Ambush vs. Steady Aim Analysis (nevermind)

Demon Hunter
https://docs.google.com/spreadsheets/d/1Icnq_6TXysXcikfoK-E46c8pE9PLbz_SSqLWEfZ2xAA/edit?usp=sharing

Hey guys, I'm pretty sure my math is right on this but if someone else wants to check that'd be greatly appreciated. The first page is for you to figure out where your bonus additive damage sits (1 = 0% additive damage, 2.45 = 145% additive damage). This believes that all you have are Taeguk and +XX%Multishot going toward it (pretty easy to add the few other possibilities).

Second page

First I'd like to note that Ambush gives you +10% MULTIPLICATIVE damage (probably a little more actually since if they are at 76% hp and you hit them it should do the full 40% boosted damage, but I digress).

The first column is your damage + additive damage without steady aim (eg. 100% = 0% additive damage, 300% = 200% additive damage).

The second column is that number with Steady Aim added to it (20%).

The third column is the effective damage gain you are getting out of Steady Aim for how much additive damage you already have.
Note that if you are below 100% additive damage, steady aim already wins out over ambush!

This next part is what most people forget I think! DML can double proc multishot vs enemies below 50-60% hp! That is what the next set of columns tries to represent. Notice that with the worst possible roll on a DML you win with Steady Aim as long as your additive damage is <200%. With the best possible roll on a DML Steady Aim wins <220% (This would be an equivalent of 3.2 on the first sheet, I haven't even listed that as it is an ABSURD amount).

This sounds a little odd at first, "Hey doesn't everything get affected by DML since it is an independent multiplier? So shouldn't we just ignore it when considering how much extra damage Steady Aim gives us?" Yes. Typically speaking that is. But since Ambush ONLY works above 75% hp, DML does NOT amplify Ambush. What this means is one of our STRONGEST independent multipliers is not affecting Ambush and so when considering other options for that passive slot we need to take DML into account. Even though Ambush is multiplicative, and DML is multiplicative, they do NOT affect each other. This is a very very unique situation and unless I screwed something up horribly I believe we have much better options than Ambush.

Edit: I missed something, ambush is definitely better in most scenarios.
well you could look at it this way though:
ambush lets you get to DML range much quicker.
01/27/2016 05:47 PMPosted by shaunika
well you could look at it this way though:
ambush lets you get to DML range much quicker.


Easy example: Enemy has 1000 hp, you do 50 damage a second with a 100% additive damage bonus (no steady aim, no ambush). If you add ambush your damage goes from 50 to 70 for the first 250 hp, 250/70 = 3.5714 to get to 750 hp. We are now at 3.5714 seconds. 750-600 = 150 damage to go through before DML range. 150/50 = 3 seconds. We are now 6.5714 seconds. DML kicks in. 600/100 = 6 seconds to KO. We are now at 12.5714 seconds.

Get rid of ambush. Add steady aim. You are now at 120% additive damage. You have effectively gained 10% more damage than you previously had due to steady aim. 55 damage. 400/55 = 7.2727 seconds to get to DML range. We are now at 7.2727 seconds. DML is now causing you to do double damage. 55 becomes 110. 600/110 = 5.4545. 7.2727+5.4545 = 12.7272 seconds.

Apparently you are right but this absolutely baffles me... I must have messed up my math somewhere in that excel sheet O.o. You should ultimately be doing 16% more damage according to my calculations. If someone can tell me where I went wrong I'd love them, in the meantime Shaunika is right, it appears ambush IS better <3 O.o
I found out that my average rift clear is a bit faster with Ambush as I ran Steady Aim for quite awhile.

A critical damage hit with Ambush active can cause white mob to drops their threshold into DML much easier and Ambush helps downing elite much more effective while waiting for CoE proc. As I think CoE is the instrument killing elite here, 20% skill damage increase from Steady Aim seems small.

