It is not about uptime in the sense of seconds it is up, it is about reduced attacks per time period. For example, if you have 0 avoidance and get hit once every 2 seconds, in 1 minute time (BS cooldown) you have reduced 3 of the 60/2 = 30 attacks, which is 10%. If you get 33% avoidance, you take on average only 20 hits, meaning you BS reduces 15% of all incoming attacks. In this sense BS increases in value as avoidance goes up.

Bone Shield also increases the Blood Shield per Damage taken ratio. Eg. if you have a Blood Shield for 25k, and you get hit for 50k, you absorbed 50%. If you use Bone Shield, you get a shield for 25k on a damage taken of (50k - 20% =) 40k = 62.5% absorbed. Also note that after the absorbs, in the first scenario you get hit for 25k, while in the second you get hit for (40k - 25k) 15k, which is 40% less, while Bone Shield by itself only provides 20% reduction. With the new Bloodshield stacking, you can also increase the average value of the Blood Shield by increasing your avoidance.

As you can see there is quite some synergy between Avoidance and Bone/Blood shield value.

But BS still only reduces 3 attacks per minute regardless of your avoidance (unless you get hit less than 3 times outside the ICD of course, but that isn't going to happen). Why does it matter what percentage of attacks it reduces when the absolute number of reduced attacks stays 3?

Yes, it does. But you have to time it properly and use Bone Shield in the Blood Shield window and not before so your potential Blood Shield size does not get 20% smaller. This is somewhat true of any damage reduction CD like IBF, DRW and even AMS; use them in the Blood Shield period if you can, not before.
I still don't get how this behaviour would make avoidance stacking for Bone Shield any more valuable though. :/

Honestly, the only situation I could see Bone Shield/avoidance to be useful for is when you are fighting a boss with magic damage in short intervals, like every 10-15 seconds. Avoidance might help you keep Bone Shield for 2 magic bursts there but that's pretty much all it does. Mastery might still eclipse avoidance stacking because magical damage contributes to bigger Blood Shields etc.

Don't get me wrong, I am not saying DKs won't be stacking avoidance. As a matter of fact with the Death Strike nerfs (Scarlet Fever requiring a U rune) and the 5% heal nerf avoidance might become better than mastery for most encounters anyway. DRW and Swordshattering would also synergize pretty well in such a setup because they add undiminished avoidance (I have to admit that I use DRW as a glorified threat CD right now; if I had more avoidance it would be more powerful as a survival CD). Nothing of this has to do with Bone Shield though.

Well, Bone Shield does kind of sync well with DRW too. A great example is Cho'Gall. His Shadow Orders do those three aoe pulses. With Bone Shield up and high avoidance, I can keep BS up longer and reduce more damage. This also lets me save AMS for Flame Orders since I'm (pretty sure) that those are direct damage that takes off BS charges and the flame attacks cannot be avoided or blood shielded.

I prefer avoidance (it also helps on heroic fights!). I reforge all hit/expertise to parry/dodge and keep the mastery that is present on an item.

It matters because you have a relative amount of damage taken vs. an absolute amount of damage reduced.

The damage that BS reduces is indeed only dependant on the amount of damage from the boss's hit (ie. in one minute, you take 20% reduced damage on 3 hits regardless of avoidance), but that doesn't mean the _value_ of the BS is always the same:

If you take 100 hits in 1 minute (not likely but easy to make a point), BS reduces 20% of the damage on 3% of the hits, which is a laughably small number making it a useless CD. On the other hand, if you take 3 hits in 1 minute (also not very likely), BS reduces 20% of the damage on 100% of the hits. Ie. the larger the amount of hits you take, the weaker BS becomes, and vice versa, the fewer hits you take, the stronger BS becomes.
The effectiveness of BS therefor scales with avoidance, meaning that the question that sparked this entire discussion ("is it worth stacking avoidance to improve BS, since BS value will increase by 33% next patch") is a valid question.

