Prot Warrior Incoming Damage Calculations

The following is potentially a cavalcade of fail.

My goal was to put some numbers in front of me so I could best gauge my incoming damage from a raid boss's physical attacks. Two side projects quickly emerged: 1) A calculator allowing me to see if I reforged parry or dodge, how much post-diminishing returns avoidance would I potentially gain. 2) A comparison of the Eternal and Austere Meta Gems.

Here is the link:
https://spreadsheets.google.com/ccc?...CLPP7OsD#gid=0
The default values are set to Xav's as I did the fishing quest this morning and didn't equip my shield before heading to work.


Warnings and Apologies:
- I've tried to find verification on the calculations I've used and think I am pretty accurate on most, but if I took a swing and missed here, please be gentle with your criticism.
- I've never used Google Docs before, so any tips with that would be lovely.
- Sorry that some of the inputs are clunky (the Dodge calculation is especially so as the dodge you get from base agility doesn't contribute to the DR of dodge, but the dodge you receive from all other agility does).
- I posted this earlier on Elitist Jerks and wanted to post it here as well to get more feedback.

One conclusion I've come to if this math is correct:
The Eternal Meta starts resulting in less average incoming damage over the Austere at basically the "Heroic-Ready" gear levels if they reforge and focus on Mastery, even without using shield block.

Questions:
A) How much does Hold the Line justify suffering additional Parry DRs versus equalizing Parry and Dodge to avoid DR?
B) What are the up times of Hold the Line in relation to Parry chance? With that I would think we could formulate incoming damage overall as opposed to having four categories.
C) Is this useful at all, or did I waste a ton of time?
D) If useful, are their any additional trinket cool downs that should be added?


EDIT: Link Updated

quick question... line 26, g-j - why 0% ?

Sorry, there were a few iterations of this table, so I could probably have made it make a bit more sense by altering the view. Probably just suffered from too much time staring at it.

Basically, that section of the table shows you how much of the incoming damage is in each of those categories. If you block 50% of the time, that means 50% of the attacks will do 70% of their damage (with no Eternal meta), thus for incoming damage, my blocks represents 35% of the damage for me.

Well, regardless of how much dodge/parry rating you have or your to-be-missed chance, you will take 0% of incoming damage if you don't get hit, so those values all represent 0% of your incoming damage.

Hope that makes sense.

I have some constructive criticism about the layout and possibly the way things are being calculated but I'm still sorting through the sheet. Unless I'm mistaken, one thing I've noticed is that your total damage reduction formulas don't seem to take into account the base 10% from defensive stance.

It does, it's in the "Damage Reductions:" part
It doesn't include the Shaman/Priest buff uptime because besides it being completely out of your hands, it's a very unreliable uptime and I personally consider it more part of the healer's abilities than your own.

Quote:

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Originally Posted by tanis

I have some constructive criticism about the layout and possibly the way things are being calculated but I'm still sorting through the sheet. Unless I'm mistaken, one thing I've noticed is that your total damage reduction formulas don't seem to take into account the base 10% from defensive stance.

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A new version is being worked on, a new link will be up in a few. I'm trying to make it a bit more readable, was originally just going to be something I toyed around with but I thought it would be good for me to have others make suggestions (which is good cause I missed the defense modifier. :) )

New version is done, thanks Tanis for the catch.

Quote:

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Originally Posted by Tharamis

Questions:
A) How much does Hold the Line justify suffering additional Parry DRs versus equalizing Parry and Dodge to avoid DR?
B) What are the up times of Hold the Line in relation to Parry chance? With that I would think we could formulate incoming damage overall as opposed to having four categories.
C) Is this useful at all, or did I waste a ton of time?
D) If useful, are their any additional trinket cool downs that should be added?

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I can answer both A and B at once.

I did some work on this in 4.0 before Cata. Basically - improving your Parry by 1% is about a 2.5% increase in HtL uptime (in realistic heroic gear levels). In a 5 minute fight, that translates to about 8 secs of additional uptime.
my original post for formula, etc is here
http://www.tankspot.com/showthread.p...Line-and-Parry
(the ratings per Parry percentage are level 80, but the formula and percentages per HtL uptime are accurate regardless of level.)

Regarding how much swapping out affects DR:
In my gear set I have 1389 Dodge Rating and 1851 Parry Rating - hardly equal at all. My Parry rating is about 33% higher than my Dodge rating. If I completely flip-flop these numbers - 1389 Parry and 1851 Dodge, my total avoidance goes from 30.34 to 30.25.

100 rating here or there is irrelevant. Even a nearly 500 rating difference barely budges the total avoidance - which is probably unrecognizable when you're actually standing in front of a boss.

I can not view the spreadsheet at work, so I can not answer your other questions.

Thanks for the HtL information, I'll dive into that in a bit.

