Hold the Line: A guide to WoW warrior avoidance

So, some of you may remember, I did a thread a while back about Hold the Line. As was pointed out to me, I used some slightly flawed maths so I've gone through and redone a lot of it. For example, I had crit block chance increasing overall avoidance, which it doesn't, and I also ignored [Shield Block]. And thus, I've fixed all this and decided to have another shot at this.

So anyway. The main point was to look at Hold the Line and see how it affects stats compared to other ones. We get warriors in here stacking the hell out of parry, thinking it'll give them this ultimate uptime on Hold the Line which is obviously, the best thing evar.



1. Preliminaries
To clarify again the terms that I'll be using.
Avoidance: Anything that is not a hit on the combat table. So this includes block. I realise some people favour Combat Table Coverage, but that reminds me too much of awful trinkets. It's probably a better term though.
Damage reduction: I'm referring to overall damage reduction over the course of a fight. If you have, say, 20% dodge chance, ignoring other forms of avoidance, you remove 20% of the damage from melee attacks. Thus, 20% damage reduction.
So, I'm also looking solely at averages. I don't care about lucky avoidance streaks, I'm looking at averages.

So, the formulae that I'll be using:

reduction = miss + dodge + parry + 0.2 * blocknosb .* (1 + critblocknosb / 100) + 0.1 * blocksb .* (1 + critblocksb / 100);

Yes, that's a bit of a handful. The people who looked at the last formula (It's still floating around forums) will hopefully notice two things:

The biggest is that I changed how the block formula works. As was pointed out to me, the correct form of the dr from block is

block(1 - critblock) * 0.3 + block*critblock*0.6

A little algebra converts this into 0.3 * block (1 + critblock), which is the form I've used. The /100 is because the formula for critblock (Which I'll give in a sec) gives it as a percent, this converts it into a form usable by this equation.

The other change is this blocknosb and blocksb business. You might also have noticed that 0.3 doesn't actually appear at all in that equation, when this is the blocked amount for warriors. The answer's pretty simple actually: This is me taking shield block into account. I've used a seperate formula to calculate the block/critblock chance for when shield block is and isn't up, and sb obviously is when it's up, nosb is when it isn't. Shield block is up 1/3 of the time (10 second duration, 30 second CD = 1/3 uptime) so 0.3 * 1/3 = 0.1 and thus, we get an average figure.

So! Crit block formula!

uptime = 1 - (1 - parry/100).^(10/swingSpeed)
critblocknosb = 1/119.52 .* masteryRating + uptime * 10 + 12
critblocksb = 1/119.52 .* masteryRating + uptime * 10 + 12 + overflow

Swingspeed being how quickly you're being whacked by the boss/whatever else you're tanking (Unless stated otherwise, it's 2.25, which is your average boss after Thunderclap), overflow being how far over 77.4% avoidance you are. (Since Shield Block converts that into critical block chance)
(Thanks to Steelflank and Kalle for helping me get the updated uptime formula. Jathine gave it to me too, but I'm an idiot and ignored it). Just having a look at this new formula, instead of what it used to do, which was basically figure out the chance you had of getting a HtL proc then give you 10 seconds of 10% extra critical block. What this does now is it figures out the chance HtL has procced in the last 10 seconds and calculates the uptime from that. This should give more accurate figures.

Right, so before I get into the big meaty bits, one last wee comment. One of the biggest flaws with my previous thread was that everything I did was with theoretical, ballpark figures. I wasn't using any gear sets as models and, in all honesty, apart from confirm a few hypotheses, I didn't give any overly useful results. So, I'm gonna correct that. I'll redo all my little tests from the last thread, although I doubt I'll see any overly significant changes, just some more accurate figures. But this time, I'm gonna use four base gear sets. I'm also hoping to give some more usable results.

So, firstly, the gear sets. Note that the actual items aren't important. What's important is the total ratings provided by each. So, I've picked each as a full set, excluding trinkets (Which may not have ratings) of 333, 346, 359, 372 and 391 gear. One for each current tier, excluding entry level Firelands gear which isn't high enough above the 372 gear for me to think it warrants its own slot. I might change my mind on this if people think I should:

333 set (Using normal Thundercall because there's no 333 gun): Total rating: 3526 + 658 from STR

346 set: Total rating: 3831 + 744 from STR

359 set: Total rating: 4256 + 888 from STR

372 set: (Using normal Deflecting Star because there's no 372 gun): Total rating: 5014 + 952 from STR

391 set: Total rating: 6220 + 1036 from STR

Right, so!

