Friday, March 01, 2013

Diablo III: More Numbers!

Both Snuggles and Sky have commented recently with mechanic based information for Diablo III that is pretty informative. My new build has been working out spectacularly and I want to know more about how things work so I know where the best places to invest money would be in order to get more powerful. Should I be saving up for a socketed weapon? A set source? Should I just be crafting more gloves/bracers/shoulders? I don't really know how things work so it's really hard to accurately answer those questions. I've read some guides and such so I know what other people think I should do, but I hate listening to just other people. I want to understand things myself so I can make decisions!

First off, proc rates on things. Snuggles found a post from a guy who did a lot of testing on the 'life on hit' mechanic. It turns out the amount of life you gain on hit isn't what is listed on your gear. Instead every skill in the game has a 'proc coefficient' number (listed in this spreadsheet) which determines what ratio of your 'life on hit' you actually get. So while my gear says hits add 893 life in actually wicked wind is only adding 112 life per hit because it has a .125 pc. It works similarly with the critical mass passive which makes crits knock a second off of all my cooldowns. Apparently some people on the forums have been doing some testing and think the chance is actually twice the pc here. I don't know why, and people are still testing. But for now I'm willing to assume that a quarter of my wicked wind crits will reduce my cooldowns by 1 second. The other spells I'm using are storm armor/shocking aspect which has a 0 pc, diamond skin/diamond shards which has a .167 pc, and explosive blast/chain reaction which has a .111 pc.

Ok, but what counts as a hit? Chain reaction is easy. It pulses for damage three times, and therefore is 3 hits for one spell cast. Each hit has a .111 pc, so every time I hit the chain reaction button I heal for 300 life per enemy near me and do 291% damage. (On a time delay, but you can stack up a bunch of them if the cooldown refreshes often enough.) Diamond shards is also easy. It has a similar delay (when the shield runs out or when you cast it again) and does damage to everyone around me once for 150 life and 210% damage. This is worse than chain reaction, except it also puts up an 11k shield and has no resource cost. I also think it's off the GCD? And I can cast it while frozen which is nice when I screw up. Wicked wind, on the other hand, is super complicated. You cast it and it spins around for 6 seconds. How many times it ticks over those 6 seconds depends on your attack speed according to the formula/chart in this thread. I currently have 2.187 attack speed, which means I get 28 ticks per cast. This means each cast of wicked wind heals me for 3126 per enemy hit. It also does 252% damage which means it does less damage than explosive blast. (And has a smaller area of effect.)

All those extra ticks also mean big things for my 'chance on crit' effects. I have a 31% crit chance and have 28 arcane power on crit on my gear. This also uses the same pc ratio as life on hit. This means chain reaction, in the long run, will return 3*.111*.31*28 = 2.89 arcane power per enemy it hits. It costs 20 arcane power, so I can't spam this. Diamond shards gives .167*.31*28 = 1.45 arcane power, on average, per enemy it hits. Diamond shards is completely free. Wicked wind gives 28*.125*.31*28 = 30 arcane power, on average, per enemy it hits. It costs 35 arcane power. So against a single target I'll run myself out of arcane power by spamming wicked wind, but if you add in a second enemy I'll have infinite arcane power in a very short amount of time. In practice I find I have infinite arcane power all of the time except when something goes wrong. If the enemies get out of stunlock for an instant and blink away, or if I'm in a party and they knock the enemies out of my winds it can set me back. Or if I just hit the wrong buttons because I'm bad or my hand cramps up or something. I'm wondering if I can afford to drop the 8 arcane power on crit from my source and buy a more powerful one. I may test it out at some point. I know if I get more attack speed and crit I shouldn't need all 3 pieces, but I'm still pretty low on both values. The guides have recommended getting up to 36 ticks per wind as a baseline and I only have 28.

As far as cooldowns go, dividing each of the above numbers by 14 should give me the number of cooldown seconds shaved off per cast. Which means chain reaction should take off .2 seconds per cast per enemy, diamond shards should take off .1 seconds per cast per enemy, and wicked wind should cut 2.1 seconds per cast per enemy. My spells have cooldowns of 10.2 seconds (frost nova), 12.75 seconds (diamond shards), and 5.1 seconds (chain reaction). With full diminishing returns a monster will break out of frost nova in 1.05 seconds, which means I need to shave off 9.2 seconds from the cooldown every second in order to maintain stun lock. With only 2.187 attack speed this means every second spell needs to be worth 9 seconds of cooldown. Well, except I think diamond shards is off the GCD so I can just spam it when the cooldown refreshes. And by looking at the guide closer it claims explosive blast is also off the GCD, so I can spam it too. (I just mash all the buttons constantly!) This isn't enough reduction to stun lock one monster, which is definitely something I've noticed. I can keep a single elite mostly locked down but if he has teleport he'll often get away which is a big pain. Three enemies is absolute gold since a single wicked wind is then worth 6.3 seconds of reduction. Note the initial frost nova is a full 3 second stun so I have a ton of time to get winds up and ticking! Also reality is discrete, not continuous, so I don't get .1 second of reduction per diamond shard. Mostly I get nothing but sometimes I get a full second off.

Ok, fine, so I can see that getting some more crit chance will up my cooldown reduction more, and will give me more arcane power. Upping my attack speed will let me both cast more spells and get way more life, arcane power, and cooldown reduction. Dropping some arcane power on crit is probably a fine thing to do, especially if I get more attack speed or crit chance. But given that I can mostly stun lock stuff as is, and I can survive most single hits, how can I do more damage?

