The Burning Crusade has changed things around quite a bit with regards to damage mitigation. The two biggies being the ratings system and the changes to the druid class. I'll start with an overview of what happened with these two things before going into mitigation.

Warning: if you can't stand reading and hate math, scroll down to the fourth post. I've summarized my findings there, and afterwards have included a ranked list of quality tanking gear. (Ctrl+F:"Item List") You'll be missing out on a lot of the theory of mitigation, but it'll serve for those of you that just want to find out what item is better than what. However, please avoid derogatory comments unless you read the whole guide. Thank you, enjoy!

The Ratings sytem
The reasoning behind this system is that straight percentages scale too well into 70, which would result with characters having obscene things like 60% crit rates (which is actually mostly useless, see http://www.wowwiki.com/Attack_table), 50-60% damage avoidance, uselessly high to hit %, etc. So what blizz did was to create a rating system, which assigns a point value to these percentage ratings. This effect is two fold: it allows things like +.5% crit to exist and it allows Blizzard to scale percentages with level (reducing the %/rating ratio at higher levels to avoid the items mentioned above).

One big question with this is how much is one rating actually worth? The posters at wowwiki have put together some together some wonderful info http://www.wowwiki.com/Combat_Rating_System with regards to that.

I'm sticking to the mitigation aspect for now, here are those ratings:

Rating	Effect		Requires at 70

Defense	1 defense skill	2.4

Dodge	1% dodge		18.9

Parry 	1% parry		31.5

Block	1% block chance	7.9

(stolen from wowwiki)


Changes to the Druid class
Sticking just with mitigation we have the following changes:

Bear is upgraded from 460% to 550% armor value from items. This puts bear armor with 3/3 thick hide at 605%, instead of 506%, a substantial increase. The reasoning for this is that the armor from leather does not scale as well as plate.

***In patch 2.0.10 the armor value from items will change from 550% to 500% untalented, or 550% talented. This change has been reflected in the calculations***

Druids now need ~14.5agi for 1% dodge, up from 20/1%. This puts druids on par with rogues, and somewhat makes up for not having parry, although rogues have both, but their armor sucks, so nyah nyah.


Item Values
Another great article on wowwiki: http://www.wowwiki.com/Formulas:Item_Values is item values, a crucial part of choosing gear, which is almost entirely overlooked. Somewhat complicated, it boils down to a few rules:

Items have a certain number of "points" to assign to stats/ratings/etc, higher level items have more points.

40agi will cost more points than 20str and 20agi, which will in turn cost more than 10str, 10agi, 10int, 10 spirit.

Using these two rules to guide your thinking when you look for items will ease things tremendously.

Blizzard assigns these point values to tanking stats:

Stat		Mod

ANY rating	1

EXTRA armor	0.1

Stats (excet sta)	1

Stamina		0.67

I believe ratings also include resilience, but I'm not positive.
Extra armor is armor beyond what would normally be included in the item; weapons, rings and trinkets being much easier to calculate than pieces with armor to start. The easiest way to fudge it is to look at other pieces of armor the same level and subtract the average. Ex: Verdant gloves http://www.wowhead.com/?item=30943 have 393 armor and an item level of 109. Other blue leather gloves around that level average 175, so they gave verdant gloves a whopping ~220 extra armor, or put 22 item points into extra armor.

If you want to get into this more read the wowwiki article about it, it's very well done. In general though realize that every stat on an item is worth points, and if it's in a stat you don't use, such as block/parry rating or int(for tanking), that's a point away from a stat you could have been using, such as agi or sta. This not taken into account by this system are on equips, procs and sockets, I haven't seen much regarding these, so deal with them more on personal preference. For me I prefer on equips to procs (I already have enough to pay attention to as it is), and non-socketed for leveling, socketed for end game (sockets scale, but are expensive).


Mitigation
Now for the meat of it. This will be specific to druids, although it shouldn't be hard to extrapolate it to warriors.
Please note, this my definition of mitigation. This is not tank points, or any other measure of tanking ability. Others may define mitigation as something different, but we aren't talking about the same thing. When I say mitigation, damage reduction or avoidance I'm talking precisely about the following definitions and nothing else. If you wish to prove my theorizing wrong, you'll have to prove that my definition is wrong, not provide another way of looking at mitigation, as you'd then be describing some other phenomenon and labeling it mitigation, which has absolutely nothing to do with what I'm talking about.

Avoidance(A): The percent chance to avoid an incoming attack, based off the the combat tables. Direct variables (all in percents) being dodge, miss chance, chance to be crit and parry. Indirect variables being agility (affects dodge), defense rating (affects all of them), dodge rating, parry rating and resilience.

Damage reduction(R): When hit, the percent incoming damage is reduced by. Direct variables are armor and resilience. A minor indirect variable is agility.

Mitigation(M): (A + R - A*R)*100. In other words, the expected percent of damage an incoming attack will be reduced by. Derived from total expected damage.

Percent chance to be hit: (1 - A)*100

Damage Taken on hit: (1 - R)*Incoming damage
Total expected damage: (1 - M)*Incoming damage, or more easily understood, (Percent chance to be hit)*(Damage Taken on hit)

Note: Remember A, R and M are in percents, so when applying them to any formula, you'll need to divide by 100.

Keep these terms in mind while reading. Please take note that these may be called by different names in other articles, and in many cases Damage reduction is used freely for all of these terms. I even did so before this edit, thanks to Ranma, Planesnakes and especially Dreyo for providing much insight into this. Also note that this is NOT tank points, but an entirely different beast. Tank points runs under the idea of "how long will it take you to die", whereas concept runs under the idea of "how much damage are you actually taking". Similar, yes, identical, no. Tank points includes stamina in its calculations, but does take into account how much mana it will cost your healers to heal you, as it assumes you aren't getting heals in the first place. I'm simply trying to show how much damage you are mitigating, and more mitigation = less healing. Tank points is still a very good measure of tanking power, and I recommend anyone who is interested to look into it.

Overall, I'll be looking at what gives the best mitigation, although I don't think the answer will be as simple as anyone would like considering mitigation depends on both avoidance and damage reduction, making it a function of two variables, aka. a pain in the donkey.

