Mathematical study of value of Pulverize

85 Tauren Druid
9245
tl;dr mode: Pulverize gives approximately 2.5x the mitigation value for a medium-hitting boss compared to demo roar simply being down 10% of the time. If you would prioritize keeping demo up, you should REALLY prioritize keeping pulverize up.

From the SD thread, I wanted to get an actual simulation of what pulverize does for the survival and mitigation against a boss. Is it worth even taking? Is it worth keeping a high uptime on and prioritizing it over things like Mangle?

To do this, I wrote a simple simulator that simulates white, yellow, and maul attacks and a boss attack. It doesn't record damage taken or anything like that, but that's actually pretty easy to surmise from the results. For simple comparison sake I set hit and expertise levels to be capped for this comparison; in the future I'll check it with those set to more realistic levels to see.

I used the following values to start with:
crit rate: 35.2% (26.2% without pulverize)
dodge rate: 39.957
and zero haste.

This meant a 2.4 second attack speed for the bear, a 1.5 second special speed and a 3.0 second maul speed. I did not stagger mauls; I'll try that later and see if it makes any meaningful difference.

The boss has a 2.0 swing timer. This means 500,000 attacks.

I also assumed 100% pulverize uptime.

The test was to run 100 iterations of a 1 million second fight and record every time SD procced and whether it was absorbed or overwritten as well as record any time a bear got hit without SD up. It also recorded uptime for SD, number of crits, and number of overall chances with SD. These 100 iterations were recorded and the average and standard deviation were calculated.

Pulverize's results:
161793 average SD hits (hit with SD active)
138291 average SD misses (hit with SD not active)
199914 average avoids
87491 average SD overwrites (SD procced when SD already was active)
34.33% average uptime
498572 average crits during the fight.

Without pulverize:
132836 average SD hits (-28957)
167278 average SD misses(+28986)
52721 average SD overwrites(-34770)
27.89% average uptime (-6.45%)
371172 average crits (-127399)

Okay, wall of math crit hits you. What does this mean? There's lots of ways to interpret it. For instance, you can say that you took 5.79% more unblocked hits without pulverize (including avoidance). Wow, that sounds pretty bad, doesn't it? That's basically saying pulverize is worth about 6% block on the combat table. Ask a paladin if they think that's worth it.

Here's another way: assuming the boss does 70k damage per swing after armor and reductions and you block 20k per SD shield, you went from taking on average 35.5k damage per swing to 36.7k damage per swing. That sounds less than impressive and it should; the reality is that SD against a 70k swing is pretty poor already, so losing some uptime is not thrilling. By comparison, losing demo roar for 10% of the fight increases damage taken to 35.9k, so perhaps that's a good way to put it: pulverize is about 2.5x as potent as Demo Roar for a medium-hitting boss.

What was interesting to me was to see how many overwrites this actually caused. This was artificially low crit rate to start with (I'll rerun it and see what it does), but even with that happening it was still a very high amount of SD procs that overwrote each other - almost a third in the pulverize case. It decreased significantly without pulverize.

I'll be running this with a bit more realistic numbers such as better crit rates to start with and slightly staggered mauls. If you have more reasonable numbers or requests for runs, post them here; I'll run more tests and see how it goes.



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85 Tauren Druid
9245
Oops. Found a bug midstride that invalidates these. will republish a bit later. (the above numbers are fine though)
Edited by Fellhoof on 5/4/2011 3:58 PM PDT
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90 Night Elf Druid
CFT
10670
Even 5% Exp is a little optimistic I think.
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85 Tauren Druid
9245
I'm happy to use whatever numbers folks feel are reasonable. As expected, as your hit and exp rate goes up your SD #s go up. Not astoundingly but reasonably decent. What would you prefer?

I'm also curious about doing RSV type analysis. It's pretty clear that for any boss that hits remotely hard (70k isn't that hard) SD lags significantly behind avoidance as a value; what I'm curious about is how much crit really helps compared to hit or expertise.
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90 Night Elf Druid
CFT
10670
I think about 1% is as optimistic as you're going to get for 359 level gear.

