Diablo® III

ias isnt such a bad thing

Wow this was a fun read. We should all get along well as we share a common goal, to understand how skills work, right?

I´m not infallible (noone is) and if someone claims to get different results than the mechanics I´ve described in a post some time ago I always redo my tests to make sure there isn´t some kind of catch or that the mechanics weren´t adjusted over time.

So, I just retested the skill (Cloud of Bats) and it has been modified since I tested it in 1.0.7 and on the late 1.0.8 PTR.

1. What stayed is:
-> the the tick scaling formula = floor (30/aps). With more aps the ticks are displayed at a faster rate not at a constant 30 frames per second;
-> the initial (first) damage tick is also unchanged and occurs 10 frames after activating the skill, no matter what aps you have;
-> the linear mana cost (half of channeling tooltip damage per tick = -33);

Note that the the flat multiplier of the Firebats skill buff wasn´t an integer but something like 2.1387 which makes it a bit troublesome to calculate exact values. It´s not exactly 500% (250%) but more like 500.4% (250.2%).

2. What has indeed changed is that the game no longer achieves max damage faster with more aps.

Which means, the last column in the following breakpoints chart no longer applies but the other columns are still accurate and applicable
aps - frames per tick - frequency - channeling cost per sec - time until max damage
0.90000-0.90909 aps - 33 frames - 1.82 ticks - 60 mana - 5.12 sec (307 frames)
0.90910-0.93750 aps - 32 frames - 1.88 ticks - 62 mana - 4.97 sec (298 frames)
0.93751-0.96774 aps - 31 frames - 1.94 ticks - 64 mana - 4.82 sec (289 frames)
0.96775-1.00000 aps - 30 frames - 2.00 ticks - 66 mana - 4.67 sec (280 frames)
1.00001-1.03448 aps - 29 frames - 2.07 ticks - 69 mana - 4.52 sec (271 frames)
1.03449-1.07142 aps - 28 frames - 2.14 ticks - 71 mana - 4.37 sec (262 frames)
1.07143-1.11111 aps - 27 frames - 2.22 ticks - 74 mana - 4.22 sec (253 frames)
1.11112-1.15384 aps - 26 frames - 2.31 ticks - 77 mana - 4.07 sec (244 frames)
1.15385-1.20000 aps - 25 frames - 2.40 ticks - 80 mana - 3.92 sec (235 frames)
1.20001-1.25000 aps - 24 frames - 2.50 ticks - 83 mana - 3.77 sec (226 frames)
1.25001-1.30434 aps - 23 frames - 2.61 ticks - 87 mana - 3.62 sec (217 frames)
1.30435-1.36363 aps - 22 frames - 2.73 ticks - 90 mana - 3.47 sec (208 frames)
1.36364-1.42857 aps - 21 frames - 2.86 ticks - 95 mana - 3.42 sec (199 frames)
1.42858-1.50000 aps - 20 frames - 3.00 ticks - 99 mana - 3.17 sec (190 frames)
1.50001-1.57894 aps - 19 frames - 3.16 ticks - 105 mana - 3.02 sec (181 frames)
1.57895-1.66666 aps - 18 frames - 3.33 ticks - 110 mana - 2.87 sec (172 frames)
1.66667-1.76470 aps - 17 frames - 3.53 ticks - 117 mana - 2.72 sec (163 frames)
1.76471-1.87500 aps - 16 frames - 3.75 ticks - 124 mana - 2.57 sec (154 frames)
1.87501-2.00000 aps - 15 frames - 4.00 ticks - 132 mana - 2.42 sec (145 frames)
2.00001-2.14285 aps - 14 frames - 4.29 ticks - 142 mana - 2.27 sec (136 frames)
2.14286-2.30769 aps - 13 frames - 4.62 ticks - 153 mana - 2.12 sec (127 frames)
2.30770-2.50000 aps - 12 frames - 5.00 ticks - 165 mana - 1.97 sec (118 frames)
2.50001-2.72727 aps - 11 frames - 5.45 ticks - 180 mana - 1.82 sec (109 frames)
2.72728-3.00000 aps - 10 frames - 6.00 ticks - 198 mana - 1.67 sec (100 frames)
3.00001-3.33333 aps - 9 frames - 6.67 ticks - 220 mana - 1.52 sec (91 frames)
3.33334-3.75000 aps - 8 frames - 7.50 ticks - 248 mana - 1.37 sec (82 frames)
3.75001-4.28571 aps - 7 frames - 8.57 ticks - 283 mana - 1.22 sec (73 frames)

