## How DPS and Damage Works

• Oddly enough, I don't believe this topic has been addressed, and if it has, please let me know.

I've been doing some research about how dps works, and I think I have (sortof) figured it out. Most of this info is based on actual in-game numbers.

I'd like to start this off by saying damage is not DPS. This may seem obvious to most, but it's important to distinguish the two.

According to Jay Wilson, your damage is based on your weapon. Simple enough:

### Official Blizzard Quote:

@Bashiok @angryrobotics It looks like each point in Intel increases base damage by 1%, but I can't find base damage

@CherubDown @Bashiok Damage is based on your weapon, so look at it's damage. Although we'll probably add it to detailed stats.

You can figure out your actual weapon DPS by

(W_lower+W_higher)*(W_speed_factor)/2

where W_lower is the lowest dmg your weapon can do, W_higher is the highest, and W_speed_factor is your weapon speed.

Or you can figure it out by simply looking at that giant number the game throws at you :). That settles damage and weapon DPS, but what about overall DPS? According to the game,

Interestingly, Blizzard has decided to include your crit factor and crit chance into your overall DPS. So I decided to try to figure out a formula for the whole thing, and this is what I've come up with:

(W_dps)+(W_dps * dmg_increase_factor) + (W_dps) * (crit_factor) * (crit_chance)

where W_dps is your weapon's dps, dmg_increase_factor is the factor by which your damage is increased (based on your primary attribute), crit_factor is your crit damage increase, and crit_chance is obviously your chance to crit.

My calculation isn't perfect unfortunately. It's about 0.2 off and I'm not exactly sure why. If anyone can figure it out, I'd love to know what I've got wrong.

As for equipping two weapons (duel wielding), there's a thread here on the matter and the formula is quite simple:

1.15*(W1_dps + W2_dps)/2

The output of this formula can be replaced by the W_dps in the previous formula. (Thanks chippydip and romique for the correction and clarification) The 15% increase is an incentive to use 2-handed weapons.
"All generalizations are false, including this one." -Mark Twain
• Quote from CherubDown
My calculation isn't perfect unfortunately. It's about 0.2 off and I'm not exactly sure why. If anyone can figure it out, I'd love to know what I've got wrong.

The game's rounding of decimal fractions could be the reason I guess.
• The DPS number you can look up at your character screen is a easy way for everyone to check if a new item you found is overall better than the one you already have.
But I have a problem with DPS being a useful information in a game like Diablo. DPS only matters if you are fighting strong monsters for several seconds or even minutes (bosses especially), but I don't care if I my char does 200 or 250 DPS when most monsters die in one or two strikes anyway, though we don't know yet how monster HP will evolve in later difficulty levels, so we might finally start to deal actually DPS and not just damage. I hope you get what I mean.

Example:
Killing a 100 HP monster with two 50 damage attacks or two 90 damage attacks is the same DPS, the huge DPS increase on your char screen doesn't help you at all.
But fighting 10.000 HP monsters or 100.000 HP bosses with 2000 or 3000 damage attacks is a different story, you deal more DPS and finish them off faster.

What I'm trying to say is, that DPS is a number you can should tweak of course, but nothing you should try to maximize first and at all costs.
• Well, the only other arpg I've played with DPS is Titan Quest.. In Titan Quest you have 2 damage stats
Average and DPS .. Average is what you do in average pr hit and DPS is ofc. the amount of damage you do pr second so ..

So a weapon with 100 % attack speed ( 1 attack pr second ) doing 10 - 20 damage will give you 15 average damage and 15 DPS .. However if the attack speed is 150% (1.5 attacks pr second) the average damage would still be 15 but DPS would increase to 22 ..
I kinda thought the DPS would work the same way in D3..
So isn't it basicly just (your average damage * attack speed) ? ...
• Quote from CherubDown

My calculation isn't perfect unfortunately. It's about 0.2 off and I'm not exactly sure why. If anyone can figure it out, I'd love to know what I've got wrong.

All the values displayed in-game are rounded to 1 or 2 decimal places. The actual values have more significant figures than that, which will lead to small errors since you are calculating based off the rounded damage numbers.

Quote from CherubDown

As for equipping two-handed weapons, there's a thread here on the matter and the formula is quite simple:
1.15*(W1_dps + W2_dps)/2

The 15% increase is an incentive to use 2-handed weapons.

