[Theory] Parry and Warrior vs. Paladin damage intake

[Lore]

So I had this thought yesterday and I'm not exactly sure how the math would work out, but here's the theory and some preliminary numbers.

Warriors have 10% melee damage reduction from defensive stance. We have 6% from improved RF. This means that over the course of a fight, if both classes are faced with the exact same amount of incoming damage, the Paladin will take 4% more total damage. This isn't news.

However, Warriors do a hell of a lot more melee attacks than we do over the course of that fight. Obviously they still have every auto attack, but nearly every global cooldown they will hit another attack (revenge, shield slam, or devastate) which can be parried as well. Occasionally they have to use a GCD to refresh Commanding Shout, Intimidating Shout, or Thunderclap, but for the most part they will execute a parryable attack every 1.5 seconds. In addition, nearly every Warrior tanking weapon is 1.6 speed, while endgame Paladin tanking weapons are 1.8.

The base Parry chance for a boss is generally considered to be around 14% (this number is taken primarily from random WWS reports). Expertise lowers this chance - Warriors and Paladins both get expertise skill from talents (5 for us, 6 for them), and various pieces of gear have expertise as well. Most endgame (Illidan-killing) Warriors seem to have somewhere around 11-16 expertise skill. 16 expertise is a reduction of 4% parry, putting the parry chance at 10%. Most Paladins ignore Expertise, leaving us at a 1.25% reduction.

So here's the question: How much extra damage do Warriors take from Parries, particularly at the endgame level, and how does that compare to 4% across-the-board damage reduction?

Some fair (I think) numbers to start with:
Paladin:
Melee attack speed (Hammer of Judgement or Tempest of Chaos): 1.8
Expertise: 5 (-1.25% parry)

Warrior:
Melee attack speed (The Brutalizer, or Human with The Unbreakable Will): 1.6
Expertise: 11 (-2.75% parry)
Gauntlets of Enforcement (most Warriors wear T6 gloves): +5 Expertise (-1.25%)
Orc Racial (with The Brutalizer which also has Expertise): +5 Expertise (-1.25%)
Special Attack speed: 1.5

It's worth mentioning that Warriors will often ask for Windfury Totem as well, which results in more melee attacks, which results in more parries. Paladins tend to stick to wizard oils.

I have no idea how to figure out how parries relate to damage intake; the math is a little over my head. Could one of our resident calculus majors (I'm looking at you, Jere) take a stab at it?

[Rasmfrackn]

My job actually has me doing stuff for once, so I'll just back-of-the-envelope this for now instead of modeling it properly.

So we're using roughly these numbers:
Parry vs paladin: 12%
Parry vs warrior: 10%
Parriable attack speed for paladin: 1.8
Parriable attack speed for warrior: 0.85 (I assume a parriable special every 2 seconds or so, and no windfury)

Parrying attack gives what, 40% haste?

So every 0.85 seconds a warrior has a 10% chance of boosting their damage intake by 40%, and every 1.8 seconds a paladin has a 12% chance of boosting their damage intake by 40%.

the expected time between parries for a warrior would be 8.5 seconds
the expected time between parries for a paladin would be 15 seconds

in 255 seconds, the warrior is parried 30 times
in 255 seconds, the paladin is parried 17 times
in 255 seconds, a 2.0 speed boss attacks 127.5 times
(sorry, i did a least common multiple here b/c i'm not thinking especially quickly. heh)

30 parries * 0.4 extra swings = 12 extra swings
17 parries * 0.4 extra swings = 6.8 extra swings

the warrior takes 127.5+12 = 139.5 swings
the paladin takes 127.5+6.8 = 134.3 swings

the warrior takes 3.87% more swings

* also, D stance vs imp RF is 90% vs 94%, so paladins actually take 4.44% "more" damage per hit, not just 4%.

[Mortehl]

Wow. Add in Ardent Defender and you get some surprises there don't you.

[tinven]

Hey there, long time reader, first time poster (what a post to pick eh? but I find theory just so fascinating)

Anyways, here goes. from "Question on Parry" in this form here:

* If the next attack would normally occur within 20% of your weapon speed after the parry, there is no effect.
* If the next attack would normally occur between 20% and 60% of your weapon speed later, it happens 20% of your weapon speed later instead.
* If the next attack would normally occur more than 60% of your weapon speed later, the time until your next attack is reduced by 40% of your weapon speed.

Edit: For reference

.2*1.8 = .36
.2*1.6 = .32

.6*1.8 = 1.08
.6*1.6 = .96

This may just complicate things, but I believe the math done above assumes the third situation - I.e. that both tank and boss started swinging at each other at the same time. As I don't do any high end tanking, I am not sure if this is a valid assumption.

Granted, considering this will just affect the haste number

Edit 2: Realized a mistake, changed the numbers slightly (.85 is effective attack speed, 1.6 is the war's weapon speed which is relevant) and may have made my point irrelevant, but just putting it out there and it might still be useful to have the parry info here.

[Splug]

Various WWS parses have yielded wildly varying estimates for boss parry chance. I've seen anything from 7% to 15%, but most tend to gravitate around 12% (without expertise). I'm curious: at what level parry % do those numbers hit equalibrium? Though, as has been mentioned several times elsewhere, this is an especially important topic due to the burst damage issue created by parries. Even if the numbers do come up at equalibrium, the advantage lies on the side taking fewer parry backlashes.

Nitpicky sidenotes: The defiance tallent grants 6 expertise, not 5. An orc with gauntlets of enforcement and a brutalizer thus has 21 expertise.