Mitigation for druids boils down to five stats in two sections:

armor		R

agility		A and a tad of R

defense rating	A

dodge rating	A

resilience	A and a tad of R

Armor: Reduces the amount of damage taken when hit with a melee attack. The bread and butter of tanking stats.
Formula:

Reduction = Armor/(Armor + B)*100
B = (467.5 * Enemy Level - 22167.5) <---- For mobs greater than or equal to level 60

This is great, but it's worthless for comparing items, so I derived a more useful formula:

d = change in (delta, not derivative in this case)
Ar = starting armor
B = Scalar from above, it's 10557.5 for a 70 mob and 11960 for a 73 mob
R = Reduction

dR = (B*dAr)/((B + dAr + Ar)*(B + Ar))*100

It's somewhat complicated, but was the best I could come up with algebraically without having to try a zillion different "tricks".

Since it scales I'll provide a few comparison points. Using the formula above, here's the damage reduction per TEN points of armor (remember, armor's item value is 1/10 of ratings and core stats). Also note, 10 points of armor is actually 55 points of armor for bear, I'm using 55 for dA, and 10557.5 for B, or a level 70 mob.

at:
10k = 0.137 R per 10 armor
15k = 0.0887 R per 10 armor
20k = 0.0621 R per 10 armor
25k = 0.0459 R per 10 armor
20k = 0.0353 R per 10 armor


Agility: For avoidance it gives 1% dodge per 14.5 points along with a negligible amount of armor. HOWEVER, it also gives 0.05% crit per point, which is quite useful with improved leader of the pack (~133.3 Health a tick at 10k health) and primal fury.

Calculating avoidance for agility is easy, 1/14.5 or 0.0670 A per agility.

On a side note, warriors get 0.05% dodge per agi, so their A/agi sits at 0.05.

Defense Rating

Defense is compared with weapon skill level to decide what an attackers base chance to miss, get dodged, get parried, get blocked and get a critical is. If you flip it around and remove block and parry you get: increases enemies' chance to miss, increases dodge, and reduces enemies' chance to score a critical.

Each point of defense gives 0.04% to each of these effects. This the actual defense score mind you, not the rating. At 70, 2.4 defense rating gives 1 defense, so the avoidance calculation is thus:

1/2.4 = 0.417 defense per defense rating
0.04*3 = 0.12 A per defense
0.417*0.12 = 0.05 A per defens

Dodge rating: Like agility, but without the crit and negligible armor. From the combat ratings table on wowwiki, it sits at 18.9 rating per 1% dodge,

This gives the simple formula 1/18.9 = 0.0529 A per dodge rating. This puts it a bit above defense rating.

Resilience: This idea for this stat came in BC and reduces your chance to be crit, as well as reducing the damage taken by a crit, for both physical and magical damage. It does so at the rate of -1% crit and -2% crit damage per 39.4 rating at 70. This makes it 1.5 times as good as +defense for reducing crits, but does not offer dodge, miss, parry and block.

The avoidance is simple, you get 1/39.4 = 0.0254 A per resilience rating.

For the reduction, a level 70 mob has a 5% chance to crit against a level 70 character (wowwiki combat tables), so you get 0.05*0.02/39.4, or 0.00254 R per resilience rating. The funny thing is, the effect of this actually decreases as you gain more resilience and defense. So an ideal tank sitting at -5.6% crit rate gains absolutely no benefit to physical mitigation from the -crit damage part of resilience, making the second half of this stat useless for physical mitigation on PvE tanks. One very important thing to not is that spells cast by mobs do not crit, giving resilience very limited use in PvE.

Where resilience really shines is in PvP, when crits are high enough that you're getting major gains from the -crit damage on resilience.

For resilience overall, I'd say it's bad at physical mitigation, a decent place holder for the -crit % from +defense for tanks, and a great stat overall for PvP.

PvE tank - just enough to fill out that 0% crit
PvE magic tank - Frankly, let the warriors do it, they are much better at it
PvP - Keep it in mind when considering your available item points

Analysis
As far as avoidance goes, here's how the cards lay. Regardless of damage reduction and mitigation, these are the values of the avoidance stats:

Stat		Avoidance		Note

1 Agility		0.06700		*Also adds crit and a bit of damage reduction

1 Dodge Rating	0.05290		*Just avoidance

1 Defense Rating	0.05000		*Greater miss chance and crit avoidance, less dodge

1 Resilience	0.0254		*Also grants magical DR, physical DR and magical Avoidance.

10 Armor		0		*No effect on avoidance

For Damage reduction we have the following snapshots:

Stat				Reduct	Note

10 armor @ 10k armor		0.137	*Just damage reduction 

10 armor @ 15k armor		0.0887	*Just damage reduction

10 armor @ 20k armor		0.0621	*Just damage reduction

10 armor @ 25k armor		0.0459	*Just damage reduction

10 armor @ 30k armor		0.0353	*Just damage reduction

1 resilience @ 60% crit		0.0254	*Also grants magical DR, physical avoidance and magical Avoidance.

1 resilience @ 30% crit		0.0152	*Also grants magical DR, physical avoidance and magical Avoidance.

1 resilience @ 5% crit		0.00254	*Also grants magical DR, physical avoidance and magical Avoidance.

Remember not to compare the damage reduction table to the avoidance table, it's meaningless. Alright, we're halfway there. Now, we have to find a way to compare avoidance to damage reduction. This is where things get tricky.

First I'm going to provide some snapshots.

One common point I think druids will be at come level 70 is ~25% dodge, ~60 defense rating, 20k armor and 0 resilience (not worth it, and it's a pain to add in since it overlaps reduction and avoidance).
The 60 dodge rating would give 1% less crits, 1% more misses and %1 more dodges, putting total avoidance at 36% for a level 70 mob. (base 5% miss and 3% survival of the fittest)
20k armor will give 65.5% reduction, these two combining to 77.1% mitigation. Not bad at all, if you can achieve this you'll probably be alright for most five mans, although raiding might be troublesome.