Your explanation does not match your equation and the linked thread. What you mean is that equipping 2 one-handed weapons (dual wielding) will increase your average attack speed by 15%. This is something entirely different from equipping "two-handed" weapons which take both hands to hold a single weapon. ;-)

Quote from NullerGnuen

So isn't it basicly just (your average damage * attack speed) ? ...

That's exactly how it works.

It would definitely be nice if the game displayed average attack damage (and perhaps average attack speed) in addition to dps. As far as I know, spell damage scales based on average damage, no average dps. Attack speed effects how quickly you can use a skill with no cooldown. Overall the skill systems seem fairly balanced to account for this, but there are some builds that would benefit from faster attack speed and others that would benefit from larger average weapon damage.
• wtf. the dps number on your char page changes based on your crit chance?

i didnt notice that. you sure?
"once the pretty hardcore gamers we had testing inferno found it fairly difficult, we then we doubled it" -trolololol jay wilson
• Quote from CherubDown

As for equipping two-handed weapons, there's a thread here on the matter and the formula is quite simple:
1.15*(W1_dps + W2_dps)/2

The 15% increase is an incentive to use 2-handed weapons.

Your explanation does not match your equation and the linked thread. What you mean is that equipping 2 one-handed weapons (dual wielding) will increase your average attack speed by 15%. This is something entirely different from equipping "two-handed" weapons which take both hands to hold a single weapon. ;-)

I didn't think this required explanation but I guess it does.
You can simply replace the result of the DPS from that formula and put it where W_dps is in the first formula.
"All generalizations are false, including this one." -Mark Twain
• Quote from CherubDown

Quote from CherubDown

As for equipping two-handed weapons, there's a thread here on the matter and the formula is quite simple:
1.15*(W1_dps + W2_dps)/2
The 15% increase is an incentive to use 2-handed weapons.

Your explanation does not match your equation and the linked thread. What you mean is that equipping 2 one-handed weapons (dual wielding) will increase your average attack speed by 15%. This is something entirely different from equipping "two-handed" weapons which take both hands to hold a single weapon. ;-)

I didn't think this required explanation but I guess it does.
You can simply replace the result of the DPS from that formula and put it where W_dps is in the first formula.

This is clear I guess, though it won't hurt to add it to the opening post. But what chippydip was saying is that you are refering to a 2-handed weapon (one weapon held with both hands), while providing the dual-wielding dps formula (for two one-handed weapons, mh and oh), and that's confusing. The formula is fine, it's the description that needs a little correction.
• As romique said, you wrote down formula for 'dual wielding', but described it 'two handed'. Everyone who's accustomed to formulas will understand you, but without any knowledge of game mechanics (and i believe that your post targets such people) might be confused after reading your post.

Would be a good idea to change this 'typo'

Also i believe that your current attack speed is included in detailed version of your character statistics?
• Does all of this relate to casters also? Say a wizard or witch doctor's spell damages are reflected on their DPS number in their character attribues.

Also, does increased attack speed help a witch doc or wizard cast their spells faster? Or is there something else for that?
• Yeah if I'm honest, the impact that items have on caster dps is really poorly defined.

If my wizard finds a 12.2 dps short sword, and I'm using an 11.2 dps wand, do I switch to the short sword, only to find that my physical damage is increased, but not my spell damage? How does +weapon speed on a javelin affect +casting speed on a witch doctor?

The tooltips for skills are so incredibly brief, they don't even begin to mention quantity of +damage, +speed, etc.

I find the current incarnation of how items impact damage output to be un-necessarily obtuse and confusing, and this is coming from a gaming veteran. In trying to make the system simpler, they've made it extremely complex.

Edit: I tried to explain damage modifications to my girlfriend yesterday, who has never gone beyond king's quest in the gaming department, and I realized in completely failing to explain it clearly, that I did not understand it well myself.

(I made her a char, and she proceeded to play 4 hours straight. I'm so proud of her.)
"Ridicule is the only weapon which can be used against unintelligible propositions."
-Thomas Jefferson
• Quote from JohnMoney

Does all of this relate to casters also? Say a wizard or witch doctor's spell damages are reflected on their DPS number in their character attribues.

