Iksar Shaman - Solo Challenges?

[Troxx]

Truth: you will have lots of fights with no procs at all
Truth: you will have lots of fights with lots of procs
Truth: the nature of this proc is that it does not stack additively to add extra value
Truth: some fights you will proc early.
Truth some fights you will proc very late

It is truth 3 specifically that is going to hose you. If the proc was a raw 500+ DD it would indeed average with time. Those fights where you went ham with early and frequent procs would result in a measurably shorter kill time. But if you score an early proc it is not like any subsequent procs will add more than the tiny DD component.

Bcbrown’s analysis is correct. Understanding it requires fluency in these mathematical principles. I will admit I’m nowhere near as fluent in this realm as bcbrown … but I’m also not an engineer or a mathematician.

[Troxx]

“Successful event” here meant a successful proc. We all know you can proc on a miss. Im not sure how you misinterpreted that.

[bcbrown]

Proc rate is independent. Damage dealt is not.

Two procs back to back don't result in twice as much damage.

[DeathsSilkyMist]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

Two procs back to back don't result in twice as much damage.

For Direct damage spells you do get twice the damage. For DoTs specifically you get the Direct Damage component of the DoT + X amount of ticks. That is why I reduced the damage by 50%, because on average it will proc halfway through the fight. You are getting half the DoT ticks on average.

[1 roll, 2 rolls, 3 rolls, 4 rolls, 5 rolls, 6 rolls, 7 rolls, 8 rolls , 9 rolls, 10 rolls, 11 rolls, 12 rolls] / 12 roll attempts = 6.5 rolls on average to get any specific number one time on a D12. This means you will get a proc halfway through the fight on average, as you will roll the specific number you want after 6.5 attempts on average.

[Danth]

Point is that since it's a DOT, when you get multiple procs in rapid succession the later procs go largely wasted because the effects don't stack. Just refreshes the already longer-than-needed duration. Hence the effective useful proc rate is lesser than the real proc rate. Other weapons with long-acting procs, like Narandi lance, suffer a similar limitation.

A Barbarian using the Winter's Roar hammer between bracer clicks does well for this type of thing, especially if he slows himself.

I'm more interested in average clicks-per-minute for the two playstyles. It's already established that actual killrate for the bacer shaman and non-bracer shaman are broadly similar. How much labor is the bracer saving?

[DeathsSilkyMist]

Originally Posted by Danth [You must be logged in to view images. Log in or Register.]

Point is that since it's a DOT, when you get multiple procs in rapid succession the later procs go largely wasted because the effects don't stack. Just refreshes the already longer-than-needed duration. Hence the effective useful proc rate is lesser than the real proc rate. Other weapons with long-acting procs, like Narandi lance, suffer a similar limitation.

A Barbarian using the Winter's Roar hammer between bracer clicks does well for this type of thing, especially if he slows himself.

I understand precisely what they are saying, and I have always taken that into account:

https://www.project1999.com/forums/s...&postcount=553

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

Maybe we can simplify the problem even further, and just consider two swings. This is a 16 second fight, meaning the third JBB results in mob death.
Ticks happen at times 0, 6, 12
One swing happens at t=0. If it procs, it does 44 + 24 * 3 or 116 damage
The second swing happens at t=8. If there was no prior proc, it does 44 + 24 * 1 or 68 damage. If there was a prior proc, it does 44 damage.

If both swings proc, the total damage is 116 + 44, or 160 damage.
If just the first swing procs, the total damage is 116.
If just the second swing procs, the total damage is 68.
If neither swing procs, the total damage is 0.

You with me so far?

You still haven't addressed this post, you can't simply ignore it: https://www.project1999.com/forums/s...&postcount=553

[Danth]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

I understand precisely what they are saying, and I have always taken that into account

The way you worded that it appears you're discussing procs individually. If you're accounting for it, then it's merely a muddled word choice issue, thanks for clearing it up. Due to the length of this particular weapon effect, a late proc means you lose both the un-used portion of the DOT once the mob dies, as well as future procs in the same encounter go largely wasted. This similated activity works against this specific weapon; as noted the Barbarian variant would be preferred. How does the Velious ice proc spear compare for non-barbarians?