Now, say you have the opportunity to get a trinket enchant that gives 10 armor or 1 agi. The quest to take it will cost 10,000 gold and require exalted with five reputations, so you want to make sure you choose wisely. What will you choose?
1 agi will give 0.067 avoidance, and 10 armor will give 0.0707 damage reduction. HOWEVER, you get off that easy, you have to use the mitigation formula to derive their true values:

original = 0.655 + 0.36 - 0.655*0.36 	= 77.9200% M -> 0% change

+1 agi = 0.655 + 0.36067 - 0.655*0.36067 	= 77.9431% M -> 0.0231% change

+10 armor = 0.655707 + 0.36 - 0.655707*0.36 	= 77.9652% M -> 0.0452% change

(Remember, avoidance and damage reduction are percentages, so they were divided by 100.)
In this case, armor wins! So now we know if you ever are at 33% avoidance and 65.5% reduction, and have the choice between an equally valued avoidance stat and armor, go for the armor. Yet, one snapshot is still pretty useless.

Another snapshot, the hardcore avoidance druid: 45% dodge, 120 defense rating, 10k armor, 0 resilience.
That's 45% dodge, + 2% dodge, + 2% minus crit + 2% miss + 5% miss + 3% minus crit for 59% Avoidance.
Reduction is: 10k/(10k + 467.5 * 70 - 22167.5) or 53.20% reduction.

Doing the same deal we get:

original = 0.532 + 0.59 - 0.532*0.59 	= 80.8120% M -> 0% change

+1 agi = 0.532 + 0.59067 - 0.532*0.59067	= 80.8434% M -> 0.0314% change

+10 armor = 0.5350 + 0.59 - 0.5350*0.59 	= 80.935% M -> 0.1230% change

Armor is still the winner, with HUGE mitigation gains per point.
So, what does this mean exactly? Who knows, that's why functions of two variables suck. I'll do one more snapshot before I really blow things up.

Here lies the hardcore +armor druid. 15% dodge, 0 defense rating, 30,000 armor (is that even achievable?), 0 resilience.
Total avoidance, 20%, total reduction, 74.53%, near max.

original = 0.745 + 0.20 - 0.745*0.20 	= 79.6000% M -> 0% change

+1 agi = 0.745 + 0.20067 - 0.745*0.20067	= 79.6168% M -> 0.0168% change

+10 armor = 0.745410 + 0.20 - 0.745410*0.20	= 79.6328% M -> 0.0328% change

Here we see, armor is STILL the winner, although the high armor druid has really screwed his gain per item point in this case.

With these three snapshots and a little bit of me cheating by looking at the graph, you can see that'll you gain more mitigation per point if you focus on avoidance over damage reduction, but you'll nearly always (except at some likely unachievable point greater than 30k armor) gain more mitigation immediately by focusing on higher armor. Ideally you'll want use the mitigation function to decide what piece of armor will be better for you, while focusing on enough avoidance to keep those high mitigation gains coming.

Remember, armor is better than agility under normal circumstances, but too much armor and not enough avoidance will lead to poor mitigation gains in the future.

But, I didn't really answer the question did i? So how does one figure out when damage reduction becomes less effective than avoidance? And how can I keep my mitigation per item points gains maximized? Neither of these questions matter in the long run, as the turning point is unachievably high and the loss in per point mitigation by taking higher armor over avoidance will for the most part be made up for by the increase mitigation gain from the higher armor. However, they are still valid questions and I'll continue to work on them and see what I can come up with. For now, I will provide the information needed to solve the problem, along with the steps that should be made. I'll also try my best to provide a description of what this graph looks like to assist the less mathematical of you.

The problem to be solved:

The mitigation graph is as follows:
Av= Avoidance
Ar= Current armor
B = 11960 = 467.5 * 70 - 22167.5
M = Mitigation

Av + Ar/(Ar + B) - Av*Ar/(Ar + B) = M

This will create a three dimensional object akin to a piece of paper laying on the edge of a slightly inclined surface, so that one corner hangs off (0% reduction).
You will need to find the plane that intersects this object in such a way that the mitigation gains per item point for avoidance and armor are equal. You can probably do this by setting Mitigation equal to zero and solving for Av or Ar using whatever math tricks available to you. Play with it, see how you sit and what your gains will be from avoidance and damage reduction. You don't really need to be strict with it until end game, and at that point upgrades are so few and far between that you can afford to spend some time calculating mitigation for each piece.

Here's the Maple command for plotting this function if any of you college sorts have access to it:

R:= Ar/(Ar +467.5*73 - 22167.5);
plot3d(Av + R - Av*R, Ar=0..36000, Av=0..1);

Good luck!

Item Value
So now you're thinking, "ALRIGHT! Time to go load up on my agility!", or "SWEET! It's ARMOR TIME!" WRONG. Remember fewer stat items have their point values increased. From the wowwiki article on item values it goes something like this.

magnitude = the numerical value of the stat, aka. 25agi, 200 armor, etc.
value = the item value, aka. all ratings = 1, armor = 0.1, sta = 0.67, other stats = 1, etc.
S# = magnitude * value


Item value = (S1^(1.5) + S2^(1.5) + S3^(1.5) + ...)^(2/3)

So, we have this great formula, but it's somewhat difficult to extrapolate some meaning out of it. I'll do so with an example.

We have our favorite Cleansed Fel Pauldrons http://www.wowhead.com/?item=30369 (oh how I wish I chose Aldor)

Their item values is: ((35*1)^(1.5) + (20*1)^(1.5) + (21*.67)^(1.5) + (20*0.5^)(1.5))^(2/3) (Str, Agi, Sta, AP) = 52.55

Now we say, "Forget all the junk, Ima kat, STR ROCKS!" and manage to locate blue shoulders that also have 79 item points.

Our formula would be (AGI^(1.5))^(2/3) = 52.55, or ~53 str, as that's how the formula works out. So, you'd be losing out on 20 agi, 21 sta and 20 AP to gain a whopping 18 str. That barely covers the AP from the agi and bonus AP, much less the dodge, crit and sta you'd be losing out on. Although I used an example relating to dps, the same applies to mitigation. If you grab an item with 50agi and nothing else because agility is the best DR for a druid, you're screwing yourself, as the lost stats from a single stat item would have more than made up for the difference between agi DR and the DR of the other mitigation stats.

Your best bet is to calculate out how much DR an item will give you based on the table I provided above. HOWEVER! Mitigation doesn't make a good tank, you'll need to provide enough threat to hold aggro, as your raid's dps is only as good as your threat, and enough sta to provide a hit point buffer large enough to let your healers react to damage spikes.