Also, does increased attack speed help a witch doc or wizard cast their spells faster? Or is there something else for that?

In older beta patches there was a separate "Increased Attack Speed" for barb/monk/dh and"Faster Cast Rate" from WD and Wizard. Currently, IAS applies to all five classes. Not hugely game changing but a reasonable simplification all the same.
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• I'm happy I found this thread. I was one of the 100k that ended up getting an invite in the last wave and from what I've played so far I've had this exact question. It feels like there's a lot of factors they are putting into the DPS number, and the mere presence of the DPS number makes me feel like we'll eventually actually care about DPS vs Damage in the later difficulty numbers. I think anyone who ends up playing D3 in a serious manner (such as PVP) will end up wanting to crunch out numbers, and the way the tooltips and other things that contribute to DPS and Damage are currently done it seems like it's going to be a very tiresome process to arrive at a consensus about formulas/numbers. I like the idea they've put in place but I just wish they'd put a little more clarity on it. I actually started trying to crunch out some numbers for the Demon Hunter (the only char I've really made so far) using knowledge from other games but it feels like it's an uphill battle right now.
• Quote from Dolaiim

Yeah if I'm honest, the impact that items have on caster dps is really poorly defined.

If my wizard finds a 12.2 dps short sword, and I'm using an 11.2 dps wand, do I switch to the short sword, only to find that my physical damage is increased, but not my spell damage? How does +weapon speed on a javelin affect +casting speed on a witch doctor?

The tooltips for skills are so incredibly brief, they don't even begin to mention quantity of +damage, +speed, etc.

I agree with you on this. D2 they listed on the spell the damage range. This might be a good idea for Blizzard to do, maybe even if it is just the more complex explanation of the spell (I know there is a word for this but can't think of it).

In older beta patches there was a separate "Increased Attack Speed" for barb/monk/dh and"Faster Cast Rate" from WD and Wizard. Currently, IAS applies to all five classes. Not hugely game changing but a reasonable simplification all the same.

Thanks for clearing this up. I like the idea of IAS is also the same faster cast rate. It gives it a much simpler approach.

The best, and clearest way would be if they listed the damage now on the spell itself (magic or physical) and every time you changed out your weapon or gear, you could hover over it to see exactly what it shows.
• I'm so confused. This thread along with others I've commented on, yet I see no such comment. Am I being modded without my knowledge?! D=

Edit: Aha! Two threads of about the same topic, mah bad.
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• TL;DR at the bottom.

I have some insight to provide you since I looked into this just last week and got a calculation that only was 0,02 off (it is my theory that it's the calculated aps [after ias effects] that Blizzard rounds, but it could be anything really).

First off it's not a good idea to separate 15% dw ias from the rest of the ias effects like you do in this formula.

1.15*(W1_dps + W2_dps)/2

This is only true for cases where there are no %ias effects on the gear (or active on you, such as Frenzy shrine). For a 100% true formula, you'll have to rework the dw ias bonus (and all other ias% bonuses) into calculating the aps of the weapon, or the W_speed_factor as you label it, like you're doing here:

(W_lower+W_higher)*(W_speed_factor)/2

(W_lower+W_higher)/2 * (W_speed_aps*(1+footnote))

footnote: this is where you put dw ias (0,15), frenzy shrine (0,25), gear ias (0,0x) and so forth. As another note, this is the formula we're speaking about when we're saying ias is additive (for multiplicative, the effect is multiplied to the aps, rather than added together with a bunch of other effects). We do this because almost all (if not all) ias effects are additive, or at least this was the case when I discovered this several months ago in another topic somewhere in the theorycrafting forum.

Now, let's say (W_lower+W_higher)/2 * (W_speed_aps*(1+x)) is our W_dps.

Also, let's say for simplicity's sake that we're only calculating the estimated tooltip when using one weapon (ie 2handers OR sword n' board OR just one 1hander equipped) so we can ignore the shared swingtimer when dualwielding.And let's say that we don't have any crit% either.

In that case, the tooltip dps should show W_dps*(1+ DIM / 100)

Dim: would then be the damage increasing modifier (strength, dex and so on).

