Dps increase given by x% of area dmg versus n enemies - Theorycrafting and Analysis - Diablo III Misc Forums - Forums - DiabloFans

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I was wondering how strong stat area dmg is and did some math on it, and here is what i came up with.

The formulas might not be in the most simplified possible form, and they only work in ideal conditions (spell that hits all targets in the area of splash in this case). This should still give you a good idea of how strong stat it is when hitting multiple enemies at once, for example versus 5 targets going up from 50% (paragon) area dmg to 70% area dmg gives an 11.43% dmg increase as long as enemies stay clumped and alive, and you have resources for an area spell.

edit: some typos and last formula fixed
edit2: added total damage formula for x% area damage. It seems the same results (last 2 formulas) apply for single target spells versus n enemies, i will put up the math later on.

Thanks for pointing out the blunder in the end and checking it out, i corrected it and cleaned the first formula up a bit.
Leaving out the percentage stuff would give the output in percentages, instead of for example 0.02 one would get out 2, i prefer the aforementioned. I could remove the denominator, but i'll keep it for now as it should be more obvious where the numbers come from.

Initial thoughts are your calculations might be a little off. I've seen reference to it being proportional to n*(n-1) but that might be overall and not on a per mob basis. I'll have to run some numbers myself sometime tonight and get back to you on it.

Area damage does do damage to a singular target, by the way. It's an aoe centered on the target that procs it, and the target that procs it does the aoe damage. I believe it works in a very similar way to Blade of Prophecy in that it causes a second condemn to explode on a mob hit by the initial condemn, but on a single target it still does effectively double condemn damage. Not sure if that would have an effect on your calculations, but I'm eager to see where this goes. It'd certainly be nice to know exactly how valuable a 20% aoe damage roll on something is.

Area damage does do damage to a singular target, by the way. It's an aoe centered on the target that procs it, and the target that procs it does the aoe damage. I believe it works in a very similar way to Blade of Prophecy in that it causes a second condemn to explode on a mob hit by the initial condemn, but on a single target it still does effectively double condemn damage. Not sure if that would have an effect on your calculations, but I'm eager to see where this goes. It'd certainly be nice to know exactly how valuable a 20% aoe damage roll on something is.

It seems it does not do damage to the target you are attacking. I tested this multiple times on high torment ghom, doing him with 0% area dmg and 50% area dmg with exact same gear and timing the kill times, the kill time was long enough (around 4min) and the deviation was around 1% of the kill time to random direction. 50% area dmg should have given a 10% dmg boost to a single target (1+0.2*0.5*1).

I was first formulating it with the target that triggers area dmg taking the dmg itself also, but then decided to test it to be certain.

The only possibility where it would do single target dmg is that instead of the normal hit dmg the target would take your area dmg %'s worth of dmg, but in this case it would have lowered my single target dps by 10% (1-0.2*0.5*1 or 4.5/5).

Initial thoughts are your calculations might be a little off. I've seen reference to it being proportional to n*(n-1) but that might be overall and not on a per mob basis. I'll have to run some numbers myself sometime tonight and get back to you on it.

I will write down the thought process behind the first formula, might be helpful for finding errors or confirming it.

This is all with 100% area dmg. In all the the cases i have used the total dmg caused by the initial area attack to 1, n could be used just as well but you'd just have to divide in the end by n to get the increase out.

n=2Chance for getting 0 area dmg procs is 0.8*0.8 (one possible way), in this case you do 1 dmg.Chance of getting exactly one area dmg proc is 2*0.8*0.2 (first one triggers or second one triggers), this area dmg proc together with the normal hits will cause 1.5 dmg. Chance of getting 2 area dmg procs is 0.2*0.2 (this can only happen in one possible way), this double proc together with the normal hits will cause 2 dmg.

When we put all this together we get 1*0.8*0.8*(1+0*(1-(1/2))) + 2*0.2*0.8*(1+1*(1-(1/2))) + 1*0.2*0.2*(1+2*(1-1/2)))= 0.64*1 + 0.32*1.5 + 0.04*2 = 1.2.

The factor (1+k(1-(1/n))) means with k procs on n targets you will do this amount of dmg together with the initial dmg. First 1 is the normal attack's dmg, k the numer of procs, (1-(1/n)) the amount of dmg each of the k procs does, they would do 1 dmg if they hit the target that procced area dmg but instead they will do 1/n:th less dmg than 1.