Here´s a test I just did:

1.20 weapon aps +8% IAS from gear = 1.296 aps
33-48 base weapon damage white weapon
+33 minimum damage ring
= 66-66 base weapon damage
2058 intelligence = 1 + (2058/100) = 21.58 multiplier
100% weapon damage = 66 * 21.58 = 1424.28

now the individual ticks:
frame 0 skill activation
+10 frames = 3564 damage tick (#1) = 250.2% weapon damage
+23 frames = 3839 damage tick (#2)
+23 frames = 4114 damage tick (#3)
+23 frames = 4389 damage tick (#4)
4664 damage tick (#5)
4939 damage tick (#6)
5214 damage tick (#7)
5489 damage tick (#8)
5764 damage tick (#9)
6039 damage tick (#10)
6314 damage tick (#11)
6589 damage tick (#12)
6865 damage tick (#13) = 482% weapon damage
6865 damage tick (#14)
6865 damage tick (#15)

Before the change, I got a multiplicative 20% damage boost on the second tick, 30% on the third tick, 40% on the fourth tick etc.

Now, to say it as simple as I can. At 1.00 aps, Cloud of Bats displays damage each 30 frames after the initial tick which always deals 250.2% weapon damage. Each subsequent tick gains a multiplicative bonus equal to one tenth (1/10 or 0.1) of 100%/aps.

In case of 1.00 aps CoB you would gain 10% more damage each 30 frames and if you had 2.00 aps you´d gain 5% more damage each 15 frames. Faster attack speed no longer makes you achieve max damage faster like it did in 1.0.7 and on the 1.0.8 PTR.

Also as you can see, the maximum damage wasn´t 2x the base damage like it should have been, but instead 1.926 times the normal damage, which is probably due to rounding. In this case, the game probably calced 12 ticks (after the initial) to get to full damage floor(10 * 1.296 aps) = 12, but when it calced the bonus for subsequent tick until #13 (#2->#13) only gave you a (10%/aps) = 7.716% damage bonus.

I still need to do a bit of testing and thinking to give you an exact formula but it seems the game uses something like floor(10 * aps) to calc how many ticks you´ll need to get to max damage and the aforementioned 10%/aps for the damage bonus.

I´ll repeat it again. Despite having a higher tick frequency with more aps, you no longer achieve max CoB faster. No matter what aps you have, it should take 280 frames (almost 5 seconds) +/- a few frames depending on the rounding in each case to achieve the highest damage potential with the skill. The difference between aps still lies in mana cost, which is linear - it means that you´ll burn more mana per second with more aps.

Hope that both sides are now happy as both were right, in a way. Peace.
Edited by Nubtro#2147 on 5/22/2013 4:42 PM PDT
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Nubtro
your mechanics work is well done (as well as your barb work) and certainly well thought out. Clearly,blizz fixed thh skill from PTR to live 1.08 to actually do what the description of the skill says (DoT). I can say from a qualitative personal stand point that your latest modifications are confirmed meaning it does indeed take 5 seconds to reach full damage potential. I tested a fast and slow weapons on longer fights like ghom to figure out which kind of weapon I wanted, but it always took about 5 sec to reach full damage potential.

I guess the take home message (as if you did not know) for the efficiency junkies wanting to optimize DPS and mana consumption, is it may be most efficient to use a heavy hitting weapon for fights lasting 5-8 sec or less to best optimize damage output as a function of mana.

Further extrapolating, people can easily figure out where the crossover point lies between when IAS starts to out perform damage per hit (DPS vs DoT) to further optimize, assuming you remove running out of mana variable.
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I´ll repeat it again. Despite having a higher tick frequency with more aps, you no longer achieve max CoB faster. No matter what aps you have, it should take 280 frames (almost 5 seconds) +/- a few frames depending on the rounding in each case to achieve the highest damage potential with the skill. The difference between aps still lies in mana cost, which is linear - it means that you´ll burn more mana per second with more aps.

Hope that both sides are now happy as both were right, in a way. Peace.


Thanks Nubtro...

I guess this pretty much settles this argument.

Seems the WD vets know what the heck they are talking about lol
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haha yep. they definitely do ;)
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gj and thx to Nubtro
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delete! wrong thread
Edited by EvoIution#1710 on 1/20/2014 1:36 PM PST
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