Combat Tables
You can really stop now, you have a good enough idea of what your stats will do for your tanking at this point, but I thought I'd add a bit extra in because I think it's important. This idea is the Attack table http://www.wowwiki.com/Attack_table. The idea is that every time a mob attempts to hit you it does a /roll, and uses a table to map a number to one of these values: miss, dodge, parry(non-druids), glancing blow(only players attacking mobs), block(shield wearers), critical, crushing blow(mobs attacking players), and anything leftover becomes an ordinary hit.

I'm going to compare a few different gear sets and see how the tables look. This is good for analyzing if you're going to be taking alot of spike damage when tanking, what your total mitigation is, and for dual wielders, if as a warrior are you pushing CBs and crits off the table with your Shield block, and if as a dual wielder, are you wasting alot of your +crit because your +hit sucks.

Your typical high armor, no +def, massive agi druid tank being thumped by a 73 boss. This is from the mob's view point.

Action		Chance

Miss		04.40%

Dodge		50.00%

Critical		02.60%

Crushing Blow	15.00%

Ordinary Hit	28.00%

Lets give him 28k armor, putting him at ~70% DR from armor, ~55% avoidance and so, 86.5% mitigation. So, he takes 0.6x or 0.45x damage from 17% of attacks, 0.3x damage from 28% of the attacks, and the rest miss. It doesn't sound like much, but when the boss is hitting for a base 5k, that's 3000 on a crit, and you're going to want to be able to predict when those are landing so your healers can handle it.

Now, Lets give our buddy here +65 def (156 defense rating, 156 item points, -2.6% crit, +2.6% dodge, +2.6% miss), and drop his agi and armor by an equivalent amount, say ~6000 armor (1000 base, or 100 item points) and 56 agi to match (~3.85% dodge, 56 item points).

Action		Chance

Miss		07.00%

Dodge		48.75%

Critical		00.00%

Crushing Blow	15.00%

Ordinary Hit	29.25%

With that +def, you're avoidance chance is still at ~55%, it even increased a bit because of the increased miss chance, you've completely knocked off crits, and your DR is down to ~65%, putting your mitigation at 84.25%. A bit lower than above, but the boss can only hit for a max of 2650, reducing spikes by 11.7%. In this case you'd also end up losing ~3% to crit from the lost agility, but that's up to you to decide if it's worth it based on what you're fighting.


Now, as point of comparison I'll put up a warrior's attack table, which does a good job of showing how different their tanking really is. I'll give our typical badass warrior +336 defense rating, the amount needed to nullify crits, since they dont have survival of the fittest. Of course, their armor actually has +defense rating, unlike ours, making it alot easier for them to stack defense. http://www.wowhead.com/?items=4.2&filter=cr=42;crs=1;crv=0 Enough rings, trinkets, weapons and cloaks do have +def though, so the 156 def rating from above is achievable on a druid without screwing yourself. I'll also reduce his armor to 18k, or ~60% reduction, and his dodge to 10%. I'm going to give him 15% parry and 10% block, but I'm just playing these numbers by ear, I don't know how close they'll be to actual warrior tanking numbers.

Action		Chance

Miss		10.00%

Dodge		15.60%

Parry		20.60%

Block		15.60%

Critical		00.00%

Crushing Blow	15.00%

Ordinary Hit	28.20%

So, our warrior has 46.2% avoidance, and 60% damage reduction, putting him at 78.48% mitigation (not a whole lot less considering the ~15% reduction between avoidance and DR from above), but ~15.60% of normal attacks are reduced in damage by the block amount, somewhere around 400 I'm been told, which adds quite a bit to mitigation. Our warrior here will get hit for a max of 3000, BUT warriors also get the /cheat button of shield block, increasing their block by 75% on the next attack, completely removing crushing blows and normal hits from the table. They also get last stand, shield wall, POTIONS, magical damage reduction, spell reflection and a wider variety of attacks to choose from, making them better at tanking situations that are likely to cause damage spikes or magical damage, as their class is set up to be much more flexible in tanking than druids are.


Conclusion
Very adequately described by Qina,

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Q u o t e:

Also, as a general guideline, the more armor you have the less each additional fixed increment of armor will do for your overall damage mitigation, while the more dodge you have, the more each additional fixed increment of dodge will do for your overall damage mitigation--but for all reasonable points on those curves, armor outperforms dodge (that is, even when armor is at its worst and dodge is at its best, armor outperforms dodge).

---

Remember that in all reasonable cases armor will out perform agility, and that boosting avoidance will also boost your overall mitigation gains per item point. Also, take the mitigation formula to heart, it's not that hard to remember, you can even slap it in your graphing calculator for instant calculation when that sweet piece of tanking loot drops: (Armor + Damage Reduction - Armor*Damage Reduction)

Overall Blizzard has done a really great job at making tanking stats a complex, interwoven system of avoidance and damage reduction. Hopefully this guide will provide some insight for those of you, like me, that want to maximize your tankability. However, Blizzard has also done a great job of creating an innate system of balance to this system, so those of you who could care less about the math don't have to worry about it, as long as you dont try to min/max your items, it'll all balance out and your mitigation will be great.

In summary, spread out your stats, focus on armor and agility, pump that crit immunity (156 defense skill for crit immunity on a 73 mob, or 120 for a 70 mob), don't go out of your way for resilience (for PvE tanking), don't forget about threat, let the warriors tank those iffy situations (it leaves you room to dps, heal and innervate anyways), and most of all, have fun!

Cheers,

Tel

Helpful hints for those with short attention spans

Mitigation = Avoidance + Damage reduction - Avoidance*Damage reduction

Mitigation is NOT tank points, tank points are NOT mitigation, use them both, they are both great ways of analyzing tanking potential.

Spread out your stats, single stat items are less effective than multi-stat items.

