Has anyone tried to calculate the value (average increased chance to crit) for this passive? Here is the description, "Gain 3% Critical Hit Chance every second. This bonus is reset 1 second after you successfully critically hit."
So 3% crit per second until you critically strike and the bonus crit lasts for a 1 second 'buffer' period. Let's assume a best-case scenario of a 1.1 attack/sec weapon speed, a base crit chance of 5%, and that each attack only hits 1 target. What is the average increased chance to crit?
This passive is designed to be used with slow weapons, aimed shots/combos.
The effective crit rate is completely dependent on the weapon you use, and if you focus on spam clicking or careful targetting.
For example if you are focusing more on a dropping a heavy shot every few seconds, with a higher damage but slower weapon you will get better use of this passive.
This passive is designed to be used with slow weapons, aimed shots/combos.
The effective crit rate is completely dependent on the weapon you use, and if you focus on spam clicking or careful targetting.
For example if you are focusing more on a dropping a heavy shot every few seconds, with a higher damage but slower weapon you will get better use of this passive.
Yeah, now actually answer my question and help me figure out a formula that includes base crit chance and attack speed. Then you can have your cookie.
Unfortunately that is not the kind of formula that I am looking for. I just want to know how high, on average, your crit will be before you get a crit with this talent.
Unfortunately that is not the kind of formula that I am looking for. I just want to know how high, on average, your crit will be before you get a crit with this talent.
At 0 stacks you will take 20 attacks on average
At 1 stack you will take 12 attacks on average
At 2 stacks you will take 9.0909(repeating) attacks on average
At 3 stacks you will take 7.142 attacks on average
At 4 stacks you will take 5.882 attacks on average
At 5 stacks you will take 5 attacks on average
At 6 stacks you will take 4.347 attacks on average
At 7 stacks stacks will take 3.84 attacks on average
......
With a 1.5 attack speed weapon
Your math becomes 1.5/20+1.5/12+1.5/9.09+1.5/7.142+1.5/5.882+1.5/5
Chance per bin (Second) = 7.5% + 12.5 (20) + 16.5 (36.5) + 21 (57) + 25.5 (82.5) + 30 (112.5%)
That being said on average you should crit between 5-6 seconds with no added crit besides your ONE passive.
Or to answer your question your average crit will be 4-5 stacks ... so 17-20%.
Now keep in mind this changes with weapon speed. The faster your weapon the more attacks you make per bin, the higher your chance is of critting within that second. Slower weapons will crit less frequently, but sharpshooter helps to ensure you see crits with those weapons. Its also good for traveling between monster packs when you have a few second of non combat to acrue your stacks.
Now keep in mind this changes with weapon speed. The faster your weapon the more attacks you make per bin, the higher your chance is of critting within that second. ... Its also good for traveling between monster packs when you have a few second of non combat to acrue your stacks.
It would be a super OP talent if they extended its duration to 2 seconds. Throw out a fat AOE @ ~100% crit, as many fast attacks as you can fit in the 2 seconds, pack cleared, loot, crit back up to ~100%, repeat.
I wonder how sentry or say, the wolf pet, is affected by your stats? If the crit translates to the summon, there might be a build to be made based around high-crit sentry+wolf since I'm pretty sure either of them hitting won't reset your Sharpshooter. I could be wrong on that, but you could still summon both with a full stack and shoot some things before it expires.
I wonder how it will work with skills like Cluster Arrow's Cluster Bombs rune. It may be an instant kill to most mobs for every new pack you meet. I don't even mention ridiculous discipline regeneration with some passives. It is so cool we will be able to check all of this out so easily.
Now keep in mind this changes with weapon speed. The faster your weapon the more attacks you make per bin, the higher your chance is of critting within that second. ... Its also good for traveling between monster packs when you have a few second of non combat to acrue your stacks.
It would be a super OP talent if they extended its duration to 2 seconds. Throw out a fat AOE @ ~100% crit, as many fast attacks as you can fit in the 2 seconds, pack cleared, loot, crit back up to ~100%, repeat.
I wonder how sentry or say, the wolf pet, is affected by your stats? If the crit translates to the summon, there might be a build to be made based around high-crit sentry+wolf since I'm pretty sure either of them hitting won't reset your Sharpshooter. I could be wrong on that, but you could still summon both with a full stack and shoot some things before it expires.
I don't think I understand your post right... Right now the passive increases your critical hit chance by 3% every second since you've last landed a crit. If they extended it up to 2 seconds... that would underpower... not overpower it?
I was referring to the "This bonus is reset 1 second after a critical hit" portion. If THAT were 2 seconds, it'd be pretty BA.
