Iksar Shaman - Solo Challenges?

[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.

[Danth]

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

The DoTing Shaman requires a lot more labor.

Right. I was curious if you tried to put it into exact values for expected actions-per-minute in the manner that you did the kill-rate calculation down to the second. We know the JBB is less actions, but how much less? Is it five per cent less, or ten per cent, or fifty per cent less, or something in the middle?

If not, that's fine too, I'm not about to specifically ask someone to add up something I could do myself if I was sufficiently motivated. Just checking if you already calculated that as part of tyhe simulation.

[DeathsSilkyMist]

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

Right. I was curious if you tried to put it into exact values for expected actions-per-minute in the manner that you did the kill-rate calculation down to the second. We know the JBB is less actions, but how much less? Is it five per cent less, or ten per cent, or fifty per cent less, or something in the middle?

If not, that's fine too, I'm not about to specifically ask someone to add up something I could do myself if I was sufficiently motivated. Just checking if you already calculated that as part of tyhe simulation.

I didn't actually, but I can do a quick calculation.

You would cast 22 spells on average for the JBB Shaman. 20/22 of those spells are JBB. You are pressing 4 buttons for slow + root, as you are also clicking your GCD item once each. 20 buttons for JBB, and 1 button for pet attack. Roughly 25 buttons over 2 minutes of combat. Then you press sit and rest for 1 minute. 26 Actions over 3 minutes I would say, or 8.66.

You would cast 15 spells on average for the DoTing Shaman. Each of these spells requires a GCD click, so that is 30 buttons minimum (assuming you have a macro for canni dance) and 1 for pet attack. 31 actions over 3 minutes I woul say, or 10.33. Maybe 32 if you need to sit manually after your final spell if it was not canni dance.

Neither of these numbers are very big, so I wouldn't say the APM difference matters too much. It is all the other things I mentioned before that really widen the gap between JBB and DoTing.

[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]

You aren't even attempting to engage with me. The linearity of expectation does not hold, and this is why your calculation is founded upon false premises.

You need to actually sum up all the possible outcomes, weighted by the probability for each outcome. This is the calculation I did.

[DeathsSilkyMist]

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

You aren't even attempting to engage with me. The linearity of expectation does not hold, and this is why your calculation is founded upon false premises.

You need to actually sum up all the possible outcomes, weighted by the probability for each outcome. This is the calculation I did.

I am engaging with you. You are incorrect, but you keep asserting you are not. This is why I say you don't understand averages. I am genuinely not insulting you here, you are simply wrong.

I've given you the proper averages multiple times now:

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 [if they proc twice in a row consecutively without a resist]. For DoTs specifically you get the Direct Damage component of the DoT + X amount of ticks [assuming no resist]. 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. [This means you are getting roughly 10 DoT ticks (60 seconds) on average in the specific example of a 2 minute fight where you get 1 proc per fight]

[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.

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

Case 1 happens with probability 1/12 * 1/12
Case 2 happens with probability 1/12 * 11/12
Case 3 happens with probability 11/12 * 1/12
Case 4 happens with probability 11/12 * 11/12

The total expected damage is the sum of the expected damage of each of the four cases, weighted by the probability
160 * 1/144 + 116 * 11/144 + 68 * 11/144 + 0 * 121/144

The total expected damage is 15.1 in this scenario

[bcbrown]

Now let's instead assume the proc is a DD that does 44 damage.

1) If both swings proc, the total damage is 88
2) If just the first swing procs, the total damage is 44.
3) If just the second swing procs, the total damage is 44.
4) If neither swing procs, the total damage is 0.

Case 1 happens with probability 1/12 * 1/12
Case 2 happens with probability 1/12 * 11/12
Case 3 happens with probability 11/12 * 1/12
Case 4 happens with probability 11/12 * 11/12

The total expected damage is the sum of the expected damage of each of the four cases, weighted by the probability
88 * 1/144 + 44 * 11/144 + 44 * 11/144 + 0 * 121/144

The total expected damage is 7.33

Your calculation in this case would be: on average, there's a 1/6 chance of a proc. 1/6 * 44 is 7.33. The numbers match, because the damage is linear to the number of procs.

It does not match in the DoT example, because the damage is not linear to the number of procs

[DeathsSilkyMist]

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.

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

Case 1 happens with probability 1/12 * 1/12
Case 2 happens with probability 1/12 * 11/12
Case 3 happens with probability 11/12 * 1/12
Case 4 happens with probability 11/12 * 11/12

The total expected damage is the sum of the expected damage of each of the four cases, weighted by the probability
160 * 1/144 + 116 * 11/144 + 68 * 11/144 + 0 * 121/144

The total expected damage is 15.1 in this scenario

I think I see the disconnect here. You don't seem to realize how nicely the DoT time and the fight time happen to align in my specific example of 53 DPS on a 7000 HP mob. The fight lasts 132 seconds, and the DoT lasts 132 seconds if you include the initial DD.

Let's assume we still have the 0.5 PPM (procs per minute) value. A 3 tick fight doesn't have a 0.5 PPM value, because it doesn't last a full minute. You should get 3 swings with the hammer if the fight lasts 18 seconds. You'll hit initially, and once after each JBB cast. Our example assumed we swing 6 times per minute, which is how we got the 1/12. This means you have a 0.5 x 0.5 chance to proc = 25% chance to proc per fight. The number is a bit weird here because you swing as soon as you turn on auto attack.

Damage per tick set based on when the weapon procs: [0 damage (no proc), 40 (0 ticks), 64 (1 tick), 88 (2 ticks), 112 (3 ticks)] / 5 = 60.8 x (0.5 PPM x 0.5) = 15.2 damage (the value you got)

Damage per tick set based on when the weapon procs: [0, 40, 64, 88, 112, 136, 160, 184, 208, 232, 256, 280, 304, 328, 352, 376, 400, 424, 448, 472, 496, 520, 544] / 23 = (279 x 0.5 PPM) x 2.0 = 279 damage, or 2.1 DPS (the damage value I got)

Now obviously the DoT in my fight will last 2 ticks less on average, since I am not meleeing for the first 2 ticks. But the real PPM is 0.65, and we are ignoring the white damage, so in reality 2.2 DPS is a very reasonable number, it is probably closer to 3 DPS.

[bcbrown]

My example was two swings over a 16 second fight. Your example was three swings over an 18 second fight. You came up with a number that was similar but not the same as the number I came up with. You've refused to address my calculations: https://www.project1999.com/forums/s...68#post3671968

I'm bored with trying to teach you probability. I consider my previous posts a sufficient explanation, and won't bother correcting you on this topic any more.