When given the choice (as a PvE tank), work your way down this list (ordered from most effective mitigation per item point to least effective per item point):

Armor @ 0.037% Mitigation per IP (10 armor)
Agility @ 0.026% Mitigation per IP (1 agi)
*Defense rating @ 0.019% Mitigation per IP (1 def rating)
**Dodge rating @ 0.020% Mitigation per IP (1 dodge rating)
***Reslience @ 0.009% Mitigation per IP (1 resilience)

(Percentages were calculated using 20k armor and 30% avoidance)

*Up to the crit cap, 5.6% for a 73 mob. (2.6% with talents)
**Dodge rating actually has a bit better avoidance than Defense rating, but defense rating reduces damage spikes, so I moved it above dodge rating.
***Also mitigates spell damage and is the most efficient way to reach the crit cap. Good for fill in when you can't get enough +def to reach the crit cap, but overall a bad PvE tanking stat since you don't want to get crit, and mobs can't crit with their spells anyway.

Dump defense for resilience if you're going to be pvping.

Don't forget to stack stamina, even the best healers need a decent sized damage buffer.

Don't try to maximize your armor at the cost of avoidance. Your mitigation per item point will drop below the point where the extra mitigation gained from armor over avoidance will make up for it. This will result in poorer mitigation and poorer mitigation gain per item point.


How to compare mitigation between two items

1)Take off both items.

2)Record your damage reduction from the armor tooltip and calculate your total avoidance

3) Calculate your mitigation given the above DR and Avoidance.

3) put on item A, repeat step two and three.

4) put on item B, repeat steps two and three. If you don't have the item, calculate each stat based on the item stats given.

5) See which is bigger.


Formulas
Mitigation = Avoidance + Damage reduction - Avoidance*Damage reduction

A = Avoidance
M = Mitigation
R = Damage Reduction
Ar = Armor
B = (467.5*Enemy Level - 22167.5) = 11960 for a 73 mob or 10557.5 for a 70 mob
d = the change in (delta) [this isn't an actual variable, more of a modifier to a variable]

R = (Ar)/(Ar + B)*100
dR = (B*dA)/((B + dA + A)*(B + A))*100
Percent chance to be hit = (1 - A)/100
Damage taken on hit = (1 - R)*Incoming Damage
Total expected damage = (1 - M)*Incoming damage
Total expected damage = (Percent chance to be hit)*(Damage taken on hit)
S# = (stat magnitude)*(stat item value)
Item value ~= (S1^(1.5) + S2^(1.5) + S3^(1.5) + ...)^(2/3)
Total avoidance = agi/14.5 + 5% base miss + 0.2%*(mob level - your level) + defense rating/60*3 + dodge rating/18.9 + resilience/39.5 + talents


Any helpful comments are much appreciated, I'll be more than happy to add any futher insights about mitigation into this post.

Thanks to Qina for her fixes and insightful analysis, Dreyo for helping me to completely grasp the concept of avoidance and damage reduction and how they combine to form mitigation, to Ranma for his insight into resilience, Ranma as well as Planesnakes for commentary and insight into what was wrong with my original calculations, and to everyone else who has found this post helpful enough to report for a sticky.

From the Theorycraft above I've derived a formula to calculate the %Mitigation an item will grant based on your current Avoidance and Damage Reduction. Using this formula I've compiled a list of the items in the game that offer the best mitigation. This is not a complete list. For the most part it shows the best few items, along with some decent easier to obtain items, some of the classic level 60 tanking items, and a few I personally found interesting. I'm using 20k armor and 30% avoidance in these mitigation calculations, which is about the level of avoidance and mitigation you'd be at when you start looking into getting some of these items. I've recalculated the list using many combinations of avoidance and damage reduction, and in all but the most drastic scenarios the item ordering remained the same even though the mitigation of each item changed.

Formulas used:

Ar = 20000
Dr = Ar/(Ar + 11960)
Av = 0.30

dAv = (Dodge rate/18.9 + Agi/14.5 + Def rate/60*3 + Resil/39.4)/100
dDr = (Item Armor*5*1.1 + Ar)/(Item Armor*5*1.1 + Ar + 11960) - Ar/(Ar + 11960)

***Updated for 2.0.10***
changed from (Item Armor*5.5*1.1 + Ar) to (Item Armor*5*1.1 + Ar)

%Mitigation = ((1 - Av)*dDr + (1 - Dr)*dAv - dAv*dDr)*100 (look familiar? >.>)

As far as socketing goes, I've included the %Mit on the best blue tanking gems, and have socketed all items accordingly:
Meta = Tenacious earthstorm
Red = Delicate Living Ruby
Yellow = Thick Dawnstone
Blue = Shifting Nighteye

This will provide a realistic mitigation value to the sockets, as all these gems are not terribly expensive or hard to come by, yet rare enough to adequately represent the value of having an item properly socketed.

Please take note of the extras portion at the end, as this ranking is purely based on item mitigation. Also, this is not by any means a complete list, I haven't included most PvP gear yet (they are all really good), and I'm sure there's some I've missed. I don't intend for it to show the tanking stats for every feral item, as most obviously suck for tanking, or can be easily compared to the items that are on the list. If you have any decent suggestions for the list, by all means comment, and I'll put them on.

Item List

Gems
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Color)Name, "Extras [sockets, + bonus]"
0.224-[0,12,0,0,0](Meta) Tenacious Earthstorm, "Chance to restore health on hit"
0.206-[0,0,0,0,8](Red) Delicate Living Ruby
0.158-[0,0,8,0,0](Red) Subtle Living Ruby
0.150-[0,8,0,0,0](Yellow) Thick Dawnstone
0.103-[0,0,0,0,4](Red, Blue) Shifting Nighteye, "6 sta"
0.075-[0,4,0,0,0](Yellow, Blue) Enduring Talasite, "6 sta"
0.000-[0,0,0,0,0](Blue) Solid Star of Elune, "12 sta"

Weapons
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity)Name, "Extras [sockets, + bonus]"
2.134-[500,24,0,0,0](e) Earthwarden,"FCR 24, FAP 525"
1.870-[550,0,0,0,0](r) Braxxis' Staff of Slumber
1.783-[300,0,0,0,29](e) Feral Staff of Lashing,"FAP 525, 35 str, 33 sta"
1.265-[360,0,0,0,0](r) Greatstafff of the Leviathan, "36 str, 33 sta"
1.201-[260,15,0,0,0](e) Warden Staff,"11 sta"
1.133-[320,0,0,0,0](e) Staff of Natural Fury,"30 str, 30 sta, FAP 525, shift -200"

