat on monks, and I would bet all classes work the same way. I don't have a wizard, though, so I'm not sure whether skills like Glass Cannon show up in your character sheet DPS.
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@McSwagger: Does Blood Magic show up in your character sheet, and are you including it in the 133,625 figure? If it does, and if you are, I believe the calculation goes like this:

Echoing Fury:

Tooltip damage: 434–835
+36% Damage
+159 Minimum Damage
+294 Maximum Damage

Base minimum damage: 434 / 1.36 = 319.12 - 159 = 160.12, which is rounded to 160
Base maximum damage: 835 / 1.36 = 613.97 - 294 = 319.97, which is rounded to 320

Real minimum damage: (160 + 159) x 1.36 = 433.84
Real maximum damage: (320 + 294) = 614 x 1.36 = 835.04

Real damage range: 433.84–835.04

Average damage per hit:

Your average damage is your Echoing Fury's average damage plus your source's, multiplied by 1.18 because of the three Adds X% to Elemental Damage affixes on your source.

433.84 + 835.04 + 88 + 367
= 1,723.88
/ 2
= 861.94
x 1.18
= 1,017.0892

Attack speed and IAS bonuses:

Judging by what Eiryena's wearing, you're using the Enchantress at the moment, and she adds 0.03 to your EF's attack speed. You're also wearing 55% in IAS gear. So:

1,017.0892 x (1.20 + 0.25 + 0.03)
= 1,505.292016
x 1.55
= 2,333.206248

Intelligence:

2,333.206248 x (2194/100 + 1)
= 53,523.668212912

CHC and CHD:

You're wearing an extra 41% in CHC gear and an extra 226% in CHD gear, so your multipliers are 46% and 276%, respectively.

53,523.668212912
x (1 + 0.46 x 2.76)
= 121,477.3173760251

Blood Magic:

Assuming Blood Magic is reflected in your character sheet, we can simply multiply the result by 1.1, which is the same as multiplying the effect at the beginning of the calculations.

121,477.3173760251
x 1.1
= 133,625.0491136276

Whether this is accurate depends in part on how Blood Magic is treated and whether you've got it on when you're looking at your DPS. It would be quite a coincidence if I arrived at this number with some guesswork, but the guesses were just wrong.

BTW, if this is how it works, you can let Blood Magic expire and check your character sheet to see if your DPS is 121,477.32. If so, we have a winner; if not, it's back to the drawing board for us.
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Math isn't my strong spot...what do you make of this?

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.


I see you then say at the bottom that...

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.


Which seems to say it does so reflect the damage on character sheet dps...

So does "Add X% to Elemental damage" show up on character sheet dps?

I totally should have paid more attention in math class...
Edited by Brando#1490 on 11/12/2012 8:53 AM PST
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nice info, thanks!
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very nice work

Here´s some stuff I´m trying to figure out (apologize in advance for posting barb damage on monk forums), but I have not found a similar topic anywhere else.

6-10 base weapon damage
+24 min dmg ring
1998 str
+5% to arcane (soj)
+22% elites (soj)
+4% elites (hellcat)
+174% crit dmg

case 1: into the fray (15%), 5 stacks maniac (20%) against an elite monster, ingame damage = 1228 (3364 crit)

((6-10) + (24-0)) = (30-30) * 20.98 (str) * 1.35 (br+maniac) * 1.1 (frenzy) = 934.659
a) * 1.31 = 1224.40329 (1.31 is the sum of all 3 bonuses)
b )* 1.26 * 1.05 = 1236.553857
c) * 1.22 * 1.04 * 1.05 = 1245,19010616 (all 3 bonuses separately)
d) (6-10) + ((0.05 * (6-10)) + (24-0) = 30.3 = 944.00559 * 1.26 = 1189.4470434 (elem bonus added first)

all theories are incorrect, the closest is a)

case 2: just bash (165% weapon damage)
ingame vs elite = 1364 (3738 crit) = +31.28852341333518%-31.3848152106811%
ingame vs trash = 1090 (2988 crit) = +5%
ingame vs trash without soj = 1039 (2846 crit)
calc = 30 * 20.98 (str) * 1.65 (bash) = 1038.51

seems like the game rounds "naturally" I mean 1038.51 as 1039 and 1090.4355 as 1090.