2. Comparing each stat

I realise I've just introduced my awesome gear sets above, but I'm gonna ignore them for the moment and look at something else. The first thing I did in my previous thread was to vary dodge/parry/mastery while keeping the other two at a set value. This time around, I'm varying the one from 0-11000, while keeping the other two at 1000. It'll give us a reasonable look at the value of each stat and is a much bigger look than what it used to be. Why? I want to see what happens when you cap your block and your critical block.

You'll notice there are also two bars showing your block chance and critical block chance (Both without shield block up) that weren't in the pre-4.2 version of this guide. I've added these in just for clarity, so you can see where these break points are. You can see the plateau clearly where you reach full combat table coverage and where you reach 100% critical block chance and your mastery's value is hard capped. You might notice another wee bump at around 6k mastery that wasn't present before. What's this? It's where your shield block starts pushing your critical block chance over 100%. What's surprising is just how close this is to the block cap value, and it's kinda implied here that this is your ideal mastery value, not necessarily because your mastery becomes terrible here, but more because it means your shield block is going to be a guaranteed physical damage cooldown.

But going back to the next test: Halving the uptime of Shield Block by popping it once a minute, rather than on CD:


Aaaaand... nothing much changes. Well, your overall damage reduction goes down but what do you expect? You're hitting your short term damage reduction CD less than you should be. There's still no decrease of mastery's value at 77.4% and still no change in how each stat is valued compared to each other. The other change is that mastery's value flattens out a little after 100% avoidance.

You might also notice that there's a point between ~1000-2000 rating where parry and dodge are superior to mastery. More on that in a sec. But first, a new chart. This time, I'll do the same thing as before, varying dodge/parry/mastery from 0 to 11000 but keep the other two at 1500, rather than 1000 since that's a more realistic dodge/parry rating value:

Obviously, you're block capping sooner. That's not a surprise. Do note that this is happening at about 4500 rating though, which is quite realistic for Firelands gear. This does distance the value at which you reach 100% critical block chance (This is always going to be a static number, by the way. You need 58.67 Mastery, or 10501 mastery rating to reach this)

I haven't done anything new or interesting yet, so, back to the age-old question: How good is parry compared to dodge? (And by age old, I mean since 4.0.1)

3. Parry vs Dodge 2: The Avoidance Strikes Back

Yes, that lame joke had to be done. So! Now I get to use my awesome gearing things.

For each set, I'm gonna give you a nice wee 3d mesh plot thing that'll show mastery vs parry and the total damage reduction of each. Then I'll give you one showing damage reduction vs mastery, then one with parry vs dodge.

So, first up, let's look at the 333 gear.
I'm not going to get too deep into it at first, because there are a few odd things that show up and I think it's important to address them first. So, just so you know what exactly is going on, along the y axis (Labeled Mastery Rating),

I'm varying mastery rating from 0 to 3831. Along the x axis, I'm varying parry from 0 to 3831-mastery (Since the total ratings cannot exceed 3831), then dodge makes up the slack. So, as the parry rating increases along the x axis, dodge rating decreases. Parry rating is then increased by the parry rating from str, since this cannot be reforged away. The z axis is damage reduction. The higher it is along there, the less damage you take (The colours match height too, blue is low, dark red is high) Right, so let's look at this mesh plot then:

Hopefully, you noticed the first huge thing that jumped right out at me straight away; mastery rating does not decrease damage taken. What? What's up with this? Mastery is king, right?

I sat and pondered this for a good hour before I realised what was going on here. Mastery rating is better than dodge and parry rating because it does not suffer from diminishing returns. Clearly, 1% of dodge is superior to 1% of block because dodging an entire hit is better than blocking it. What we're seeing here is that the gear we're using is so low, the avoidance on it is small enough that diminishing returns isn't hitting it hard enough to cause mastery rating to be better. (This is what I mentioned above with parry and dodge being better than mastery between 1000-2000 rating. Told you I'd get back to it in a sec!)
Let's take a side-on look at this chart though, looking at damage reduction vs mastery:

We see the same thing here. The more mastery rating you get (And thus, parry and dodge rating you lose), the more damage you take. The solution must be to reforge out of mastery, right?!

Well, not quite. There are two things that aren't quite right with that. Firstly, we're talking about 1% damage reduction over the course of a fight. Yeah, every little bit counts, but some would argue that more avoidance (which mastery will give) will make the healer's life easier. Spiky damage is bad.