I think that time was given to let you shoot whatever else you want once if you are quick. It's not bad as it is till some point when we have really good gear and this passive is not worth it anymore. Ahh.., once again I love D3 for letting me choose my skills anytime I want so I can experiment.
Figuring out how long it takes to crit isn't all that hard, though it's a little annoying. Basically, it's like this:
C = max(c + .03*floor(t), 1)
n = ceiling(a*t)
p1 = 1 - c
pn = (1 - C) * pn-1 * pn-2 * ... * p1
c = base crit chance
t = time in seconds
C = modified crit chance
a = attacks per second
n = number of attacks by t given a
pn = probability of not critting by attack n, given a and c
Examples:
a = 1, c = .2:
t n p
1.1 1 .800
2.1 2 .616
3.1 3 .456
4.1 4 .324
5.1 5 .220
6.1 6 .143
7.1 7 .089
8.1 8 .052
a = .5, c = .2:
t n p
0.1 1 .800
2.1 2 .592
4.1 3 .403
6.1 4 .250
8.1 5 .140
10.1 6 .070
12.1 7 .031
14.1 8 .012
BTW, sorry about the table formatting but this forum software apparently thinks it knows better than I do what the formatting should look like...
Figuring out the real contribution to DPS is a lot harder, but we could probably approximate it by figuring out the average contribution to crit chance as the OP mentions.
If DPS is a*d*c*m where a is attacks per second, d is damage per attack, c is one plus crit chance and m is crit multiplier, Sharpshooter DPS would be approximated by a*d*v*m where v is one plus average crit chance with Sharpshooter.
v can be determined using the tables derived from the formulas at the beginning of this post. Subtract p on the first line from 1 and multiply the result by the crit chance for that attack. Subtract p on line 2 from p on line 1 and multiply the result by the crit chance for attack 2 and add the result to what you got from line 1. Continue this process until you account until your leading coefficiencts sum to 1. IE using the second table, .2*.2+.208*.26 + .189*.32 + .153*.38 + .11*.44 + .07*.5 + .039*.56 + .019*.62 ... There are 7 more terms which I don't feel like finding that would round out the last 22%, but all of those cases involve holding the attack button for more than 15 seconds, so I think the approximation here is good enough, which would be 33%. Since the base crit considered was .2, and 1.33/1.2 = 1.108, this is at least a 10.8% increase in damage in this specific case.
However, this may not be a great estimate in practice for a number of reasons. First, as damage from an individual attack increases (particularly spiky damage like crits), more and more of the damage ends up wasted because the monster would have been dead with less. Second, we're not considering that Sharpshooter also basically means an automatic crit on your first attack after not having engaged a group of mobs for a while. Also, keep in mind that this specific case is kind of a best-case-scenario because we're using a very slow attack here so Sharpshooter gets reset less often.
EDIT: I don't think damage is as simple as a*d*c*m above (particularly the crit multiplier term), but my brain is a little too fried to fix it right now. The point should still hold up though I think.
Rollback Post to RevisionRollBack
...and if you disagree with me, you're probably <insert random ad hominem attack here>.
Throw out a fat AOE @ ~100% crit, as many fast attacks as you can fit in the 2 seconds, pack cleared, loot, crit back up to ~100%, repeat.
Basicly what this does is give you a massive damage boost for your first 2 attacks (if you attack fast enough)
Let's assume you have 20% crit. You walk around for 10 seconds, now you have 50% crit for 1 second before it resets to 20%. So you want to initiate with a high damage aoe ability, obviously.
Fan of Knives + Cluster Arrow seems like a good choice.
Rollback Post to RevisionRollBack
"Traitors! Even in death, the armies of Khanduras will still obey their king!"
To post a comment, please login or register a new account.
So 3% crit per second until you critically strike and the bonus crit lasts for a 1 second 'buffer' period.
Let's assume a best-case scenario of a 1.1 attack/sec weapon speed, a base crit chance of 5%, and that each attack only hits 1 target. What is the average increased chance to crit?
The effective crit rate is completely dependent on the weapon you use, and if you focus on spam clicking or careful targetting.
For example if you are focusing more on a dropping a heavy shot every few seconds, with a higher damage but slower weapon you will get better use of this passive.
(((0.05)+(X)+(0.03*Y))*Z)
X = Additional crit chance from other skills and items
Y = Seconds since last crit
Z = Weapon attack speed.
Example:
* No Additional Crit Chance
* 1.6 Attacks per Second
* 6 Seconds since last crit
(0.05+0+0.03*6)*1.6
23*1.6
You have a 36.8% chance to crit within that 6th second.