Don´t understand the correlation of adds +% damage and +% elite damage :/ where does the 31.29-31.38% come from? Does the game round a number somewhere?

The variables in case 2 are:

+24 min damage ring
+22% elite soj
+5% arcane damage soj
+4% elite hellcat

thanks in advance

EDIT: You´re saying that the adds +5% to arcane damage is added right on the 6-10 base weapon damage range or to ((6-10) + (14-0))?

Also the formula for aps = ((base weapon aps * weapon IAS) + (attacks per second from legendaries and enchantress)) * (gear IAS + skill IAS + dual wield IAS)

from my ww/rltw tick frequency scaling topic
http://us.battle.net/d3/en/forum/topic/6037344497

By the way monks, do you have skills that scale with aps similar to run like the wind = X ticks over Y seconds (not DoTs that tick each 0.5 second) or channeling skills like Whirlwind or Strafe?

Asking because I´m unfamiliar with monk skills but I can give you aps breakpoint charts to those skills as I´ve figured out a way to calculate them as you can see in the link above. All I need is damage per tick (hit) of the particular skill.
Edited by Nubtro#2147 on 11/13/2012 9:58 AM PST
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@Brando: When I say "tooltip DPS" and "tooltip damage range," I mean the DPS and damage range that show up when you hover over your weapon. The Adds X% to Elemental Damage affix does not show up in the weapon's tooltip but does show up in the DPS on your character sheet.

@Nubtro: I've got a level-14 Barb, as I recall, so I'm not very familiar with the barb's skills and haven't yet tested the Adds Damage to Elites affix. I'll put it on the list, but no promises. The Adds 5% to Arcane Damage affix adds to the weapon's base (or "black") damage and all black-damage modifiers from gear. So it's adding to the modified 30–30 damage range of your weapon.
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Both elite bonuses and demon bonuses gave me diminishing returns and headaches while testing :) but I figured them out.

elite bonus modifier = 1 + ((1 - (1 - bonus#1/100) * (1 - bonus#2/100) * (1 - bonus#3/100) ...)

demon bonus modifier = 1 + ((1 - (1 - bonus#1/100) * (1 - bonus#2/100) * (1 - bonus#3/100) ...)

The formulas seem too difficult at first sight but they´re pretty simple:

example +10% sun keeper and +4% unity don´t give you a 14% (1.1 + 1.04) nor a 14.4% (1.1 * 1.04) boost but a 13.6% boost.

1+ ((1 - (1-0.1) * (1-0.04))) = 1 + (1 - (1 - 0.9 * 0.96) = 1 + (1 - 0.864) = 1 + 0.136 = 1.136

The damage formula modifier is 1.136 so +13.6%. I can give you my exact test results if needed, but it´s 100% accurate. Feel free to simplify the formula if you want :)
Edited by Nubtro#2147 on 11/14/2012 10:45 AM PST
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Thanks for the info, Nubtro! I'll be sure to use this post as a reference when I get around to testing those modifiers.
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also would you mind reading this post?

http://www.diablofans.com/topic/65055-d3rawr-online-diablo3-dps-ehp-calculator-comparison-tool/#entry1081786

there´s everything I´ve tested considering the damage formula

If you find anything there that collides with your test results, please tell me.

EDIT: read your posts again, seems like I´ve placed rubies somewhere else than you. I´ll be honest, they really confuse me. I´ll have to retest them to be sure.

OK my formula is right on the +min/max affixes on jewelry, they don´t get the +% damage boost of the weapon but you were right about rubies, they´re directly added to the base weapon damage. I´ll fix my formula accordingly.

Here´s the tests I made to confirm the above.

58-86 base +13% damage +31 min amulet, 1953 str, bash (165%)

a) (58-86 + 31-0) * 1.13 * 20.53 * 1.65 = 100.57-100.57 * 20.53 * 1.65893406.758465
b) (58-86 * 1.13 + (31-0)) * 20.53 * 1.65 = 96.54-97.18 * 20.53 * 1.65 = 3270.24423-3291.92391

I got more that one different damage (in the calced damage range) so it´s option b). If it was a), I would only get one damage each hit.