But that's a fairly minor and inconsequential point compared to the other: Buffs. So far, I've been doing all this unbuffed. So, let's throw in Battle Shout (549 strength) and Blessing of Kings (5% strength). You're guaranteed to have the former, not necessarily the latter but the results are mostly the same:

 

It's not as obvious there, this is the DR/mastery one: 

Yeah, buffs play a fairly huge part in your avoidance at this low gear level. Newly heroicing warriors, if you aren't using Battle Shout, you should be. Unless someone else is covering the buff. But anyway! For ultimate maximum DR, you apparently still want to have 0 mastery and just focus on dodge and parry. But since whatever gear you're using is going to have some mastery on it, you're not going to reach that. So let's look instead at this dip down the bottom there, at 1608 mastery. Or basically 1600. (Which is about 2.6k combined dodge and parry rating, including parry rating from strength) If you're less than that, you want to get rid of mastery, if you're more than that, you want more mastery.

However, your best bet is probably to do the latter. You're not going to stick with 333 gear for very long and your best bet is to reforge to help you more in the long run so as not to waste gold, not to mention less spiky damage makes for happy healers.
The other peak, at 2289 mastery is another interesting point. This is the point where dodge and parry start being superior to mastery since diminishing returns is barely hitting them. This is also a rather important point as I'll address in a bit.
The peak here is flatter than the pre-4.2 version, which is understandable since the agility from Battle Shout and Kings no longer gives us any avoidance, and we're only working from the strength to parry conversion which was always going to be weaker even with the buffed conversion rate. So, in short, this is nothing surprising, buffs no longer contribute as highly to avoidance than before 4.2.

So anyway. Let's have a look at parry vs dodge:

Ooh, pretty. What all the lines mean, just so you know, are the varying values of mastery rating. I'd also like to point out, I've removed the parry rating from buffs. The values down the bottom are parry rating only from actual parry rating and from the strength on your gear. So anyway. You can see the big peak there to the right there. This is where mastery rating = 0 and is at 2098 parry rating and 2086 dodge rating, or basically exactly the same. This isn't too surprising. Hold the Line isn't going to be anything flash if you don't have any actual block chance to convert into critical blocks.
The other peak is the one at 2289 mastery rating. This occurs at 1011 parry rating and about 884 dodge rating. Parry rating is about 120 higher than dodge rating. Here, we're seeing Hold the Line's benefit more since your block chance is much higher. This is also an important point because basically, you don't want to reforge out of them if it'll put your parry and dodge ratings below these numbers.

Aaaand that's above all we can do with the 333 gear. I'll go through the other gear sets faster, that was really just being used as a basis to make sure we know what's going on, and because I won't consider avoidance without buffs.

346 gear set
If you're too lazy to scroll up, we're working with 3831 total rating and 689 from strength. So, straight into the mesh plot:

 

And the mastery/damage reduction graph:

As you can see, mastery is no longer a bad stat at all. In fact, it seems to be awesome again all of a sudden. Until you reach 1776 mastery, apparently. Which is odd that that point occurs before the same point in 333 gear. That's rather interesting.

So, looking at parry vs dodge:

You can see the two peaks here, the one to the right again being the one where mastery rating is 0. I'm going to ignore this because again, the gear you have will have mastery rating on it and quite frankly, you don't want to have that low mastery anyway. So let's look at the left one, at 1776 mastery. This one has a parry rating of 1457 and a dodge rating of 1342, so parry is again about 120 higher than dodge rating.

Anyway, moving on:

359 gear set
This time around, it's 4256 total rating and 888 from strength. So, mesh plot again:

And the mastery/DR one again:

Here, this is what prevented me from updating this thread for ages, because this is very weird. Mastery isn't your best stat, in fact, it seems you want to minimise it. Well, this is true for overall damage reduction. Kinda. Look at the scale. You're not going to go over about 2400 mastery, and we're talking about 0.05% of damage reduction between that and the maximum value. This version of the graph is, quite frankly, really misleading because it's basically flat.
Really, it doesn't overly matter what you do, as long as you keep your parry/dodge roughly even. But I'd still recommend prioritising mastery, because well, it's gonna smooth out your damage intake and reduce the chance of spike damage, which is what kills tanks, not 0.5% of damage reduction. I'd also like to note, this nearly happened in the pre-4.2 version of this chart. However, what's really surprising about this chart to me is the fact that this flattening of the value of mastery doesn't occur in the 333 or 346 gear, where it should be happening because of the low DR on parry/dodge.

But let's look at the parry/dodge chart:

 It's suddenly becoming difficult to read off the values for parry/dodge here. But, we can see a clear peak to the left where your mastery is at 1130, or the minimum sensible value. Here, parry is at 2030 which gives us a dodge value of about 1985, or 50 more parry than dodge. Again, with the low mastery 333 gear one, HtL isn't doing much if your mastery is low, which is why you don't need your parry much higher than your dodge.
I'm gonna look at another value now, with 2400 mastery, because I mentioned it earlier. And so:

Here, we have our parry rating at 1432 and our dodge rating at 1312, 120 more parry rating than dodge again.