The formula itself should be sound, been gone through by another math major also, but it's possible i got something wrong in the mechanics of area dmg.

The question that interests me the most is why bringing 1 extra target will always (as it seems) increase the dmg by 20% compared to non-area dmg attack. This ended up being fairly difficult to prove as it includes the binomial coefficient, might try to brute force it open after holidays.

The exact value of for example 20% area dmg is hard to judge because it changes according to the amount of enemies you can hit with those area dmg procs. Assuming you would always play with a monk with cyclone strike as I do, area damage is very valuable stat, for rifting purposes i would take it over ias on rings for example, and as a dual wielder possibly over any other dps stat on weapon apart from main stat and socket of course (so weapon would have some elem dmg, main stat, socket and area dmg as 4 primaries).

After doing some t5 & t6 rifting area dmg seems to me like the best way of speeding things up once you are about in the best possible gear otherwise. Even those normal monsters start being rather tanky, when the aim is to blow everything up in matter of seconds.

There are some problems with area dmg, it won't do anything to bosses and very big monsters like the charging dogs/dinos(something like that) that cant be clumped up properly. The boss thing is no problem though, the amount of time you spend killing the boss in a rift is very minimal compared to getting the red bar to 100%.

That's the same approach I was going to use, and after throwing together a quick spreadsheet for 2 or 3 mobs.

For 2 mobsI get the same answers. Basically you do 240% damage against 2 mobs, so 20% more than expected.

Against 3 it's 420%, which is 40% more than the 300% base. So for 3 mobs I get the same answer.

Against 4 mobs it's 640%, which is 60% more than the 400% base, which agrees with your answer.

That's the same formula as bonus damage = n*(n-1)*0.2*x where x is your Area Damage Amount%. In the cases above, x = 100% so it ends up being 40%, 120%, and 240% for 2, 3, or 4 mobs. That's the formula I saw on the official forums, but I don't really like presenting the info that way. I prefer the layout of your calculations more, so it's more like 20%*(n-1)*x overall damage gain, so against 2 mobs you do 20% more damage with 100% area damage. Against 3 mobs you deal 40% more damage. That's much easier to understand.

@Herecius

I'd use 2 mobs as a basis to be somewhat conservative. That means 0.2*x bonus damage, so with a 10% roll, that's about 2% more damage. Keep in mind that's 2% of your base dps, so if you have 100k dps, 10% area damage is worth about 2k dps (against 2 mobs). If CC would put your dps to 105k, then you're better off switching that area damage to CC.

You're more than welcome to use 3-4 mobs as a basis of course, especially if you kill a lot of trash mobs and feel that's more of a limiting factor in your play time.

From an abstract standpoint, I think the 0.2n(n-1)x formula is accounting for the aggregate damage a skill deals on n targets, but all AoE skills deal n times additional damage on n targets, so you can just factor out the n.

From an abstract standpoint, I think the 0.2n(n-1)x formula is accounting for the aggregate damage a skill deals on n targets, but all AoE skills deal n times additional damage on n targets, so you can just factor out the n.

Yeah, that's more or less what I got around to trying to say in my post above.

The formulas might not be in the most simplified possible form, and they only work in ideal conditions (spell that hits all targets in the area of splash in this case). This should still give you a good idea of how strong stat it is when hitting multiple enemies at once, for example versus 5 targets going up from 50% (paragon) area dmg to 70% area dmg gives an 11.43% dmg increase as long as enemies stay clumped and alive, and you have resources for an area spell.

edit: some typos and last formula fixed

edit2: added total damage formula for x% area damage. It seems the same results (last 2 formulas) apply for single target spells versus n enemies, i will put up the math later on.

The formulas look quite a bit cleaner if you leave out the percentage stuff.

0.2x(n-1)

(Maybe this is just how I do math, but in your summation, the first multiplication dot seems strange and unnecessary to me.)

I think in your final formula, you need to negate the whole thing.

(It should be minus 1, not 1 minus).

Leaving out the percentage stuff would give the output in percentages, instead of for example 0.02 one would get out 2, i prefer the aforementioned. I could remove the denominator, but i'll keep it for now as it should be more obvious where the numbers come from.