Back
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras"
1.393-[285,21,0,0,0](e) Gilded Thorium Cloak, "27 sta"
1.251-[216,26,0,0,0](e) Burnoose of Shifting Ages, "15 sta, 29 Block"
1.177-[212,10,12,0,0](e) Cryptfiend Silk Cloak, "14 sta, 10 HR"
1.126-[318,0,0,0,0](e) Thoriumweave Cloak, "35 sta"
1.093-[223,16,0,0,0](r) Bogstrok Scale Cloak, "22 sta"
1.055-[217,15,0,0,0](u) Cloak of the Valiant Defender, "21 sta"
0.920-[143,9,12,0,0](e) Sandstorm Cloak, "12 str, 12 sta"
0.899-[214,7,0,0,0](r) Cloak of Warding
0.875-[85,0,0,0,22](e) Dr@pe of Dark Reavers,"18 sta, 15 HR, 30 AP"

Chest
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
2.512-[255,8,24,0,40](r) Auchenai Monk's Tunic,"19 HR 18 AP, 2R(8agi), 1Y(8def) + (6 AP)"
2.510-[383,8,0,0,42](e) Breastplate of Malorne,"29 str, 28 sta, 15 int, 14 spi, [1R, 1Y, 1B + (4 HR)], set"
2.487-[429,0,0,0,41](e) Nordrassil Chestplate,"42 str, 42 sta, 16 int, [2B, 1R + (4 str)], set"
2.427-[238,0,0,0,63](r) Warden's Hauberk,"30 sta, [3R + (4 HR)]"
2.157-[378,0,0,0,34](r) Chestguard of the Talon, "36 str, 21 sta"
2.012-[425,0,0,0,22](r) Jerkin of Untamed Spirit, "23 str, 22 sta"
1.998-[290,44,4,0,4](r) Heavy Clefthoof Vest,"58 sta, [2Y, 1B + (4 Dodge)], set"
1.941-[318,0,0,0,33](e) Chestguard of Conniver,"30 sta, 18 HR, 82 AP"
1.455-[343,0,0,0,10](u) Nickwinkle's Harness Experiment, "20 str, 54 sta"
1.411-[337,0,0,0,9](u) Bear-Strength Harness, "20 str, 52 sta"

Feet
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
2.010-[201,0,25,0,32](r) Nimble-foot Treads, "24 sta"
1.810-[219,8,0,0,35](e) Edgewalker Longboots,"25 sta, 10 HR, 38 AP, [1R, 1Y + (3 HR)]"
1.560-[177,0,11,0,28](u) Wrangler's Boots, "32 AP"
1.540-[219,0,0,0,30](e) Shadowstep Striders, "27 sta, 52 AP"
1.509-[352,0,0,0,11](u) Supple Leather Boots, "19 str, 24 sta, 20 AP"
1.457-[198,32,3,0,4](r) Heavy Clefthoof Boots,"43 sta, [1Y, 1B +(3 Dodge)], set "
1.440-[219,0,0,0,26](e) Zierhut's Lost Treads, "32 str, 30 sta"
1.404-[201,0,0,0,27](r) Silent-Strider Kneeboots,"30 sta, 50 AP, 1 stealth"
1.201-[181,0,23,0,4](r) Southshore Sneakers,"22 sta, 42 AP, [1R, 1B +(6 AP)]"
1.127-[157,0,0,0,22](e) Boots of the Vanguard, "22 str, 11 sta"

Hands
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
1.873-[183,8,3,0,40](r) Wastewalker Gloves,"33 sta, [1R, 1Y +(3 Dodge)], 16 AP, set"
1.715-[393,0,0,0,14](r) Verdant Gloves, "23 str, 27 sta"
1.575-[267,0,0,0,25](e) Nordrassil Handgrips,"28 str, 27 sta, 14 HR, 14 Int, 11 Spi, set"
1.483-[269,0,0,0,21](e) Gloves of the Hidden Temple, "18 str, 22 sta, 6 Shadow Resist"
0.855-[238,0,0,0,0](e) Gauntlets of Malorne,"29 str, 24 sta, 13 Int, 12 Spi, 21 Crit, set"

Head
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
2.259-[321,20,0,0,31](e) Stag-Helm of Malorne,"36 str, 24 sta, [1M, 1Y +(4agi)], 15 int, 14 spi, 12HR, set"
2.135-[358,12,0,0,27](e) Nordrassil Headdress,"38 str, 27 sta, [1M, 1R +(4 HR)], 16 Int, 12 Spi, Set"
2.033-[232,0,0,0,48](r) Stylin' Purple Hat, "45 sta"
2.014-[249,0,0,0,45](r) The Night Watchman,"25 sta, 68 AP, increase stealth detection"
1.874-[237,20,0,4,25](r) Helm of the Claw,"21 sta, 14 HR, 66 AP, [1Y, 1M +(4 res)]"
1.765-[249,0,0,0,35](e) Cobrascale Hood, "52 sta, 70 AP"
1.725-[237,0,0,0,35](r) Savage Mask of the Lynx Lord,"34 sta, 15 HR, 58 AP"
1.711-[237,0,30,31,0](r) Cowl of the Guiltless, "28 sta, 52 AP"
1.685-[276,0, 12,0,19](e)Guise of the Devourer, "19 str, 17sta"

Legs
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
2.716-[278,0,28,0,48](e) Skulker's Greaves,"34 sta, 56 AP, [2R, 1B +(4 Dodge)]"
2.267-[382,0,0,0,38](e) Nordrassil Feral-Kilt,"39 str, 27 sta, 19 HR, 16 Int, 12 Spi, set"
2.023-[475,0,0,0,16](u) Ash Tempered Legguards, "26 str, 31 sta"
1.934-[251,42,4,0,8](r) Heavy Clefthoof Leggings,"54 sta, [2B, 1Y +(4 Dodge)], set"
1.912-[256,0,0,0,40](r) Leggings of Assasination,"33 sta, 22 HR, 44 AP, set"
1.895-[342,0,0,0,28](e) Greaves of Malorne,"38 str, 33 sta, 17 Int, 16 Spi, set"
1.753-[214,0,25,0,20](r) Skulldugger's Leggings,"30 sta, 16 HR, 40 AP, [2R, 1B +(4 Dodge)]"