So, next set of gear: 372 gear

Again, we're using 5014 total rating points and 952 from strength.
So, first up, mesh grid:

And the mastery/dr one:

I... don't think there's anything really that I need to say about that. If you're in full heroic gear, you want to stack the hell out of mastery. You're going to get some insane benefits out of it and if you're low on mastery, your damage reduction is going to suffer hugely.
This does raise one slight problem. There's no clear "This is the ideal mastery value" point, well apart from at 5000 rating and if you get that, I'd like to give you a medal. The other point is, you're never going to get 5000 mastery rating in only 372 gear. It's simply not possible. So, I'm going to use the 2400 value I used earlier. (And by that, I mean 2402 value) I'm not sure why I'm using that, but for the pre-4.2 version, I used 2386 for no particular good reason:

Here, we've got our parry at 1836 which gives us a dodge rating of 1730, this time about 100 more than dodge but still close enough to 120.

So! With that all done, let's move on to heroic Firelands gear!:

And the final set of gear: 391

For this, we've got 6220 rating and 1036 from STR (That's a hell of a lot of parry o_O)

So, first of course is the mesh plot:

I do believe I spy a block cap! Also, it looks a little like a beak. Hmm. But anyway, moving on, mastery/dr!

That's quite cool actually. At around 5000 rating, you reach block cap and your damage reduction takes a nose-dive (Get it, because I said it looks like a beak? Yeah, it was a pretty lame joke :( I'll stick the theorycrafting), but you're not going to reach that value anyway, especially since they like not putting mastery on Firelands gear. So I'm gonna use another realistic mastery value, and do what I probably should've been doing from the start and take the mastery value on that gear there, then add 40% (What you get when you reforge) of the other ratings on to that and look at the parry/dodge rating there. What I got was 3363 but I'm gonna use 3367 because I can:

Here, we have a parry rating of 2001 and a dodge rating of 1888, so 120 more parry than dodge.

4. MANY WHELPS, LEFT SIDE, NOW HANDLE IT

Yes, that reference had to be made too. So. As you may be aware if you've ever tanked anything, is that you sometimes need to tank multiple mobs. Throughout all this, I've been using a swing speed of 2.25 seconds (Which is 1.8 seconds, fairly average for most boss mobs, after having been Thunderclapped) So now, I'm gonna play with this a little to see how it affects the parry-dodge relationship we're seeing. Specifically, by adding in an extra mob, thus halving the swing speed to 1.125 seconds.

You might recognise this as being basically identical to the related chart with only 1 mob for 333 gear. Not surprising. You're going to get slightly more damage reduction from Hold the Line but it's going to have some rather poor uptime at this low gear level.

This one here, the big peak to the left has moved to the right and grown slightly. Apparently being able to get a higher uptime on Hold the Line increases the value of parry.

This is a bit more interesting as well. The left peak has magically disappeared, or at least, been flattened out. I think this is showing mastery's increasing value.

And this one really doesn't. The peak is in basically the same place. Interesting. Apparently parry isn't really worth that much more even tanking two mobs in 372 gear.

Same deal again. Parry's value isn't increasing.

5. Conclusions (aka tl;dr)

Well. Hopefully this has all been informative. Or at least, you got to look at lots of pretty graphs! :D But I imagine you want some interesting conclusions. I'd hoped to be able to give you a formula that you can use to plug in your stats and get your ideal parry and dodge and I might still deliver on that but I tried figuring it out and I broke maths, I think. So instead, I will leave you with two things:

Firstly, if you have low gear, you really need to be using battle shout. It helps your avoidance quite significantly (Including at high gear levels) and you probably need it to help your healer out. Secondly, if you have below 1011 parry and 884 dodge, you want to get them up to that level.

In general, you want to have your parry rating about 120 points higher than your dodge rating for ideal results.

But... I will leave you with this spreadsheet and hope it works alright. You'll need to either download it or make your own google docs account, but when you do, chuck your stats into the box and it'll give you your damage reduction from avoidance.

All percentages are whole numbers (So 13%, not 0.13):

Chuck your stats in there, chuck what stats you want and see what sorts of ideal damage reduction numbers you can get.

6. Ending stuff

A huge thanks to everyone who helped me get the maths correct (Forgive me for not listing names, there are a fair few of you). An especially huge thanks to all the OTers who got confused when I started rambling about maths to you all.

You guys are awesome and make these forums entirely worth visiting. :D

The formulae used are my own inventions, or come from this thread on ElitistJerks. That thread has been a huge help to me. :D