I'd dearly love to get my hands on more Exp/Mastery gear, but it just doesn't exist.
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85 Night Elf Druid
6660
From a couple of better geared Bears here:
Katjia (iLvl 360, 1 T11, Tia + FD): 2.5% hit, 1% exp, 25.35% crit, 24.93% dodge
Reesi (iLvl 370, 4 T11, loves exp): 2.83% hit, 6.25% exp, 28.64% crit, 23.90% dodge
Tangedyn (iLvl 363, 2 T11, FD): 3.12% hit, 2.5% exp, 26.14% crit, 26.17% dodge

Note that this are armory values, so crit & dodge will be a bit higher due to talents (+5% crit, +10% dodge) and more Agi from MotW, HoW, Tia + FD. And both will be a bit lower due to hitting a boss 3 levels above you.

And then there's the +5% crit to Lacerate from the glyph.

Edited for correctness, I misremembered the crit rate for the lacerate glyph, thanks Fellhoof for pointing that out.
Edited by Ptarr on 5/4/2011 4:13 PM PDT
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85 Tauren Druid
9245
And then there's the +10% crit to Lacerate from the glyph.
It's actually only 5%, but I've added that into the simulator.

Getting the crit rate from the paper doll is...challenging. Rawr doesn't actually list the crit rate directly either. I suspect I'll end up just using somewhat rough numbers based on WoL reports.
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85 Tauren Druid
9245
Here's Arielle's numbers:

avoid: 45.3
hit: 4.1
exp: .8
crit: 38.4

With Pulverize:
146k SDs hit
126k unblocked
84k overwritten
227k avoided
463k crits
37.8% uptime

without:
124k SDs hit (-23k, 4.6% less blocked)
150k unblocked (-23k)
54k overwritten (-30.3k diff)
227k avoided (duh)
356k crits
31.6% uptime (-6.17%)
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85 Night Elf Druid
12535

good stuff felhoof.
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90 Night Elf Druid
CFT
10670
05/04/2011 03:51 PMPosted by Ptarr
Reesi (iLvl 370, 4 T11, loves exp): 2.83% hit, 6.25% exp, 28.64% crit, 23.90% dodge

Bear Deeps Set only. I'd ignore this one.
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85 Tauren Druid
9245
Reesi's:

avoid: 44.09
hit: 2.8
exp: 6.49
crit: 40.1

With pulverize:
160k SD hits
119k unblocked
102k overwritten
220k avoided
524k crits
40.17% uptime !

Without pulverize
137k SD hits (-23k)
142k unblocked(-23k)
67.0k overwritten (34.8k!)
220k avoids
408k crits (116k difference...wow)
34.08% uptime

It's interesting to see how the expertise really affects Reesi vs Arielle. Arielle has slightly more avoidance and hit and slightly less crit - but the expertise gives a lot of uptime and makes the non-pulverize case almost as good as Arielle's pulverize case.
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85 Tauren Druid
10350
very nice :)

would it be worth somehow looking at the frequency of 'three unabsorbed hits in a row' for situations like worship-stacked Cho' who can actually start bursting a tank down?
Edited by Katjia on 5/4/2011 4:50 PM PDT
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85 Tauren Druid
9245
I can probably do something like that, Katja. Let me think about that and see what I come up with.
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90 Night Elf Druid
CFT
10670
Well it's not really a fair comparison. Ri is in full 372 gear, and I'm not.

A better comparison would be 359 tier vs 359 non tier. Etc.
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85 Tauren Druid
10350
Well it's not really a fair comparison. Ri is in full 372 gear, and I'm not.

A better comparison would be 359 tier vs 359 non tier. Etc.


I don't think that's the comparison we're looking for here - it's more about before and after Pulverise being the real comparison, with different gearing levels to give an impression of how Pulverise scales.

although, Reesi's bearDPS set is probably just highlighting the fact that Expertise improves Pulverise considerably.
or at least, increases the vaue in keeping it up :)

Favouring expertise over avoidance will give you a bigger difference in damage taken with or without Pulverise, but in a context of overall more damage taken on average.
Edited by Katjia on 5/4/2011 5:24 PM PDT
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85 Tauren Druid
9245
I'm not trying to compare anything specifically, Arielle; I'm just trying to see patterns from numbers. You're right that it's not fair nor is it realistic. It's obvious that someone with 6% more expertise when you're both under the dodge cap is going to have a lot more SD uptime. I just thought it was interesting.