Quote:

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Originally Posted by Andenthal

Regarding how much swapping out affects DR:
In my gear set I have 1389 Dodge Rating and 1851 Parry Rating - hardly equal at all. My Parry rating is about 33% higher than my Dodge rating. If I completely flip-flop these numbers - 1389 Parry and 1851 Dodge, my total avoidance goes from 30.34 to 30.25.

100 rating here or there is irrelevant. Even a nearly 500 rating difference barely budges the total avoidance - which is probably unrecognizable when you're actually standing in front of a boss.

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The values of Parry and Dodge aren't really far enough apart to really see the loss of Parry from Diminishing Returns that I was thinking of when asking the question.

This is an extreme example, but I've seen some people not too far off of it.
At 2000 Parry and 500 Dodge rating you have 14.4293% Parry and 6.6073% Dodge after DR. That is 21.0365% avoidance.

If you reforged 500 parry to dodge, the %s change to 12.2207% and 9.1780% giving you 21.3987%.

While not earth shattering, it is an extra .3622% avoidance from the same exact item level. So it is a .3622% chance to avoid 100% damage vs (from what I guessed from your link) 6% more uptime to have 5% of your incoming attacks block critically vs normally (and that is assuming 2626 mastery rating, which is very solid.)

Honestly, my assumption is that it will be good to keep parry rating under twice the amount of your dodge rating.

I think you're right Tharamis, it's probably best to have quite a bit more Parry than Dodge, as the avoidance gains are quite small, with decent gains in HtL.

Also - if you factor in total avoidance including buffs, the difference shrinks even more.

I might be wrong about this, but it comes down to whether or not the 2% armor from items is multiplicative with the 10% armor from item talents. I make the assumption that it is not but don't have the meta available to test it.

If you answer 'No' to whether or not you're using the 2% armor from items meta, then the formula for what your armor would be —and thus damage reduction — if you did have it is wrong. The same misconception also affects the armor calculation for what your armor would be if you didn't have the gem.

Cell C30 branches to E63 when C9 is anything but "Y".
E63 uses the Armor value from E62 in it's dmg reduction formula.
E62 uses ((D62 - (C10)) * 1.02) + C10 as it's formula where:
D62 = C8, which is "the green number from armory"
C10 = armor from enchants
So it removes the armor from enchants, multiplies that value by 1.02 for the meta calculation, and then adds back in the enchants.

However the armor value entered above already includes a bonus 10% armor from items (assuming 3/3 Toughness) and that bonus doesn't apply to the meta as far as I know. Essentially, what your calculation does is {ARMOR FROM ITEMS} * 1.10 * 1.02 and I think it should be {ARMOR FROM ITEMS} + {ARMOR FROM ITEMS} * 0.10 + {ARMOR FROM ITEMS} * 0.02 or {ARMOR FROM ITEMS} (1.12).

Since probably every tank worth his or her salt will take 3/3 Toughness, you could calculate what his or her armor would be with the meta as:
((D62 - C10) / 1.1) * (1.12) + C10

For C62, Armor if Austere is removed, the formula becomes:
((B62 - C10 ) / 1.12 ) * 1.1 + C10

Edit: Forgot to add back in the C10 in what i believe to be the correct formula.
Edit 2: Fixed a typo in a formula.
Edit 3: Added formula for Armor without Austere gem if you do have the gem equipped.

Quote:

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Originally Posted by tanis

Since probably every tank worth his or her salt will take 3/3 Toughness, you could calculate what his or her armor would be with the meta as:
((D62 - C10) / 1.1) * (1.12) + C10

For C62, Armor if Austere is removed, the formula becomes:
((B62 - C10 ) / 1.12 ) * 1.1 + C10

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Version 0.03 is up and these two formulas have been corrected. Thanks a ton for the catch here. I tried to double check every assumption I had, but Toughness and the Meta being multiplicative raised no flags for me.

What additional things would be nice to have here? Should I break out the different sections to different sheets/tabs? Try to add in a magic damage section?

I am honestly loving this as I am learning a ton, so any requests? (I'll try and do them, but no promises.)

You could weight the four different buff states (none, Shield Block, Hold the Line, SB + HtL) by uptime to find an overall expected value.

The uptime for Shield block is: 0.333

The uptime formula for HtL is Expected Duration of HtL * parry rate / attacker's swing time. I ended up making my own spreadsheet to calculate HtL uptime because there was some incorrect math floating around the forums. Wartotem's Prot Warrior spreadsheet gives the same result as mine.

The uptime for SB + HtL would be the two multiplied.

The uptime for SB after removing overlap in SB+HtL is SB' = SB - (SB * HtL)
The uptime for HtL after removing overlap in SB+HtL is HtL' = HtL - (SB * HtL)

The "uptime" for no buffs would be max( 1 - SB' - HtL' - SB+HtL, 0)

A couple of purely cosmetic things:

Maybe rename "Incoming Damage Table" to "Weighted Damage Table" or "Expected Damage Table". I had to sort through the formulas to understand what was going on. This suggestion may not make as much sense to other people.

