In T14 normal mode gear, we start out with around 40k AP even at 0 Vengeance.

That said, the calculation is mostly moot. In the steady state it doesn't matter whether you use HoW>HW or HW>HoW. Since their cooldowns are both multiples of three, they clash once (on the first choice) and then de-synch, so they never clash again.

I've been doing a lot of thinking about a "Control" gearing strategy. So far I've only come up with more questions, and not very many answers. I used Theck's work as a base starting point - Avoidance, Mitigation, and Damage Smoothing | Sacred Duty.

It's clear to me that having hit/expertise at ~7.5%, and then going for mastery rather than dodge/parry is a gain in ShoR uptime as well as reducing spikiness. Comparing the gear set #2 and gear set #3, there doesn't seem to be a huge difference in survivability between mastery and haste.

I would really like to see numbers for:

5. Hit/Expertise to 7.5%, then Mastery > Dodge/Parry (0 haste)
6. Hit/Expertise to 7.5%, then Haste > Mastery > Dodge/Parry (maximize haste)

After that, I'd also like to get some numbers on Expertise between the soft and hard caps. I know from (again Theck's work) MATLAB DPS Simulations for 5.0.5 and Q & A | Sacred Duty that Haste is higher DPS than expertise past the cap, but I don't know how each impact's ShoR uptime. If you get more ShoR uptime from Expertise than Haste then I'd like to see a set of:

7. Hit/Expertise to hard caps, then Haste > Mastery > Dodge/Parry
8. Hit/Expertise to hard caps, then Mastery > Dodge/Parry (0 haste)

If #7 or #6 are even somewhat comparable for survivability, they will end up contributing a lot more DPS. In a 10 man group, tank DPS could very well make the difference on a kill, especially with the new vengeance.

I'm not Theck and can't speak for him, but I can take a stab at a quick and dirty answer.

First off, very roughly speaking, per point, Haste will reduce damage taken by about 10% more than Exp. Why do I say this? I'll tell you.

- Lets assume that 1% haste will increase HoPo generation by 1% (so, if we land 85 HoPo generators in a period of time, Haste would increase that by 1% to 85.85).

- Exp is a little better. Assuming Hit Cap but zero Exp, 1% Exp will increase our chance of landing CS's by 1%, from, in this case, 85% to 86%.

- 1% Exp requires about ~340 Itemization points, while Haste requires 425. So, we get 25% more Exp per itemization points than Haste.

- However, Exp does absolutely nothing for Judgment. J is roughly 38% of our HoPo generation. So this cuts Exp's value by ~38%.

So, totaling up:

1.18 (absolute increase vs multiplicative)*1.25 (better itemization conversion)*0.62 (doesn't work on J) = 0.91 So, Expertise is roughly 91% as good as Haste in generating HoPo. Obviously, this will change a bunch based on your conditions. If you add in some more Exp, Exp goes down.

The real issue here, however, is smoothing. Each 1% Haste will make every single HoPo generation opportunity very slightly closer together which will somewhat smooth your HoPo generation, smoothing your damage intake. Each 1% of Exp will instead slightly reduce your chance of having each CS be parried. So the choice is between a very slight reduction in variability each time vs a small chance of a large reduction in variability. I suspect the Exp is superior in this case, but I honestly don't know, and in particular I don't know how big the gap between the two is.

As for soft-cap vs hard-cap on Exp, there's no difference. Each 1% Exp from 0% up to 15% will provide the same amount of HoPo increase. Each incremental point however increases it by a flat amount against an increasingly large base, so its value may appear to slide, but its equally valuable all the way up.

The potential value of Soft-cap vs Hard-cap is that the value of the variability reduction coming from Exp goes down as Exp goes up. I'll illustrate with an example. If you're Hit-Capped and have zero Exp, you have a 15% chance of missing (well, really getting Parried/Dodged) a CS. Your odds of having it happen twice in a row is 0.15*0.15 = 2.2%. A third time drops to about 0.33%.