Here's another study, done with just to see the value of expertise vs crit on SD uptime.
Starting values:
hit: 3
crit: 38
exp: 5
avoid: 45

152k blocked
123k unblocked
91k overwritten
225k avoided
486k crits
38.85% uptime

+1% crit:
154.4k blocked
120.6k unblocked
95.2k overwritten
225k avoided
499k crits
39.49% uptime

+1% expertise
153.5k blocked
121.5k unblocked
93.7k overwritten
225k avoided
494k crits
39.3% uptime

So 1% crit is more valuable than 1% expertise in SD uptime. Is that fair though? It takes 179 crit rating (basically) to get 1% crit; it takes 120 expertise to get 1% expertise. For agility's sake, it takes 325 agi to get 1% crit. In terms of itemization points, this makes crit about 10% better than expertise (below the dodge cap) as far as getting SD goes.


So it's still better, but it's definitely much closer to comparable at this point - at least below the dodge cap.
Edited by Fellhoof on 5/4/2011 5:28 PM PDT
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85 Tauren Druid
9245
As far as dodge goes, here's adding 1% more avoidance:
150k blocks (-1.5k, yes, it goes down and that makes sense)
119.6k unblocked(+3.4k)
92.8k overwritten
229.9k avoided (+4.9k)
486k crits (didn't really change)
39.48% uptime (went up by .628%)

Again, dodge is expensive and subject to DR. To get 1% dodge without any DR it takes 176 dodge rating - but with DR at the avoidance level we're talking about it's closer to 300. This makes expertise and crit significantly better at increasing SD uptime and reducing the number of unblocked hits compared to dodge on a per point basis. That being said, because SD is so weak you will mitigate significantly more damage with a dodge setup than you would SD. The only advantage to having more SD is that your damage intake will be slightly smoother.
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85 Night Elf Druid
2395
I don't get this.
Here's another way: assuming the boss does 70k damage per swing after armor and reductions and you block 20k per SD shield, you went from taking on average 35.5k damage per swing to 36.7k damage per swing.


How if you take 70k per swing (after armor and reductions ) and you block 20k per SD shield can you only be taking on average 35.5k or 36.7k? (depending upon uptime).

Surely you are taking 70k -20k*Percent uptime ie 60+k

By comparison, losing demo roar for 10% of the fight increases damage taken to 35.9k, so perhaps that's a good way to put it: pulverize is about 2.5x as potent as Demo Roar for a medium-hitting boss.


um ok again I am confused, does not demoralizing roar reduce damage by 10% so damage reduction on a 70k hit by 10% = 7k, losing it for 10% of a fight is therefore changes the dmg taken by around 0.7k.

Perhaps I am confuised by this does it work that all damage reduction (armour talents, demo roar etc) apply then SD absorbs what is left over for a an amount X.
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85 Tauren Druid
9245

How if you take 70k per swing (after armor and reductions ) and you block 20k per SD shield can you only be taking on average 35.5k or 36.7k? (depending upon uptime).

Surely you are taking 70k -20k*Percent uptime ie 60+k
My apologies; I wasn't that clear. This included the avoidance as well. So about 40% of the time you take nothing. Then another 35% of the time you block with SD, and then 25% of the time you don't block anything at all. The dodge part massively overwhelms the advantage of SD here. That's why it's so low.

um ok again I am confused, does not demoralizing roar reduce damage by 10% so damage reduction on a 70k hit by 10% = 7k, losing it for 10% of a fight is therefore changes the dmg taken by around 0.7k.
Right - but again, you're still avoiding things and blocking them. You can't just do that in a vacuum. The average damage done from a boss doing 70k a swing after armor with the above stats was 35.5k. If you drop pulverize, it's 36.7k If you drop demo roar 10% of the time (so that the boss does 70.7k) the average damage is 35.9k.
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