Although I didn't actually do any maths. This is my experience running grift 70 with each of two passives.
01/27/2016 07:14 PMPosted by Viscaria
I found out that my average rift clear is a bit faster with Ambush as I ran Steady Aim for quite awhile.

A critical damage hit with Ambush active can cause white mob to drops their threshold into DML much easier and Ambush helps downing elite much more effective while waiting for CoE proc. As I think CoE is the instrument killing elite here, 20% skill damage increase from Steady Aim seems small.

Although I didn't actually do any maths. This is my experience running grift 70 with each of two passives.


I had always assumed ambush was better - I was just curious and decided to check things out.
This is why I shouldn't try to do math after work :/ lol
because ambush can do upto a +40% dps increase*

kill speed factor (reduced by)
[coefA/rate + coefB/rate]
= 25% / 1.4dps + 75% / 1dps
= 92.85%


1/.9285 gain == +7.69% kill speed when granularity approaches infinite
--this is the worst it does; when a mob takes nearly forever

*since you can one-shot a mob with a hit for 71.5% of it's health (1/1.4 > 0.714)
--at best it earns you +40% dps,
Now I think the reason I cleared Grift faster with Ambush may have something to do with keeping Steady Aim active and Vault usage to help with that. When I use more Vault to keep mob out of SA range, my DPS decreased because of Multishot downtime and lower Discipline from vaulting(less Multishot % from UE).

So in my opinion, the two passives has roughly equal power in term of DPS increase for solo play. Group play may steer SA in favor if another DPS is present making Ambush bit less effective.
01/27/2016 06:39 PMPosted by Marin274
01/27/2016 05:47 PMPosted by shaunika
well you could look at it this way though:
ambush lets you get to DML range much quicker.


Easy example: Enemy has 1000 hp, you do 50 damage a second with a 100% additive damage bonus (no steady aim, no ambush). If you add ambush your damage goes from 50 to 70 for the first 250 hp, 250/70 = 3.5714 to get to 750 hp. We are now at 3.5714 seconds. 750-600 = 150 damage to go through before DML range. 150/50 = 3 seconds. We are now 6.5714 seconds. DML kicks in. 600/100 = 6 seconds to KO. We are now at 12.5714 seconds.


Forgive me if I'm misinterpreting your calculations above, but I'm not sure that but such static numbers and precise decimals will actually give an accurate representation of Ambush's damage contribution. Besides damage numbers varying wildly in practice due to different skills, crits, etc., Ambush can also "overflow" against targets who are just above its 75% health threshold. To use a few of your numbers above, Ambush doesn't care how much HP the target has so long as it's above 750 - it's still going to cause the next attack against the target to deal 40% bonus damage, and this can affect the "gap time" between the target being in Ambush range and double-Multishot range.

Let's say you strike two targets with 1000 max HP with the same attack. The first target takes 251 damage, but due to natural damage variation, the second target only takes 249. Because of Ambush's mechanics, however, the second target is actually more likely to reach DML's threshold first, even if we hit them both with the same skills and get the same amount of critical hits/damage variation on each. That's because the second target still has over 75% HP and will benefit from Ambush's 40% bonus on the next attack, while the first is below 75% HP and will not. If you're measuring in fractions of a second required to hit the 75% HP and DML thresholds, though, your calculations won't reflect this possible variation.
I'm not having time to go over the calculations right now, just want to add one thing, though.

Steady Aim only provides its bonus if there are NO enemies within 10m range. That means it quickly uses its usefulness if you are confronted by leaping/charging monsters that are very difficult to keep at bay. For me that's a major drawback to the passive and the reason I usually don't use it in UE builds.
For M6 I think it is much less of a problem, though.
Without any solid numbers attached I experimented with both these passives over the past few days to see if i could tell a difference and whenever i would run steady aim in gr76s i would slowly fall behind the timer opposed to using ambush...