However, if you soft-cap Exp, your chance of 1 miss is 7.5%. Two misses in a row is 0.56%, three in a row is 0.04%. Your chance of multiple misses (which is where your big sources of ShoR uptime variability comes from) drops pretty far by just soft-capping. In fact, looking at the three-miss level, you get roughly 7/8ths of the value of Hard-capping, in terms of variability reduction, by merely Soft-Capping.

So, to recap, going all the way to hard-cap will increase your damage done and HoPo generation at a steady rate, but the value from a variability reduction standpoint drops off a bit.

As an additional complication, Haste and Exp have a positive synergy with each other. Each additional point of Haste will make Exp better and each point of Haste will make Exp better. So, I suspect the ultimate answer will be some rough rule of thumb in which you want to keep them roughly even or something, but I'm not entirely sure beyond that.

I'm pretty sure this is incorrect. The first 7.5% of expertise removes both parry and dodge. Expertise from 7.5% to 15% only removes parry. Thus it's roughly half as effective as the first 7.5%. Anyway, Theck reran a few sims (I had a PM conversation with him), and the result was that expertise to hard cap is better than haste for ShoR up-time. The remaining simulation he is running is to check the value of Mastery vs the 7.5-15% portion of parry.

Ah, my bad. The first 7.5% of expertise removes dodge only. The next 7.5% removes parry only. So I think you were correct in that expertise should be relatively the same for a tank (attacking from the front) for each point of expertise rating.

Expertise goes up to 15% the first 7.5% removes Dodge then the second 7.5% removes Parry
An empty Hit table includes 7.5% Miss + 7.5% Dodge + 7.5% Parry then 72.5% normal hits and 5.0% Critical.

Obviously not quite as useful for raiding, but the Blinding Light glyph that makes it a 3 second aoe stun could be quite useful for challenge modes where you need to be able to pull and survive large groups of trash.

Exemplar,

Yes, that's exactly how my understanding works as well, though I admit that I'd also never tested it until the abbreviated one I ran last night. The first 7.5% of Expertise removes the Dodge and the next 7.5% removes the Parry. The first 7.5% contributes to spell hit as well but I'm not sure if the next 7.5% does. If you were rocking 0% Hit and 15% Expertise for some reason, would you be spell-hit capped? I think so, but I'm not sure. Also, I believe the first 7.5% Expertise additionally removes Block but I haven't tested it.

Edit - With regard to the relative value of Haste and Expertise, one thing that occurs to me is raid buffs. Its entirely possible that, in a vacuum, the first point of Haste is better than the last point of Expertise in terms of damage smoothing, but we don't raid in a vacuum and the stats make each other better. Raid buffs don't do anything for your Expertise, but they can supply a metric crap-ton of Haste, ~4250 itemization points worth of it for melee. Its possible that buff by itself is enough of a thumb on the scale to make Expertise superior all the way up to Hard cap.

Except that the raid buff provides 0 haste, not 4250 points of it. It is attack speed and thus only boosts white swings. No effect on Holy Power generation at all.

Theck doesn't disappoint: Damage Smoothing: Expertise, Mastery, and Haste | Sacred Duty has the data for larger amounts of expertise, including hard caps. What he found is that capping hit and expertise had a massive impact on our spikes, so much so that at the bottom he even recommends that the optimal start for a control setup is to hard cap both. After that haste and mastery trade blows since they both have their pros and cons.

In the comments someone asked about gemming and whether we should go for stamina or the secondary stat of choice. As I recall, we've usually gone for enough stamina to survive the big stuff then worked on secondary stats. Active mitigation throws a bit of a wrench into that because we can do a lot to prevent damage spikes, but there is still the statistical possibility of shit hitting the fan and us getting nuked. Trinkets will probably be the way to go with that, so I suppose a list is in order:

Typical tank trinkets would be:

[Mogu Rune of Paralysis]
[Quilen Statuette]
[Iron Protector Talisman]
[Bitterest Balebrew Charm]
[Bubbliest Brightbrew Charm]
[Brawler's Statue]
[Vial of Dragon's Blood]
[Jade Warlord Figurine]
[Relic of Niuzao]
[Stuff of Nightmares]
[Lao-Chin's Liquid Courage]

I included the Mogu Rune because a stun will tend to be quite handy in certain circumstances.