From my personal napkin math it seems the value of BS (which I calculated as "damage reduced by BS divided over total damage taken") scales (roughly) inversely proportional to percentage of unavoided hits. It has a base value at 0 avoidance depending on number of incoming attacks, and the value from then on is very close to base_value / (1 - avoidance), with less than 2% deviation, which might easily be attributed to rounding errors in the program. This correctly predicts that at 50% avoidance, BS reduces relatively twice as much damage compared to 0 avoidance (as it still reduced 3 hits, but the total amount of hits is halved).

Note that damage taken per boss hit has no influence on the value, as you would expect, since both the damage reduced due to BS _and_ total damage taken scale identically with damage per boss hit and cancel eachother out in the value calculation. Of course in absolute terms, the amount of damage reduced depends entirely on boss damage per hit, and indeed does not take avoidance into account (at least for any obtainable amount of avoidance).

Also note that this calculation does not take Blood Shield into consideration, which I think would only improve the scaling from BS with avoidance even more. However Blood Shield value is very hard if not impossible to calculate, especially with stacking shields, so I will leave it at this for now.

Avoidance also increases the uptime of Blood Shield, making it easier to time Bone Shield in that window and subsequently, increases the chance to stack a Blood Shield during the Bone Shield window. Though the Bone Shield reduces the Blood Shield value by the same amount it increases the value if it was up while the hit landed, with Blood Shields now stacking you can get 2 Blood Shields up from 1 damage source, meaning Bone Shield reduces Blood Shield value by 0.2x but increases the value by 2* 0.2x if you stack it twice, or 3* if you stack it 3 times, etc. All of this scales with avoidance, since the more you have, the more often you can get multiple stacks during that window.

In the end, I do not know wether stacking avoidance is the best way to go, neither do I know if the BS changes will tip the scales in favour of one or the other, but I can at least say that yes, BS does increase in value depending on your avoidance.

I still don't quite get how the value of Bone Shield is increased by avoidance. We can use Bone Shield for 2 things: Mitigate a non-avoidable ability (for example Electrocute on Nef) or to reduce overall damage taken. The former is burst mitigation and the latter is "just" saving healer mana.
Since your avoidance doesn't matter in the former case in terms of how valuable BS is, I think we can focus on the latter aspect. And here is what doesn't make sense: You still only reduce 3 melee swings by 20% with Bone Shield regardless of your avoidance because only the absolute reduced damage matters for this. What am I missing?

Actually I addressed that in another post on this page. The gist of it was that there are just no encounters where this seems to matter because most of the non-tank damage abilities either still take a charge from your Bone Shield or don't matter as much in the overall picture. Now maybe this changes in heroic modes, but for normal modes I can't think of any boss where it would have been useful. As I said before, the only time I could see it being useful is if you can carry over your Bone Shield to cover 2 magic burst abilities (i.e. Ignacious breath possibly since he casts it pretty regularily and likes to charge off so you would only need to avoid a few swings inbetween them).
Does anyone have a different experience in Bone Shield usage (the Chogall example from Mild Confusion was a pretty good one actually)?

EDIT:

Just so I am clear, are you refering to these 2 scenarios here?

1) 2 Death Strikes in a row after eating a huge burst then popping Bone Shield (presumably with Blood Tap)
and/or
2) Death Striking as usual but getting a stacked shield just due to avoidance and lower damage taken from Bone Shield?

If it is 1), then I could see scenarios where this would be useful but it would probably end up more valuable for a mastery stacker for bigger shields. If you are refering to 2) then doesn't this mean the boss didn't get through your first bubble to begin with and you are now stacking up min heal Blood Shields? That doesn't sound particularily effective.

But now that I think of it, stacking Blood Shields plus heavy avoidance gemming could probably be useful for some niche fights where you can build up a big Blood Shield just through min heal DSes (off tanking and waiting til your assigned mob spawns or something) and then popping Bone Shield and relying on that plus avoidance to keep up the shield for quite a while since fully absorbed damage does not expend a Bone Shield charge. Sounds interesting but it's probably not anything that will come up in more normal scenarios.