Maybe its playstyle or density in the rifts i experimented on but ambush felt far superior to me personally when testing. I also run m6, not UE so the multi doublehit has no impact for my runs

I will always choose ambush over steady aim based on my own results, again no solid proof from numbers and this is with m6
01/28/2016 06:52 AMPosted by z0uNdz
whenever i would run steady aim in gr76s i would slowly fall behind the timer opposed to using ambush...


Probably the easiest answer to this would be that ambush affects all enemies at full health where as Steady Aim requires no enemies arround for the bonus to be active, as soon as an enemy gets too close you lose that whole bonus, even if just for a short period of time, if it is reproduced over and over can have a significant impact.
steady aim is far better for me

prove me wrong
01/28/2016 07:33 AMPosted by zoid
steady aim is far better for me

prove me wrong


Honeslty, I can't prove you wrong, I use both...
Ambush is tricky because of overshooting. The more you overshoot, the more effective Ambush is. This makes it amazing for speed runs where you are one-shotting almost everything.

That being said,

01/27/2016 05:32 PMPosted by Marin274
First I'd like to note that Ambush gives you +10% MULTIPLICATIVE damage (probably a little more actually since if they are at 76% hp and you hit them it should do the full 40% boosted damage, but I digress).


It doesn't give you 10% multiplicative. It gives you a minimum of 7.7% multiplicative without a DML and 11.3% multiplicative with a 60% DML (less with a <60% DML). If you overshoot or deal non-constant damage over the RG health pool for any reason, these numbers change.

We can calculate the lower bound of the Ambush damage increase by assuming that enemies have much more health than we deal damage and we never overshoot. Any amount of overshooting will increase the effectiveness of Ambush over this number.

It gets tricky though, because the effectiveness of Ambush depends on whether or not your damage is constant over the duration of the RG health pool. It's not with DML, and this actually makes Ambush more effective.

Now for math.

Without DML or Ambush:

Do 1 damage for 100%-0% health. (100 - 0) / 1 = 100 hits. 100 / 100 = 1.0 times damage.

With Ambush but no DML:

Do 1.4 damage for 100%-75% health and 1 damage for 75%-0% health. (100 - 75) / 1.4 + (75 - 0) / 1 = 92.857. 100 / 92.857 = 1.077, or a 7.7% damage increase.

With a 60% DML but no Ambush:

Do 1.0 damage for 100%-60% health and 2.0 damage for 60%-0% health. (100 - 60) / 1 + (60 - 0) / 2 = 70.

With a 60% DML and Ambush:

Do 1.4 damage for 100%-75% health, 1.0 damage for 75%-60% health, and 2.0 damage for 60%-0% health. (100 - 75) / 1.4 + (75 - 60) / 1 + (60 - 0) / 2 = 62.857. 70/62.857 = 1.113, or an 11.3% damage increase.

So with no overshooting and constant damage over RG health, Ambush is equivalent to a 7.7% multiplicative damage increase. With no overshooting and a 60% DML, Ambush is equivalent a multiplicative 11.3% damage increase. With a <60% DML, this increase is smaller.

Once you start overshooting, this effective damage increase becomes bigger.

----

To determine if Steady Aim is better, you would compare the effective damage increase from Steady Aim relative to your additive damage. So we solve for (x + 0.2) / x > a, where x is your additive damage multiplier (1 + additive damage pool / 100) and a is the Ambush multiplier (1.077 for no DML and 1.113 with DML).

This simplifies to x < 0.2 / (a - 1).

With no DML:

0.2 / (1.077 - 1) = 2.6. Steady Aim is better when you have less than 160% additive damage and aren't overshooting.

160% additive damage is pretty high for solo, so with a non-DML build Steady Aim is usually better assuming you aren't overshooting. If you are overshooting by a fair amount, then Ambush will pull ahead though.

With DML:

0.2 / (1.113 - 1) = 1.76. Steady Aim is better when you have less than 76% additive damage and aren't overshooting.