[bcbrown]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

For Direct damage spells you do get twice the damage. For DoTs specifically you get the Direct Damage component of the DoT + X amount of ticks. That is why I reduced the damage by 50%, because on average it will proc halfway through the fight. You are getting half the DoT ticks on average.

[1 roll, 2 rolls, 3 rolls, 4 rolls, 5 rolls, 6 rolls, 7 rolls, 8 rolls , 9 rolls, 10 rolls, 11 rolls, 12 rolls] / 12 roll attempts = 6.5 rolls on average to get any specific number one time on a D12. This means you will get a proc halfway through the fight on average, as you will roll the specific number you want after 6.5 attempts on average.

We're trying to calculate an expected value, the expected damage done by scourge procs. Keeping a copy of https://en.wikipedia.org/wiki/Expected_value and https://www.stat.purdue.edu/~zhangha...1%20Sec3.3.pdf open will be helpful here.

The way you calculate an expected value is by summing up all the possible outcomes, each multiplied by it's probability weight. Our random variable, X, is in this case the event of a proc.

E[X] = sum over all x of E[x]

The probability weight is the proc rate, or 1/12. The expected number of procs with your 12 rolls is going to be the sum from 1 to 12 of 1/12, or 1. We are in agreement here.

But we're not just interested in the expected number of procs, we're interested in the expected damage dealt.

There's an identity, that for a linear function of x, the expected value of the function is the function of the expected value of X:
E[aX] = a * E[X]

This is the calculation you are doing. E[d(x)] = d(E[x]). However, the expected damage is a function of time, and it is also a function of whether or not there has been a prior proc.

Therefore, the linearity of expectation does not hold, and it is neccessary to calculate the sum over all the possible outcomes.

This is why you cannot simply multiply the damage by the average time for a proc to hit.

[DeathsSilkyMist]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

The probability weight is the proc rate, or 1/12. The expected number of procs with your 12 rolls is going to be the sum from 1 to 12 of 1/12, or 1. We are in agreement here.

But we're not just interested in the expected number of procs, we're interested in the expected damage dealt.

Agreed!

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

There's an identity, that for a linear function of x, the expected value of the function is the function of the expected value of X:
E[aX] = a * E[X]

This is the calculation you are doing. E[d(x)] = d(E[x]). However, the expected damage is a function of time, and it is also a function of whether or not there has been a prior proc.

Therefore, the linearity of expectation does not hold, and it is neccessary to calculate the sum over all the possible outcomes.

This is why you cannot simply multiply the damage by the average time for a proc to hit.

This is where you are incorrect. You get 1 proc per fight on a 2 minute fight in the specific example I gave. On average that means you will get a proc halfway through the fight. That is an average of 9-10 ticks plus the DD. If you proc the weapon again during that time, you just get another DD proc (more damage), and the DoT continues to tick damage normally, as if the second proc never occured.

If the DoT is doing an average of 9-10 ticks, that is 10 x 24 (Damage per tick) + 40 (Direct Damage) = ~2.1 DPS per fight on average. This is not taking into account white damage, and the proc rate is actually 0.65, which means you are probably getting another tick or two on average.

Remember we are looking the the average over all possible fights, not an individual fight where you could get 0 procs, 10 procs, etc. Your average procs per minute is still 0.65.

[bcbrown]

Maybe we can simplify the problem even further, and just consider two swings. This is a 16 second fight, meaning the third JBB results in mob death.
Ticks happen at times 0, 6, 12
One swing happens at t=0. If it procs, it does 44 + 24 * 3 or 116 damage
The second swing happens at t=8. If there was no prior proc, it does 44 + 24 * 1 or 68 damage. If there was a prior proc, it does 44 damage.

If both swings proc, the total damage is 116 + 44, or 160 damage.
If just the first swing procs, the total damage is 116.
If just the second swing procs, the total damage is 68.
If neither swing procs, the total damage is 0.

You with me so far?