If you want to find your probably of criting by the 6th second you need to compound it which makes the math more annoying
At 0 stacks you will take 20 attacks on average
At 1 stack you will take 12 attacks on average
At 2 stacks you will take 9.0909(repeating) attacks on average
At 3 stacks you will take 7.142 attacks on average
At 4 stacks you will take 5.882 attacks on average
At 5 stacks you will take 5 attacks on average
At 6 stacks you will take 4.347 attacks on average
At 7 stacks stacks will take 3.84 attacks on average
......
With a 1.5 attack speed weapon
Your math becomes 1.5/20+1.5/12+1.5/9.09+1.5/7.142+1.5/5.882+1.5/5
Chance per bin (Second) = 7.5% + 12.5 (20) + 16.5 (36.5) + 21 (57) + 25.5 (82.5) + 30 (112.5%)
That being said on average you should crit between 5-6 seconds with no added crit besides your ONE passive.
Or to answer your question your average crit will be 4-5 stacks ... so 17-20%.
Now keep in mind this changes with weapon speed. The faster your weapon the more attacks you make per bin, the higher your chance is of critting within that second. Slower weapons will crit less frequently, but sharpshooter helps to ensure you see crits with those weapons. Its also good for traveling between monster packs when you have a few second of non combat to acrue your stacks.
It would be a super OP talent if they extended its duration to 2 seconds. Throw out a fat AOE @ ~100% crit, as many fast attacks as you can fit in the 2 seconds, pack cleared, loot, crit back up to ~100%, repeat.
I wonder how sentry or say, the wolf pet, is affected by your stats? If the crit translates to the summon, there might be a build to be made based around high-crit sentry+wolf since I'm pretty sure either of them hitting won't reset your Sharpshooter. I could be wrong on that, but you could still summon both with a full stack and shoot some things before it expires.
I don't think I understand your post right... Right now the passive increases your critical hit chance by 3% every second since you've last landed a crit. If they extended it up to 2 seconds... that would underpower... not overpower it?
I think that time was given to let you shoot whatever else you want once if you are quick. It's not bad as it is till some point when we have really good gear and this passive is not worth it anymore. Ahh.., once again I love D3 for letting me choose my skills anytime I want so I can experiment.
I will try to work out the math for you, as I have wondered the same, however, I have a hunch its pretty damn terrible on average.
"Just google "diablo 3 gold guide" and magical rainbow covered demons will assault your eyes."
C = max(c + .03*floor(t), 1)
n = ceiling(a*t)
p1 = 1 - c
pn = (1 - C) * pn-1 * pn-2 * ... * p1
c = base crit chance
t = time in seconds
C = modified crit chance
a = attacks per second
n = number of attacks by t given a
pn = probability of not critting by attack n, given a and c
Examples:
BTW, sorry about the table formatting but this forum software apparently thinks it knows better than I do what the formatting should look like...
Figuring out the real contribution to DPS is a lot harder, but we could probably approximate it by figuring out the average contribution to crit chance as the OP mentions.
If DPS is a*d*c*m where a is attacks per second, d is damage per attack, c is one plus crit chance and m is crit multiplier, Sharpshooter DPS would be approximated by a*d*v*m where v is one plus average crit chance with Sharpshooter.
v can be determined using the tables derived from the formulas at the beginning of this post. Subtract p on the first line from 1 and multiply the result by the crit chance for that attack. Subtract p on line 2 from p on line 1 and multiply the result by the crit chance for attack 2 and add the result to what you got from line 1. Continue this process until you account until your leading coefficiencts sum to 1. IE using the second table, .2*.2+.208*.26 + .189*.32 + .153*.38 + .11*.44 + .07*.5 + .039*.56 + .019*.62 ... There are 7 more terms which I don't feel like finding that would round out the last 22%, but all of those cases involve holding the attack button for more than 15 seconds, so I think the approximation here is good enough, which would be 33%. Since the base crit considered was .2, and 1.33/1.2 = 1.108, this is at least a 10.8% increase in damage in this specific case.
However, this may not be a great estimate in practice for a number of reasons. First, as damage from an individual attack increases (particularly spiky damage like crits), more and more of the damage ends up wasted because the monster would have been dead with less. Second, we're not considering that Sharpshooter also basically means an automatic crit on your first attack after not having engaged a group of mobs for a while. Also, keep in mind that this specific case is kind of a best-case-scenario because we're using a very slow attack here so Sharpshooter gets reset less often.
EDIT: I don't think damage is as simple as a*d*c*m above (particularly the crit multiplier term), but my brain is a little too fried to fix it right now. The point should still hold up though I think.
Basicly what this does is give you a massive damage boost for your first 2 attacks (if you attack fast enough)
Let's assume you have 20% crit. You walk around for 10 seconds, now you have 50% crit for 1 second before it resets to 20%. So you want to initiate with a high damage aoe ability, obviously.
Fan of Knives + Cluster Arrow seems like a good choice.