Skill damage is additive damage, so with a new DML (75-100% multishot damage), Steady Aim is basically never better.
Ambush is tricky because of overshooting. The more you overshoot, the more effective Ambush is. This makes it amazing for speed runs where you are one-shotting almost everything.

That being said,

01/27/2016 05:32 PMPosted by Marin274
First I'd like to note that Ambush gives you +10% MULTIPLICATIVE damage (probably a little more actually since if they are at 76% hp and you hit them it should do the full 40% boosted damage, but I digress).


It doesn't give you 10% multiplicative. It gives you a minimum of 7.7% multiplicative without a DML and 11.3% multiplicative with a 60% DML (less with a <60% DML). If you overshoot or deal non-constant damage over the RG health pool for any reason, these numbers change.

We can calculate the lower bound of the Ambush damage increase by assuming that enemies have much more health than we deal damage and we never overshoot. Any amount of overshooting will increase the effectiveness of Ambush over this number.

It gets tricky though, because the effectiveness of Ambush depends on whether or not your damage is constant over the duration of the RG health pool. It's not with DML, and this actually makes Ambush more effective.

Now for math.

Without DML or Ambush:

Do 1 damage for 100%-0% health. (100 - 0) / 1 = 100 hits. 100 / 100 = 1.0 times damage.

With Ambush but no DML:

Do 1.4 damage for 100%-75% health and 1 damage for 75%-0% health. (100 - 75) / 1.4 + (75 - 0) / 1 = 92.857. 100 / 92.857 = 1.077, or a 7.7% damage increase.

With a 60% DML but no Ambush:

Do 1.0 damage for 100%-60% health and 2.0 damage for 60%-0% health. (100 - 60) / 1 + (60 - 0) / 2 = 70.

With a 60% DML and Ambush:

Do 1.4 damage for 100%-75% health, 1.0 damage for 75%-60% health, and 2.0 damage for 60%-0% health. (100 - 75) / 1.4 + (75 - 60) / 1 + (60 - 0) / 2 = 62.857. 70/62.857 = 1.113, or an 11.3% damage increase.

So with no overshooting and constant damage over RG health, Ambush is equivalent to a 7.7% multiplicative damage increase. With no overshooting and a 60% DML, Ambush is equivalent a multiplicative 11.3% damage increase. With a <60% DML, this increase is smaller.

Once you start overshooting, this effective damage increase becomes bigger.

----

To determine if Steady Aim is better, you would compare the effective damage increase from Steady Aim relative to your additive damage. So we solve for (x + 0.2) / x > a, where x is your additive damage multiplier (1 + additive damage pool / 100) and a is the Ambush multiplier (1.077 for no DML and 1.113 with DML).

This simplifies to x < 0.2 / (a - 1).

With no DML:

0.2 / (1.077 - 1) = 2.6. Steady Aim is better when you have less than 160% additive damage and aren't overshooting.

160% additive damage is pretty high for solo, so with a non-DML build Steady Aim is usually better assuming you aren't overshooting. If you are overshooting by a fair amount, then Ambush will pull ahead though.

With DML:

0.2 / (1.113 - 1) = 1.76. Steady Aim is better when you have less than 76% additive damage and aren't overshooting.

Skill damage is additive damage, so with a new DML (75-100% multishot damage), Steady Aim is basically never better.


question.

vs mob with 100 life; the minimum damage needed to one shot with ambush?

hint. . the bonus is far more than 11.3%
I have a question... With DML, from what i can tell if a mob is at 100% life and you hit it once and it brings it down to <60% DML procs and you get the second hit with multishot. Am i not seeing this correct or have you guys experienced the same thing?
I drop awareness and run both.
I would too for speed runs, but awareness is on my hellfire :-/
I think the argument for what is better here is for pushing high rifts since we are trying to squeeze as much damage out as possible...therefore awareness is pretty mandatory since risks need to be taken
Use both drop awareness I beat 76 working on 77

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