I will concede in this point. You are correct when evaluating Bone Shield by itself. But with Blood Shield in the mix this does get more interesting:

I was talking about scenario 1.
In this case, the percentage of Bone Shielded hits taken compared to Non-BS hits does play a part in determining the value of avoidance, the reason being that Bone Shield uptime in % of hits taken doubly affects the Blood Shield, ie. you take 20% less damage and your Blood Shield is 20% larger. When taken on its own, it is true that avoidance does not improve the absolute reduced damage from Bone Shield, but when adding in Blood Shield this is not the case.

Let's assume that you always have enough time to get a Blood Shield in between Bone Shield charges. Bone Shield affects the stack of Blood Shields multiplicatively. At 0 avoidance, you get 3 times a +20% size on a single stack every time. The more avoidance you have, the larger the chance to stack a Blood Shield multiple times. When you get 2 DS's stacked without expending a charge, you get a shield that is 2.4 times the value of a single stacked shield, meaning (if you subtract a "non-BS hit Blood Shield) you get an additional 0,2 times a single Blood Shield size compared to the non-avoidance scenario. Every time you stack another without consuming a charge, the amount of Blood Shield you get "for free" from Bone Shield/Blood Shield synergy increases. Also avoidance helps with making sure you have a Blood Shield up for each Bone Shield charge to make use of.

But even at scenario 2, with Bone Shield up and some avoidance streaks, you can get a fairly respectable Blood Shield. For example Chimaeron melees fairly slow, where if you avoid/miss 3 in a row you can already have a couple of DS's on him. This is also a fight where you will be able to stack Blood Shield while offtanking (potentially with Glyph of Dark Succor?).

Yes, considering avoidance to reduce in value when inflated is a side-effect of viewing the issue backwards. You shouldn't be thinking "how much avoidance do I have" you should be thinking "how much less damage am I gaining". As pointed out, going from 0% to 1% avoidance is a 1% damage intake reduction. Going from 99% to 100% is an infinite one. DR was implemented to counter this exact phenomenon, it's mostly there to counter tanks getting exponentially better with avoidance. When first implemented, DR wasn't entirely enough to keep avo-stacking from being the superior choice. During late LK it was mostly fixed, and if you recall we saw a spike in Armor and Stamina stacking back then.

Also maintain in mind, interrupt duty is dependent on Hit, not expertise. Capping hit and avoiding expertise is a lot more feasible as an intermediate stage compared to (1) having as little as possible of either or (2) capping both. It is also a neater solution; Expertise soft-caps, it never caps per se. Unless your avo is gimped you'll always have to deal with ~4% parry. This is my main beef with the Plague-strike issue; IT always hits when hitcapped, PS doesn't. That's a compromise that, to my knowledge, other tanks don't have to deal with.

When setting up/learning my CD rotation for Nefarian (P1+P3) I noticed that if I use BS when he is about the cast a breath and then pop DRW, Bone shield will sometimes last until the next breath. Considering that his shadowflame does around 100k damage and is the main reason a DK Tank will die (since you have hard CDs for the Lightning Machine), this is a good example of where avoidance and boneshield work together to greatly increase your survivability.

The Downside is, I have to interrupt alone on my platform (10m) and therefore have to be hit capped which basically cripples any attempt at stacking too much avoidance. In 25m however it could look different.
EDIT: My Bad, the mobs are only level 85. Thanks a lot for pointing that out Draginclaw!

The only one I can think of is Vindication, the difference here being that Pala tanks will be spamming CS and HotR anyway, making the uptime basically 100%. When a parry occurs, it does not matter much. All other debuffs are not parryable (well not counting Infected Wounds, because you will have to be one unlucky Feral if it drops off due to boss parrying every maul and mangle attack for 30 seconds).

With PS competing with the same resources as Death Strike, DKs will be putting off applying Blood Plague untill the last possible moment, meaning if you get parried then, your debuff drops off.

Did some testing on Blood Shield stacking through duels (against a Warrior) on the PTR just now .

My relevant stats
Mastery: 100%
HP: 126423

One of several tries (with near identical results):

Death Strikes used (minimum heals only (7%)): 12 = 84% of HP (or presumably 106195 damage absorb as a stacked shield).

Ammount actually absorbed: 42950 = 33% of my HP, thus this seems to be the cap.