Ray of Frost & AP regen & Max AP - Theorycrafting and Analysis - Diablo III Misc Forums - Forums - Diablo Fans

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Ray of Frost + Crimson Rune(Snow Blast) has the potential to be a lethal combo for single target dmg. Ray of Frost + Crimson = 275% Weapon dmg increasing slowly to 715% Weapon dmg after 1.5 seconds, AP cost = 29/sec.

The mechanics of the crimson rune could drastically change the dmg of RoF given different values for of AP regeneration and Maximum AP. So this post is to investigate just how much.

Base Wizard Regen = 12.5 AP/sec.
AP Regen w/ Astral Presence = 14.5 AP/sec
AP Regem w/ Arcamot = 17 AP/sec
AP Regen w/ Arcantot + Astral Presence = 19 AP/sec

Power of the Storm reduces ability cost by 7 AP.

Energy Armor = -20 AP
Energy Armor + Energy tap = +40 AP
Astral Presence = +20 AP

There are two possible ways the dmg is calculated during the 1.5 second build up phase,
#1 Small increases over time, independent of casts.
#2 Large increases dependent on each new cast.

#1 For examples sake, lets say the dmg is calculated every 0.5 second.
Cast time is unchanged at 1 second.

Max AP = 80 => x is the maximum continual cast time beyond the first.
1) 80-29*x+12.5*x=29 => x = 3 sec = 3 casts => 4 casts total (Round down to the Nearest full cast)
2) 80-29*x+17*x=29 => x = 4.25 sec = 4.25 casts => 5 casts total

Max AP = 100 => x is the maximum continual cast time beyond the first.
3) 100-29*x+12.5*x=29 => x = 4.3 => 5 casts (Round down to the nearest full cast)
4) 100-29*x+14.5*x=29 => x = 4.9 => 5 casts
5) 100-29*x+17*x=29 => x = 5.9 => 6 casts
6) 100-22*x+12.5*x=22 => x = 8.2 => 9 casts
7) 100-22*x+17*x=22 => x = 15.6 => 16 casts

Max AP = 120 => x is the maximum continual cast time beyond the first.
8) 120-29*x+14.5*x=29 => x = 6.3 => 7 casts (Round down to the nearest full cast)
9) 120-29*x+19*x=29 => x = 9.1 => 10 casts
10) 120-22*x+14.5*x=22 => x = 13 => 14 casts
11) 120-22*x+19*x=22 => x = 32.3 => 33 casts

Max AP = 140 => x is the maximum continual cast time beyond the first.
12) 140-29*x+12.5*x=29 => x = 6.7 => 7 casts (Round down to the nearest full cast)
13) 140-29*x+17*x=29 => x = 9.25 => 10 casts

Max AP = 160 => x is the maximum continual cast time beyond the first.
14) 160-29*x+14.5*x=29 => x = 9 => 10 casts (Round down to the nearest full cast)
15) 160-29*x+19*x=29 => x = 13.1 => 14 casts

As you can see, the % avg wpn dmg does not improve by any large amount by increasing AP regen or max AP. Note: Shortening the Time Step (0.5 seconds) slightly alters the averages.

The first is rather self explanatory and without incident, so I will discuss the ramifications of the 2nd below.

The dmg of the beam might stay constant during the entire cast time.
Thus, the 1st cast might be, 275+440*0/2 = 275% wpn dmg, 2nd cast would be 275+440*1/2 = 495% wpn dmg, and the 3rd cast would finally be the 275+440*2/2 = 715% wpn dmg.

However, this would mean RoF would have a haste soft cap built in.

Lets say you have sufficient haste to reduce your cast speed to 0.75 seconds.
0.75+0.75 = 1.5 sec (Perfectly sync'd with the build up time)

7 casts = 5.25 seconds

((0.75*(275+440*0/2)+0.75*(275+440*1/2)+(275+440*2/2)*3.75)/5.25 = 620% avg wpn dmg per cast
=> 7*621/5.25 = 828% wpn dmg per second

Now lets say you got an upgrade, and your new cast speed in 0.7 seconds
0.7 + 0.7 = 1.4 sec (0.1 seconds before the build up time, thus your 3rd cast wont be max)

7 cast = 4.9 seconds

((0.7*(275+440*0/3)+0.7*(275+440*1/3)+(275+440*2/3)*0.7+(275+440*3/3)*2.8)/4.9 = 589% wpn dmg per cas
=> 7*589/4.9 = 841% wpm dmg per second

Given this method of calculating dmg, it is less advantageous than maybe it should be at higher haste levels. Depending on the cast speeds, you could see very little DPS gain, yet consume more AP/sec. Which method blizz uses is up in the air, but I am leaning towards the method described here.

I deleted the one in the main forums, that was a mistake.
And it is equally important here as the wizard forums.

PS:
I reworked the #s in a different way. I think this method should be slightly more accurate.
If you notice any permutations missing or mistakes let me know.

Rollback Post to RevisionRollBack

One is never hurt by being given additional choices, only by taking them away. A QUADRILLION MAGIC FIND is worthless if you can't kill shit!

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The mechanics of the crimson rune could drastically change the dmg of RoF given different values for of AP regeneration and Maximum AP. So this post is to investigate just how much.

Base Wizard Regen = 12.5 AP/sec.

AP Regen w/ Astral Presence = 14.5 AP/sec

AP Regem w/ Arcamot = 17 AP/sec

AP Regen w/ Arcantot + Astral Presence = 19 AP/sec

Power of the Storm reduces ability cost by 7 AP.

Energy Armor = -20 AP

Energy Armor + Energy tap = +40 AP

Astral Presence = +20 AP

Change in %dmg = 715-275 = 440% dmg

============================================================================There are two possible ways the dmg is calculated during the 1.5 second build up phase,

#1 Small increases over time, independent of casts.