Crusader DPS and EHP Spreadsheet, meant for Crusaders

My Wizard

doesdo damage to a singular target, by the way. It's an aoe centered on the target that procs it, and the target that procs it does the aoe damage. I believe it works in a very similar way to Blade of Prophecy in that it causes a second condemn to explode on a mob hit by the initial condemn, but on a single target it still does effectively double condemn damage. Not sure if that would have an effect on your calculations, but I'm eager to see where this goes. It'd certainly be nice to know exactly how valuable a 20% aoe damage roll on something is.I was first formulating it with the target that triggers area dmg taking the dmg itself also, but then decided to test it to be certain.

The only possibility where it would do single target dmg is that instead of the normal hit dmg the target would take your area dmg %'s worth of dmg, but in this case it would have lowered my single target dps by 10% (1-0.2*0.5*1 or 4.5/5).

This is all with 100% area dmg. In all the the cases i have used the total dmg caused by the initial area attack to 1, n could be used just as well but you'd just have to divide in the end by n to get the increase out.

n=2Chance for getting 0 area dmg procs is 0.8*0.8 (one possible way), in this case you do 1 dmg.Chance of getting exactly one area dmg proc is 2*0.8*0.2 (first one triggers or second one triggers), this area dmg proc together with the normal hits will cause 1.5 dmg. Chance of getting 2 area dmg procs is 0.2*0.2 (this can only happen in one possible way), this double proc together with the normal hits will cause 2 dmg.When we put all this together we get 1*0.8*0.8*(1+0*(1-(1/2))) + 2*0.2*0.8*(1+1*(1-(1/2))) + 1*0.2*0.2*(1+2*(1-1/2)))= 0.64*1 + 0.32*1.5 + 0.04*2 = 1.2.

The factor (1+k(1-(1/n))) means with k procs on n targets you will do this amount of dmg together with the initial dmg. First 1 is the normal attack's dmg, k the numer of procs, (1-(1/n)) the amount of dmg each of the k procs does, they would do 1 dmg if they hit the target that procced area dmg but instead they will do 1/n:th less dmg than 1.

The formula itself should be sound, been gone through by another math major also, but it's possible i got something wrong in the mechanics of area dmg.

The question that interests me the most is why bringing 1 extra target will always (as it seems) increase the dmg by 20% compared to non-area dmg attack. This ended up being fairly difficult to prove as it includes the binomial coefficient, might try to brute force it open after holidays.

After doing some t5 & t6 rifting area dmg seems to me like the best way of speeding things up once you are about in the best possible gear otherwise. Even those normal monsters start being rather tanky, when the aim is to blow everything up in matter of seconds.

There are some problems with area dmg, it won't do anything to bosses and very big monsters like the charging dogs/dinos(something like that) that cant be clumped up properly. The boss thing is no problem though, the amount of time you spend killing the boss in a rift is very minimal compared to getting the red bar to 100%.

For 2 mobsI get the same answers. Basically you do 240% damage against 2 mobs, so 20% more than expected.

Against 3 it's 420%, which is 40% more than the 300% base. So for 3 mobs I get the same answer.

Against 4 mobs it's 640%, which is 60% more than the 400% base, which agrees with your answer.

That's the same formula as bonus damage = n*(n-1)*0.2*x where x is your Area Damage Amount%. In the cases above, x = 100% so it ends up being 40%, 120%, and 240% for 2, 3, or 4 mobs. That's the formula I saw on the official forums, but I don't really like presenting the info that way. I prefer the layout of your calculations more, so it's more like 20%*(n-1)*x overall damage gain, so against 2 mobs you do 20% more damage with 100% area damage. Against 3 mobs you deal 40% more damage. That's much easier to understand.

@Herecius

I'd use 2 mobs as a basis to be somewhat conservative. That means 0.2*x bonus damage, so with a 10% roll, that's about 2% more damage. Keep in mind that's 2% of your base dps, so if you have 100k dps, 10% area damage is worth about 2k dps (against 2 mobs). If CC would put your dps to 105k, then you're better off switching that area damage to CC.

You're more than welcome to use 3-4 mobs as a basis of course, especially if you kill a lot of trash mobs and feel that's more of a limiting factor in your play time.

Crusader DPS and EHP Spreadsheet, meant for Crusaders

My Wizard

ntargets, but all AoE skills dealntimes additional damage on n targets, so you can just factor out then.Crusader DPS and EHP Spreadsheet, meant for Crusaders

My Wizard