Necklace
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras"
0.857-[0,21,0,0,18](e) Necklace of the Juggernaut, "30 sta"
0.773-[0,22,0,0,14](e) Kael Head Quest Tank Neck, "15 str, 34 sta"
0.711-[0,19,18,0,0](r) Strength of the Untamed "27 sta"
0.671-[0,0,0,0,26](r) Jagged Bark Pendant, "15 sta, 30 AP"
0.619-[0,13,19,0,0](e) Barbed Chocker of Discipline, "36 sta"
0.611-[0,20,12,0,0](r) Maladaar's Blessed Chaplet, "30 sta"
0.593-[0,0,0,0,23](r) Earthen Mark of Razing, "20 AP, 13 HR"
0.574-[0,10,0,0,15](r) Evil Eye Pendant
0.548-[0,10,0,0,14](e) Master Dragonslayer's Medallion, "24 sta"
0.518-[0,15,12,0,0](e) Mark of C'Thun, "24 sta, 10 HR"
0.490-[0,0,0,0,19](e) Amulet of the Darkmoon, "10 str, 10 sta"
0.462-[0,12,12,0,0](e) Medallion of Steadfast Might, "9 str, 13 sta"
0.452-[0,9,0,0,11](e) Pendant of the Qiraji Guardian, "12 str, 17 sta"
0.387-[0,0,0,0,15](r) Natasha's Pack Collar, "25 str, 15 sta"
0.361-[0,0,0,0,14](r) Pendant of Battle-Lust, "19 str, 19 sta"
0.318-[0,17,0,0,0](r) Mark of the Ravenguard, "40 sta"
0.292-[0,8,0,15,0](e) Pendant of Triumph, "27 sta, 8 Crit, 32 AP, [1Y + (2HR)]"
0.228-[0,0,0,24,0](r) Tarren Mill Vitality Locket, "35 sta"
0.218-[0,0,0,23,0](r) Thick Felsteel Necklace, "36 sta, Increase Party Sta by 20 for 30 min"
0.190-[0,0,0,20,0](r) Talisman of Tenacity, "30 sta"
0.000-[0,0,0,0,0](u) Thick Adamantite Necklace "42 sta"

Rings
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras"
1.185-[250,16,0,0,0](e) Violet Signet of the Great Protector, "33 sta"
1.105-[200,21,0,0,0](e) Ring of Unyielding Force, "27 sta"
0.929-[170,17,0,0,0](r) Iron Band of the Unbreakable, "27 sta"
0.914-[150,20,0,0,0](e) Shermanar Great-Ring, 33 sta"
0.913-[100,13,0,0,12](r) Ring of Emperor Vek'lor, "18 sta"
0.783-[180,0,0,14,0](r) Mok'Nathal Clan Ring, "16 sta"
0.750-[0,20,19,0,0](r) Elementium Band of the Sentry, "24 sta"
0.552-[110,8,0,0,0](e) Heavy Dark Iron Ring, "20 sta"
0.548-[150,0,0,0,0](r) Thrall's Resolve, "4 str, 7 sta"

Shoulder
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
1.903-[314,0,0,0,32](e) Nordrassil Feral-Mantle,"27 str, 30 sta, [1R, 1B +(3agi)], set"
1.792-[280,0,0,0,32](e) Mantle of Malorne,"30 str, 33 sta, [2B +(3Crit)], set"
1.715-[219,0,0,0,37](r) Wastewalker Shoulderpads,"19 sta, [1R, 1B +(3crit)], set"
1.705-[219,16,0,0,25](r) Shoulderpads of Assassination,"25 sta, 42 AP, [2Y(8def) +(4 sta)]"
1.476-[178,0,13,0,23](r) Demon Hide Spaulders,"18 sta, 11 HR, 32 AP"
1.398-[214,0,0,0,25](r) Sun-Gilded Shouldercaps,"26 sta, 15 HR, 48 AP"
1.290-[219,0,0,0,20](r) Talbuk Hide Spaulders,"15 HR, 70 AP"
1.252-[208,0,0,0,20](r) Cleansed Fel Pauldrons, "35 str, 21 sta, 20 AP"

Trinket
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras"
0.885-[180,0,12,0,0](r) Mark of Tyranny, "10 Arcane Resist"
0.673-[0,0,34,0,0](e) Moroes' Lucky Pocket Watch, "270 dodge for 10 sec"
0.598-[0,32,0,0,0](r) Figurine - Dawnstone Crab, "125 dodge for 20 sec"
0.598-[0,32,0,0,0](r) Adamantine Figurine, "Increase armor by 1280 for 20 sec"
0.548-[150,0,0,0,0](r) Smoking Heart of the Mountain,"7 Fire, Nature, Frost, Shadow Resist"
0.486-[0,26,0,0,0](r) Regal Protectorate, "Increase max health by 900 for 15 sec"
0.475-[0,0,24,0,0](r) Vigilance Charm
0.323-[0,0,0,34,0](e) Talisman of the Horde, "Heal 877-969"
0.313-[0,0,0,33,0](r) Alembic of Infernal Power, "2% chance to gain 260 mana when hit"
0.285-[0,0,0,30,0](r) Runed Fungal Cap,"Absorb 440 damage, 20 sec"
0.218-[0,0,0,23,0](e) Timelapse Shard, "25 sta, Reduce threat within 30 yards"

Waist
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
1.633-[164,0,21,0,25](r) Naaru Belt of Precision,"44 AP, 15 HR"
1.521-[348,0,0,0,12](u) Manimal's Cinch, "20 str, 24 sta"
1.505-[179,0,0,0,34](e) Girdle of Treachery,"33 sta, 52AP, [2R +(3agi)]"
1.505-[164,0,0,0,36](r) Dunewind Sash,"22 sta, 50 AP, [1R, 1B +(3agi)]"
1.329-[179,0,0,0,27](e) Girdle of the Deathdealer,"27 sta, 18 HR, 54 AP"
1.257-[144,0,9,0,22](u) B.O.O.M. Operative's Belt, "12 sta, 46 AP"

Wrist
%Mitigation-[Armor,Def,Dodge,Resil,Agi](Rarity) Name, "Extras [sockets, + bonus]"
1.250-[281,0,0,0,10](r) Umberhowl's Collar, "17 str, 22 sta"
1.090-[139,0,0,0,23](e) Nightfall Wristguards, "21 sta, 42 AP"
1.167-[128,0,2,0,26](r) Spymistress's Wristguards,"15 sta, 15 HR, [1R +(2 Dodge)]"
0.976-[128,0,0,0,20](r) Shackles of Quagmirran, "18 sta, 40 AP"
0.823-[99,0,0,0,18](r) Bracers of Finesse, "16 sta, 28 AP"

Great post! I'll definitely keep it in mind when leveling my druid.