Sky pointed out that the item mod 'adds X% to {elemental} damage' works in ways I didn't expect. I have a Storm Crow hat with 'adds 8% to lightning damage' and my thinking was that it would increase any lightning damage I did by 8%. Storm armor does lightning damage so this seems like a small boost. Not so! It turns out it adds 8% extra damage (from your physical damage) to every attack you do! It won't even be lightning damage if the spell has a different damage type. So my wicked wind (which does arcane damage) will be getting a damage buff from the hat. As best I can tell I have 443 physical damage on my gear and 408 magical damage on my gear. This means about 52% of my damage is eligible for this bonus, which makes this stat on my hat a 4.16% damage boost. That's pretty hot! The issue here is most of the damage on my weapon is +fire damage, and that's by design of the weapon. Theoretically I could get a different weapon to make this mod better, but that would drastically reduce my attack speed and that just seems wrong. Stunlock first, kill things later!

One of the things I like to do to work out how good stats are is build a spreadsheet and then vary the numbers a little to see what the incremental worth of a stat is going to be. You have to build assumptions as far as what you expect your rotation to be, and I think I'm going to assume 2 wicked winds for every frost nova with the other two damage spells being spammed on average based on expected crits. I'm also going to assume 100ms between casts even when stuff is cooled down. I'm really not good enough to keep that up but it should at least give a decent relative ranking of the stats. I am considering using my gaming keyboard to macro all of the spammy spells onto one button to save my poor left hand which would probably help bring things more in line with this mythical expected value.

Man, I must say, some of these numbers in my sheet get pretty absurd. A WW+WW+FN rotation with 1 target does 175k DPS, but the mob gets to run around some. A WW+FN rotation with 3 targets does 237k DPS per target and locks them all down forever. If somehow you got 20 mobs to stand around me I'd be looking at doing 18M DPS per target! (Ok, that's right insane, since the sheet now assumes I can cast chain reaction 191 times in a little over a second. This probably means the way I'm dealing with cooldown reduction from crits is wonky for big numbers.) Not like 20 mobs would live very long regardless.

Anyway, here's the DPS gain for the WW+WW+FN case on a single dude:

100 Int = 10626
6% crit = 20007
50% crit damage = 27236
3 base attacks per second (maxxed chantodo) = 2322
9% attack speed = 13462
4% damage to elites = 7806
8% damage as elemental = 8113
33 min damage = 4080

I tried to use what seemed like the max possible roll for a stat on a secondary item like a ring. It turns out the stuff I've been trying to keep an eye for is the best stuff. Int does have the advantage of also being damage reduction. The %damage as elemental stuff is interesting for sure, but it doesn't look like something I need to be targeting. The problem is definitely with my weapon, as the same 8% damage as elemental would be worth around 23k if my weapon did purely physical damage. Chantodo maxxes out at a base of 1.65 attacks per second and has to come with fire damage. The fastest other weapon is 1.5 from a rare dagger. Daggers can't roll arcane power on crit, so there are two big problems to deal with if I switched weapons: needing more attack speed to maintain the same number of wicked wind ticks, and needing to keep arcane power on crit stats on my hat and offhand. It's not inconceivable (Triumvirate is a ludicrous offhand for that plan since it can add 18% to elemental damage) but not really in my budget right now. I can't afford great pieces for one gear set; there's no reason to go branching out into a second one.

It's also important to point out that the DPS numbers here are only for once a fight gets rolling and I have enough wicked winds spinning to grant enough arcane power to keep casting all this stuff. It actually makes me pretty terrible at fighting regular easy guys. But wow, when I'm able to teleport onto a group of champions and go to town on them does it ever feel good.

As far as where I should go with my gear, I think short term goals are going to be:
  • Get enough attack speed to reach the next wicked wind tick breakpoint. That's an extra 8% on top of what I already have, but my offhand currently has none on it.
  • Try subbing out one of my sources of arcane power on crit. Like, say, my offhand. It only has 8 while my other two have 10 each. 
  • Putting those two together, the Chantodo's Force offhand has a set bonus worth 130 int and 7% damage reduction from elites. It comes with damage, int, attack speed, max arcane power, crit chance, an irrelevant wizard spell modifier, and one random mod. I've been trying to buy one with the arcane power on crit random mod but they're all really expensive. It also rolls with a minimum of 8% attack speed, which seems just perfect for the first point. So I think looking for a cheap one with a garbage random mod instead of a perfect random mod could be fantastic.
  • I don't have any bonus crit damage at all, and it looks like my best damage stat right now. So, investing in something that has it might make a lot of sense. Amulet/ring/gloves are the options for rare slots. Maybe I should try to make some of the crafted stamina gloves and see what comes out. All of my amulet/ring/gloves currently have attack speed and crit chance on them and two already have life on hit so I worry that finding one that keeps those stats while adding in crit damage will be very pricy. So maybe trying to get lucky on gloves really is right.
  • I could still use some more defensive stats. I should look to see if I can trade int in some slots for defensive stats. 100 int is worth 10 resist all, which is good, but the max roll in a slot for resist all is 80. 80 is a lot more than 10 and it feels like int isn't as good an offensive stat as I'd been thinking it was so making some trades there may be both right and cost effective. If I craft gloves it'll definitely be vitality ones!

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