-Splug

[Jarkeld]

did some quick numbers as well, just went through percentages instead of a timed simulation, I'll think about it more after supper time
assume 12% base parry chance off boss
2.0 boss attack speed, slowed to 2.4 by tclap
20% of time, parry doesn't speed attack, 40% speeds it by 20%, 40% of the time it speeds it by 40%
attacks will land at any time in the boss's swing timer
so, on average, speeds boss attack speed by .2*0 .4*20+.4*40=24%

take a warrior attacking with 1.6 speed and specials every 1.5 seconds, tclap and demo shout also have to be cast and possible rage starvation, so just make it 2 attacks every 1.6 seconds
therfore, warrior gets 3 attacks every boss attack of 2.4 seconds(ignoring extra attacks gained from the warrior parrying boss)

paladin with 1.8 speed gets an average of 4/3 attacks per boss attack

I'll compare myself with 0 expertise to a human warrior with 15(-3.75% to parry)expertise, best possible case

say the boss deals 80% of its damage from straight up melee, rest comes from special attacks or spells


so warrior has a 8.25% parry chance, paladin has 12%

warrior
8.25%*3=24.75% chance of causing a parry every boss swing

24.75%*24%*80%=4.8% boss damage increase

paladin
12%*4/3=16% chance of causing a parry every boss swing

16%*24%*80%=3.1% boss damage increase

***** so the warrior just takes 1.6% more damage

with a warrior of 10 skill(9.5%), paladin of 5 skill(10.75%):

warrior->5.5% boss increase
paladin->2.8% boss increase
**** in this case, the warrior takes 2.7% more damage

[Lore]

Nitpicky sidenotes: The defiance tallent grants 6 expertise, not 5. An orc with gauntlets of enforcement and a brutalizer thus has 21 expertise.

Edited my OP, thanks.

Parriable attack speed for warrior: 0.85 (I assume a parriable special every 2 seconds or so, and no windfury)

This may be a little generous. For the most part, Warriors are spamming the GCD, hitting something new every time it comes up, and in their normal threat rotation every one of those actions is parryable. Their GCD is same as ours, 1.5 seconds. Latency will play an issue but it probably won't be worth a whole 0.5 seconds.

The only non-parryable GCD's they should be using are Commanding Shout (2 minute duration), Thunderclap (30 sec duration), and Demoralizing Shout (30 sec duration). So around every 20 seconds (if they refresh with 10 seconds to spare) they'll use 2 GCD's on non-parryable attacks, and around every 110 seconds they'll use another. So if we use a 2 minute sample size, and call the GCD 1.6 seconds to account for latency, this is what I get:

75 total GCD's
75 swings
1 GCD used on Commanding Shout
12 GCD used on TC + Demo
= 62 parryable GCD's + 75 swings
= parryable GCD every ~1.9 seconds
= chance for parry every ~0.88 seconds

Hrm, not sure how I got to a higher number than you even with a lower GCD time.

[Lore]

Paladin should always have at least 5 expertise, unless you didn't take Combat Expertise (meaning you hate stamina).

I'm mostly interested in straight-up melee damage, because we already know the Warrior is going to take less spell damage (assuming he's specced into Imp. Defensive Stance, plus spell reflect if applicable).

[Palladia]

Was actually thinking about the same thing lately, thanks for the math.

[Ehtirno]

There is also a need to consider - the quote about Parry is about player parry effects. Mobs may or may not differ in effect from this - reports of parry causing instant attacks come to mind.

Does it reset swing timer? Can parried white attack + parried special cause 2 extra, near instant swings? Does anyone have some decent research on this?

For example - if the above stands - reports of instagibs on warriors could perhaps be caused by a double parry? While Paladins only have autoattack that is parryable, sneaking around the issue?

[Aergis]

Theres also one major difference here that no one seems to have caught yet.

Shield block is 2 charges / 5 seconds.
Holy shield is 8 charges / 10 seconds.

If a warrior gets parried, there is a chance it will be a crush which will likely mean death. When the pally gets parried, he likely still has several charges available on holy shield.

The odds of it happening are not too high, because the warrior would have to block twice ( no dodge parry or miss ) and get parried within the 5 second window, but it happens. This isn't as much of a concern for the pally, since the third attack is more possible to survive than 2 attacks plus a crushing blow.

[Lore]

Good call. Yeah parrygib tends to include a crushing blow with a Warrior tank.

[Sharlos]

Good call. Yeah parrygib tends to include a crushing blow with a Warrior tank.

any possibility of comparing a paladin with reckoning vs a warrior? would be interesting to see how reckoning effects damage taken.

[Jarkeld]

Good call. Yeah parrygib tends to include a crushing blow with a Warrior tank.

parrygib wouldn't work well for this kind of setup since it doesn't actually cause that much of an increase in damage
it's only 50% more on one attack when tehre's been 3 or more blocks in 5 seconds, and it'll be a pain the calculate
remember, the threat in parrygibbing is mostly not from a 'you take x% more damage overall from the whole fight', it's the 'oh, you just got some attacks parried very quickly and the boss hit you 3 times within a second and wtfpwned you', but that type of thing won't happen very often, just once every couple boss fights

[Jarkeld]

Good call. Yeah parrygib tends to include a crushing blow with a Warrior tank.

any possibility of comparing a paladin with reckoning vs a warrior? would be interesting to see how reckoning effects damage taken.

okay, let's say you have ~50% avoidance, the boss swings at you ever 2.4 seconds, so hits you on average every 5 seconds which has a 10% chacne of proccing reckoning
so, on average it'll proc once every 50 seconds, and be up for 8 seconds, so it's up 16% of the time
that means it increases your number of attacks by 16%, so increases the damage you take from parry hastened by 16%, not 16% more damage, just 16% more damage of the like 3% we take