Good read, thanks :P

Thanks so much - I've been looking for some proper math on this for awhile. Reporting for sticky.

Reported for sticky! Great information and mathematical analysis. Back to the top for all to see.

I’m getting the heavy clefthoof set made as the core of my Stam/boss tank set (vs. DPS trash set). I’m currently wondering what to put in for the gems. Gem slots listed (boots, legs, chest)- Yellow, Blue; Blue, Yellow, Blue; Blue, Yellow, Yellow, equalling 8 slots all up. I don’t see a metagem slot here, but I don’t fully understand gems I’ll admit.

Since this will be the core of the set for sometime I’m wondering whether to a) stack stam/def rating gems and let my other gear do the AC/dodge work or b) throw in a lot of dodge gems, or c) mix it up.

I’m thinking at present that I’ll just load up on stamina + defence rating – in which case I could just throw in Enduring Talasite (4 DR, 6 Stam) which fits in either colour. That would add up to + 32 DR and +48 Stam. This opposed to going for dodge or agility (+stam).

+131 Stam (179 Sta inc Gems)
+739 AC
+ 86 Def Rating (118 Def R inc Gems) = 49.2 Def Skill
+12 Dodge (gem set bonus)

Or I could throw in a bunch of subtle living rubies – at + 8 Doge rating – 8x 8 = 64 (76 in set bonus) Dodge on a set with quite strong stam/Def Rating might not be a bad choice. That would =

+131 Stam
+739 AC
+ 86 Def Rating = 38.8 Def Skill
+ 76 Dodge rating = 4.01% dodge

Heavy Clefthoof set: http://www.thottbot.com/?set=574

You have misunderstance AC, seems you think ac drop its value when you have very high ac.
Here is Math

For a base stats we have a bear

15000 HP, 20000 ac, 30% dodge, it is a typical 70 full blue geared druid w/ some raid buff.
You have 62.58% mitigation from ac, the tank point (total dmg taken before die) is
15000 / (1-62.58%) / (1-30%) = 57262.30

Now, we grant you 14.5 AGI, which = 29 AC and 1 dodge
Then, the tank point is
15000/(1-62.61%) / (1-31%) = 58144.90

Let's have ac instead, you would have 145 AC, make it 797.5 ac in bear form before thickhide
20797.5 ac =63.49% mitigation
TP:
15000/(1-63.45%)/(1-30%) = 58691.2

Which is clear, AC > AGI in term of damage mitigation even w/o thick hide, and even you have 20000 ac.

---

Q u o t e:
You have misunderstance AC, seems you think ac drop its value when you have very high ac.
Here is Math

For a base stats we have a bear

15000 HP, 20000 ac, 30% dodge, it is a typical 70 full blue geared druid w/ some raid buff.
You have 62.58% mitigation from ac, the tank point (total dmg taken before die) is
15000 / (1-62.58%) / (1-30%) = 57262.30

Now, we grant you 14.5 AGI, which = 29 AC and 1 dodge
Then, the tank point is
15000/(1-62.61%) / (1-31%) = 58144.90

Let's have ac instead, you would have 145 AC, make it 797.5 ac in bear form before thickhide
20797.5 ac =63.49% mitigation
TP:
15000/(1-63.45%)/(1-30%) = 58691.2

Which is clear, AC > AGI in term of damage mitigation even w/o thick hide, and even you have 20000 ac.

---

and if you use same item value for sta, you have 326.25 more HP in bear form.
that's
15326.25 / (1-62.58%) / (1-30%) = 58507.76, still better than AGI.

Of course, AGI is more desired because
1. it is related to threat and more crits = more HP from iLotP
2. unlike stamina and ac, which is linear for damage mitigation, agi has a progressive effect, the more dodge chance you have, the more effect you gain from same amount of agi.

Here is the problem, you use DR everywhere,
You think 1% DR from ac == 1% DR from dodge, however, it is not equal. because AC DR and dodge DR is calculated separately.

When you have 70% base DR from AC, and you have 1% more DR. the actual DR gain is
1/30 = 3.3%

When you have 30% base DR from dodge, and you have 1% more DR, the actual DR is
1/70 = 1.4%

I tend to fudge math, so perhaps one of you could remove my ignorance.

Based on all this info, which is better for damage mitigation...

A weapon like earthwarden, with Armor + Defense, or a weapon like the staff of beasts with lots of agility and stam?

We've been debating this in another thread on here.

reported for sticky

Thanks for the info Ranma, looking into it now. I'll edit the post when I get something conclusive.

---

Q u o t e:
Thanks for the info Ranma, looking into it now. I'll edit the post when I get something conclusive.

---

how bout this....

actual DR boost .: DR boost / (1-D) where D was your previous DR

so you went from 65% to 66%, your boost in DR is: 0.01/(1-.65) = 0.029 = 2.9%.

---

Q u o t e:
Ranma brought up some very good points about damage reduction from armor and from avoidance being different, armor likely has much better DR than I show here. I'm looking into it and I'll edit this when I get some conclusive results.

---

Yes. Armor mitigation and avoidance mitigation are not independent, and their effects are nonlinear when taken together. Higher armor means all of the other stats are comparatively more effective, and vice versa. It's a similar comparison to the AP vs Crit discussions, though for mitigation it is vastly more complicated due to there being so many more factors. Basically, I would suggest coming up with a formula for damage taken that is as general as possible and work with that. Expectation values as a function of the mitigation parameters (armor, dodge, agi, etc) based on the probabilistic functions (i.e. discrete random variable of hit/miss/crit/dodge/etc) would be a good start, and from there working with partial derivatives to look at how each parameter affects the overall expectation value.

Since the reductions are NOT independent they cannot be combined so easily.