#2 Large increases dependent on each new cast.

============================================================================#1 For examples sake, lets say the dmg is calculated every 0.5 second.

Cast time is unchanged at 1 second.

Max AP = 80 => x is the maximum continual cast time beyond the first.1) 80-29*x+12.5*x=29 => x = 3 sec = 3 casts => 4 casts total (Round down to the Nearest full cast)

2) 80-29*x+17*x=29 => x = 4.25 sec = 4.25 casts => 5 casts total

1) ((0.5*(275+440*0/3)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+2.5*(275+440*3/3))/4 = 605% avg wpn dmg

2) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*3.5)/5 = 627% avg wpn dmg

Max AP = 100 => x is the maximum continual cast time beyond the first.3) 100-29*x+12.5*x=29 => x = 4.3 => 5 casts (Round down to the nearest full cast)

4) 100-29*x+14.5*x=29 => x = 4.9 => 5 casts

5) 100-29*x+17*x=29 => x = 5.9 => 6 casts

6) 100-22*x+12.5*x=22 => x = 8.2 => 9 casts

7) 100-22*x+17*x=22 => x = 15.6 => 16 casts

3) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*3.5)/5 = 627% avg wpn dmg

4) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*3.5)/5 = 627% avg wpn dmg

5) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*4.5)/6 = 642% avg wpn dmg

6) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*7.5)/9 = 666% avg wpn dmg

7) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*14.5)/16 = 688% avg wpn dmg

Max AP = 120 => x is the maximum continual cast time beyond the first.8) 120-29*x+14.5*x=29 => x = 6.3 => 7 casts (Round down to the nearest full cast)

9) 120-29*x+19*x=29 => x = 9.1 => 10 casts

10) 120-22*x+14.5*x=22 => x = 13 => 14 casts

11) 120-22*x+19*x=22 => x = 32.3 => 33 casts

8) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*5.5)/7 = 652% avg wpn dmg

9) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*8.5)/10 = 671% avg wpn dmg

10) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*12.5)/14 = 683% avg wpn dmg

11) ((0.5*(275)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*31.5)/33 = 702% avg wpn dmg

Max AP = 140 => x is the maximum continual cast time beyond the first.12) 140-29*x+12.5*x=29 => x = 6.7 => 7 casts (Round down to the nearest full cast)

13) 140-29*x+17*x=29 => x = 9.25 => 10 casts

12) ((0.5*(275+440*0/3)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*5.5)/7 = 652% avg wpn dmg

13) ((0.5*(275+440*0/3)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*8.5)/10 = 671% avg wpn dmg

Max AP = 160 => x is the maximum continual cast time beyond the first.14) 160-29*x+14.5*x=29 => x = 9 => 10 casts (Round down to the nearest full cast)

15) 160-29*x+19*x=29 => x = 13.1 => 14 casts

14) ((0.5*(275+440*0/3)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*8.5)/10 = 671% avg wpn dmg

15) ((0.5*(275+440*0/3)+0.5*(275+440*1/3)+0.5*(275+440*2/3)+715*12.5)/14 = 683% avg wpn dmg

As you can see, the % avg wpn dmg does not improve by any large amount by increasing AP regen or max AP. Note: Shortening the Time Step (0.5 seconds) slightly alters the averages.============================================================================The first is rather self explanatory and without incident, so I will discuss the ramifications of the 2nd below.

The dmg of the beam might stay constant during the entire cast time.

Thus, the 1st cast might be, 275+440*0/2 = 275% wpn dmg, 2nd cast would be 275+440*1/2 = 495% wpn dmg, and the 3rd cast would finally be the 275+440*2/2 = 715% wpn dmg.

However, this would mean RoF would have a haste soft cap built in.

Lets say you have sufficient haste to reduce your cast speed to 0.75 seconds.

0.75+0.75 = 1.5 sec (Perfectly sync'd with the build up time)

7 casts = 5.25 seconds

((0.75*(275+440*0/2)+0.75*(275+440*1/2)+(275+440*2/2)*3.75)/5.25 = 620% avg wpn dmg per cast

=> 7*621/5.25 = 828% wpn dmg per second

Now lets say you got an upgrade, and your new cast speed in 0.7 seconds

0.7 + 0.7 = 1.4 sec (0.1 seconds before the build up time, thus your 3rd cast wont be max)

7 cast = 4.9 seconds

((0.7*(275+440*0/3)+0.7*(275+440*1/3)+(275+440*2/3)*0.7+(275+440*3/3)*2.8)/4.9 = 589% wpn dmg per cas

=> 7*589/4.9 = 841% wpm dmg per second

Given this method of calculating dmg, it is less advantageous than maybe it should be at higher haste levels. Depending on the cast speeds, you could see very little DPS gain, yet consume more AP/sec. Which method blizz uses is up in the air, but I am leaning towards the method described here.

============================================================================The equation for calculating the # of casts possible,

c =(t+(m-a)/(a-r))/t

Simplified,

c =(m-r*t)/(a/t-r*t)

a = arcane power cost

m = maximum arcane power

r = regen rate of arcane power

t = cast time

c = # of casts

Note: These values do not determine any sort of break points, because it does not include things such as +AP on crit or +max AP on gear.

One is never hurt by being given additional choices, only by taking them away.A QUADRILLION MAGIC FIND is worthless if you can't killshit!Also, my post is

And it is equally important here as the wizard forums.

PS:

I reworked the #s in a different way. I think this method should be slightly more accurate.

If you notice any permutations missing or mistakes let me know.

One is never hurt by being given additional choices, only by taking them away.A QUADRILLION MAGIC FIND is worthless if you can't killshit!