58-86 base, + 13% damage, +31 min amulet, +24 min ring +2-4 ruby, 1953 str, bash (165%)

a) 122.54-101.18 * 20.53 * 1.65 = 4150.98123
b) 122.80 * 20.53 * 1.65 = 4159.7886

I got 4160 damage which meant base weapon -> rubies -> +% damage -> +min dmg jewelry.
Edited by Nubtro#2147 on 11/14/2012 1:53 PM PST
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also would you mind reading this post?

http://www.diablofans.com/topic/65055-d3rawr-online-diablo3-dps-ehp-calculator-comparison-tool/#entry1081786

there´s everything I´ve tested considering the damage formula

If you find anything there that collides with your test results, please tell me.


I read the post. It's quite good. Aside from the barb-specific details (which I'm not familiar with) and the diminishing returns on "to demons" and "to elites" (which I didn't know--great work, BTW), it all looks spot-on to me.
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IMO. the + X% to Elemental Damage (eg. cold) is not a big factor while using FoT because its already a lightning base atk.
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I haven't been back to this thread in a while, so I hadn't known about the diablofans thread (posted about a month ago). There was some talk about SoJ and how it interacted with skills recently.

If I'm reading this correctly, for a SoJ with +30% to elites, +12% FoT:

If you are using BoH and spamming Overawe, the +12% will be added to your BoH 15% bonus and 48% Overawe bonus, meaning that particular ability from the SoJ effectively gives you:
(1 +.48 +.15 + .12) / (1 + .48 + .15) = 1.0736, a 7.36% increase in DPS to FoT.

Bonus to elites, however, is a straight up 30% bonus to your DPS to elites (assuming no other bonus to elites on other items).

So, your total bonus to elites using FoT is 1.0736 x 1.3 = 1.396, a 39% more damage total.

Please let me know if I've gotten this right.
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Another amazing thread I must've just missed by coming back like 3 weeks ago. I'm a little confused though...why isn't this thread stickied? o_O
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@bolo: I think you're confusing that affix with something like WKL's bonus. A +X% to Cold Damage affix would add X% damage to all your black (I.e., non-elemental) damage. It affects weapons, really; it doesn't affect skills.

@Demiwraith: I haven't tested the bonus-to-elites affix, in part because I don't have any gear with it. If you can point me in the direction of a thread with some good proof that it usmultiplicative rather than additive, please do.

@Stan: I have no idea, but I'm probably biased regarding this thread's quality ;)
Edited by Vrkhyz#1472 on 12/14/2012 9:46 AM PST
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12/14/2012 04:51 AMPosted by Vrkhyz
@bolo: I think you're confusing that affix with something like WKL's bonus. A +X% to Cold Damage affix would add X% damage to all your black (I.e., non-elemental) damage. It affects weapons, really; it doesn't affect skills.
i used +x% cold dmg with FoT and it would not proc the cold affix to snare enemies. i used any other main atk skill and it Does proc the cold affix. (used it with WKL/EF and black wpn/EF)
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12/15/2012 04:19 PMPosted by BOLO
@bolo: I think you're confusing that affix with something like WKL's bonus. A +X% to Cold Damage affix would add X% damage to all your black (I.e., non-elemental) damage. It affects weapons, really; it doesn't affect skills.
i used +x% cold dmg with FoT and it would not proc the cold affix to snare enemies. i used any other main atk skill and it Does proc the cold affix. (used it with WKL/EF and black wpn/EF)

I recall reading that effects like that can be overridden by other effects. FoT is lightning damage, which is probably why the snare doesn't work with FoT but works with your other generators. I have a belt with freeze on hit, though, and it works with Thunderclap, for whatever that's worth.
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Question: What about items like SOJ?

Do the "+% damage to elites" similar to +% elemental damage?
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Question: What about items like SOJ?

Do the "+% damage to elites" similar to +% elemental damage?

I haven't tested them yet. Druin may have told me that they're additive; if so, I didn't write that information down and don't remember it.
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Boss! Can post this in general forum instead? I'll help to request sticky.

It's too good to be just in monk forum.

And reserve 7 slots before you post =P
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