Cell A34 still hardcodes "... 50K DPS" rather than look at the value above it.

Another suggestion is really more of a question: Where do you want to go with this?

Wartotem's sheet is pretty good for filling in your specifics to find out "what you're made of". Rather than create a competing sheet, this one already seems to focus more on side-by-side comparisons. Perhaps run with that.

One quick note: Be aware that you're more likely to have higher parry anyway due to the plate specialization for most tanks. +5% strength reflects in higher parry values.

As for the potential "cavalcade of fail", it's better to try and learn something. You're being active about it. That's never fail.

In the formula for critical block chance with Shield Block, D63, it has mastery * 0.015 + 0.25. The first part makes sense but I where does the 0.25 base come from? Most formulas I've found are simply Mastery * 0.015. That feels wrong because without a base crit chance, warriors would have either 0 or 10% crit block (entirely from HtL) until level 80 and gear with mastery. Maybe that is the case. In any case, perhaps you've added 0.25 to the crit chance on accident because 0.25 is added to overall chance to block?

Edit: Same 0.25 constant is in E63, crit block chance during SB + HtL

Quote:

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Originally Posted by Leucifer

One quick note: Be aware that you're more likely to have higher parry anyway due to the plate specialization for most tanks. +5% strength reflects in higher parry values.

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Not fully sure what you're meaning here. All Parry derived from Strength shows up as part of your Parry rating on your character sheet.

Ultimately? You're more likely to hit diminishing returns on parry sooner. It'll be easier to increase parry as your gear increases your strength accordingly. Plate specialization, a new mechanic, will only increase that likeliness.

I don't know what that point of diminishing returns is, but it'd be good to keep in mind.

(I.E. - You land a new piece of gear with higher strength, it might serve you well to shift parry on a piece of gear to dodge, as the total strength and thus parry increase is actually higher than what the gear's listed strength stat would lead one to believe)

Leucifer, what you're saying is true. However the strength to parry conversion is done as strength to parry rating; so the parry rating on the paper doll already has strength factored into it. As long as you use the parry rating from the paper doll to seed the post-DR formula, it's a moot point as far as keeping a good balance between parry and dodge to avoid unnecessary DR.

Tanis - I understand that. Looking back, this post really hit on what I'm trying to get at.

Quote:

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Originally Posted by Tharamis

Thanks for the HtL information, I'll dive into that in a bit.

The values of Parry and Dodge aren't really far enough apart to really see the loss of Parry from Diminishing Returns that I was thinking of when asking the question.

This is an extreme example, but I've seen some people not too far off of it.
At 2000 Parry and 500 Dodge rating you have 14.4293% Parry and 6.6073% Dodge after DR. That is 21.0365% avoidance.

If you reforged 500 parry to dodge, the %s change to 12.2207% and 9.1780% giving you 21.3987%.

While not earth shattering, it is an extra .3622% avoidance from the same exact item level. So it is a .3622% chance to avoid 100% damage vs (from what I guessed from your link) 6% more uptime to have 5% of your incoming attacks block critically vs normally (and that is assuming 2626 mastery rating, which is very solid.)

Honestly, my assumption is that it will be good to keep parry rating under twice the amount of your dodge rating.

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A good portion of that parry rating is technically derived from strength, something we'll have oodles of anyway. Our source for dodge rating is going to be almost exclusively from dodge on gear.

Compare two pieces:

A) 100 Str, 100 parry, 100 dodge

B) 100 Str, 75 parry, 125 dodge

Total points for each is equal from initial appearances, BUT, how they impact your final avoidance is not likely to be identical. Additionally, which one will be worth valuable once reforged? And which way would you shift?

My answer is B, with a shift from parry to dodge. Reason why? A 30 point increase to dodge will more likely be under the DR point for dodge and yield higher avoidance than a 50 point increase to parry. Do I have the math to prove my point? Not yet. But going off of the quoted post, a 500 point shift TO parry yielded a net loss in avoidance for the example.

Plus, your "true" stat reflection on this gear is as such......

A) 100 Str +5 Str from plate spec, 100 parry + X parry from Str, 100 dodge

B) 100 Str +5 Str from plate spec, 75 parry + X parry from Str, 125 dodge

You're going to gain parry off the 100 (actually 105) strength anyway, and the gain is higher than what the posted stat would indicate.

My point is, when selecting gear, the obvious choice may not really be the best choice due to "unadvertised" modifiers.

I don't know if you guys realize this, but Plate Specialization for Protection Warriors is 5% Stamina, not Strength.

Reference: http://www.wowhead.com/spell=86526