But since we can't check that out, we'll have to rework crit into it. I'll be using base crit (5%) and base crit hit damage (50%). We can treat crit effects in several different ways, my preffered way is as a proc effect, which looks like this:

(W_lower + W_higher)/2 * Crit Hit Damage = W_Avg_Crit

This is the average critical strike. However, we have to remember that a regular non-crit hit would have occurred if it hadn't been a crit, which means to get the actual crit damage we have to subtract the regular swing.

(W_lower + W_higher)/2 = W_Avg_Hit
W_Avg_Crit - W_Avg_Hit = W_Crit_Damage

Now we're ready to roll. W_Crit_Damage can be thought of as a simple add damage like wounding, only that it only happens at a ratio determined by our crit chance (we're using base, so 5% proc rate)

(W_Avg_Hit) + (W_Crit_Damage) * Crit Chance = W_Actual_Avg_Hit

And the DIM:

W_Actual_Avg_Hit * DIM

And the aps:

W_Actual_Avg_Hit * DIM *(W_speed_aps*(1+x))

Which means, in total the calculation looks like this:

((W_lower + W_higher)/2 + ( ((W_lower + W_higher)/2 * Crit Hit Damage) - (W_lower + W_higher)/2) * Crit Chance) * DIM * (W_speed_aps*(1+x))

Let's check it out ingame shall we? Here is my Barb. I removed all crit% so I'm at base. I have some strength from the legs and the axe. Yeah you can see his total stats. As you can see the dps is 37,72.

He is using this weapon:

((10+18)/2 + (((10+18)/2*1,5)-(10+18)/2)*0,05) * 1,89 * 1,39 = 37,698885, which is rounded to 37,7

And this is as close as I think we can get, since this calculation does not use any rounded numbers.

Just as another demonstration, I'll show you what happens when I equip Ruthlessness:

((10+18)/2 + (((10+18)/2*2)-(10+18)/2)*0,10) * 1,89 * 1,39 = 40,45734 which is rounded to 40,46

Ingame picture:

TL;DR

This is my take on the char screen DPS (for non dw only):

((W_lower + W_higher)/2 + ( ((W_lower + W_higher)/2 * Crit Hit Damage) - (W_lower + W_higher)/2) * Crit Chance) * DIM * (W_speed_aps*(1+x))

Edit: the equivalent formula for dual wield will require a new post for reasons that are too long to post in this edit.
• whats the highest DPS anyone here was able to achieve in the beta?
"once the pretty hardcore gamers we had testing inferno found it fairly difficult, we then we doubled it" -trolololol jay wilson
• Quote from GladHeHasBeta

whats the highest DPS anyone here was able to achieve in the beta?

The highest numbers can only come from patch 5 with wounding amulet + rings and all crafted attack gear. In that patch I had 130~ dps on my 3 hours played Barb. I wouldn't doubt DH's should be pulling higher numbers with 2x rare req lvl 13 xbows though.

edit: patch 5 and subsequent patches*
• Quote from Superstate

whats the highest DPS anyone here was able to achieve in the beta?

The highest numbers can only come from patch 5 with wounding amulet + rings and all crafted attack gear. In that patch I had 130~ dps on my 3 hours played Barb. I wouldn't doubt DH's should be pulling higher numbers with 2x rare req lvl 13 xbows though.

edit: patch 5 and subsequent patches*

talking now though.... i was easily able to get in the 60-70s without even trying for it.
"once the pretty hardcore gamers we had testing inferno found it fairly difficult, we then we doubled it" -trolololol jay wilson
• Quote from Superstate

TL;DR at the bottom.

I have some insight to provide you since I looked into this just last week and got a calculation that only was 0,02 off (it is my theory that it's the calculated aps [after ias effects] that Blizzard rounds, but it could be anything really).
...

Awesome post, this thread would deserve a sticky for it unless it's already somewhere else. Also, shouldn't this be moved to the Theorycrafting section?

Quote from Dolaiim
In trying to make the system simpler, they've made it extremely complex.

That's exactly what I love about it, although I wouldn't say it's "extremely" complex as to be unintelligible, since it is well done. You can make complex things simple (on the surface) in order to work, if they're well done. If they're not, you have a mess.

Often times games will have a simple system that is just too boring due to lack of intelligent complexity brought by a unique system with diverse classes and skill mechanics. As a gaming veteran, you should actually look forward to being better informed and have a complex system to explore and use in the years to come.