Of the others I'm partial to the on-use items that grant actual stats instead of an NPC. [Lao-Chin's Liquid Courage] in particular should be one of our starting trinkets because it's a reputation buy. All of the proc trinkets grant dodge which I've never really noticed while tanking, but extra stats are extra stats.

Oddly enough there are no parry trinkets past ilvl 450 so far in MoP, so if we want parry from a trinket we'll have to go with strength. There are also no armor trinkets whatsoever.

If we look at trinkets that grant expertise, haste, hit, or strength the list expands to include the following. I've added parry values next to the ones with strength. According to the OP 952 strength equals 1% parry, or 888 parry rating before DR, so that's what I'll be going by.

Theck's post below indicates the parry rating for 1% parry is 885, and the strength conversion is ~951.15 strength for 1% before Kings et al, thus it's ~905.86 after. I've adjusted the numbers for strength after Kings to show raid-buffed numbers. Of special note here is strength after kings grants 97.7% the amount of parry as parry rating itself (~905/885). Since secondary ratings get double the itemization on gems we won't really be able to take advantage of this much, but it's nice to note for purposes like trinket selection.

[Zen Alchemist Stone] (5.03% parry, 4455.97 rating equivalent)
[Daelo's Final Words] (7.01% parry, 6211.58 rating equivalent)
[Lessons of the Darkmaster] (4.67%, 4134.54 rating)
[Lei Shin's Final Orders] (2.80%, 2480.53 rating)
[Jade Charioteer Figurine] (1.05%, 933.98 rating)
[Relic of Xuen] (1.05%, 933.98 rating on base, 3.34% or 2957.29 rating on proc)
[Darkmist Vortex] (1.12%, 997.48 rating)
[Iron Belly Wok] (1.19%, 1054.15 rating)

Chances are you'll get some odd looks from wearing these as a tank but you can be safe in the knowledge that those you can't reforge all grant at least 1% parry. The extra oomph to WoG (and SoI if you're using it) might also be helpful.

They all make excellent DPS trinkets as Theck has shown at MATLAB DPS Simulations for 5.0.5 and Q & A | Sacred Duty, so if you're happy with your survivability and just want to kick some ass then any of these are good choices.

Edit: Just for the hell of it I'm going to do a rough comparison of tier gear versus other same slot items to see if they're actually worth it.

Tier pieces are:

[White Tiger Shoulderguards] (exp/mastery)
[White Tiger Legguards] (dodge/mastery)
[White Tiger Faceguard] (parry/exp)
[White Tiger Handguards] (dodge/hit)
[White Tiger Chestguard] (parry/hit)

2P bonus: Reduces CD of Ardent Defender by 60 seconds.
4P bonus: Increases WoG healing by 10% and damage reduction of SotR by 10%

The set bonuses are very nice. AD every 2 minutes instead of 3 will save your life (and likely the raid) plenty of times. The 4P is roughly equivalent to 6000 mastery rating (assuming it's 600 mastery for every 1% like in the OP), but isn't quite there because it doesn't increase block percent too. There is no gear combination in those few slots that will make up for that, which means 4P is definitely the way to go.

Speaking of stats, I expect the 4P to raise the value of expertise, haste, and hit a bit since HoPo generation is worth more.

All of the pieces are good depending on your gearing style. If you want to cap hit and expertise then the legguards are the odd man out with no accuracy stats. Swapping over to [White Tiger Legplates] will give you expertise and mastery. If you'd rather not use a Ret tier piece then the following are all pretty decent options for prot pallies:

[Legplates of Regal Reinforcement]
[Jang-xi's Devastating Legplates]
[Kovok's Riven Legguards]
[Legguards of the Unscathed]
[Articulated Legplates]
[Legplates of Durable Dreams]

[Articulated Legplates] and [Kovok's Riven Legguards] should be noted as items Blizz has taken strength out of and put into secondary stats (parry and dodge respectively).

Thank you for the number corrections Theck.

In other news from Tanking Damage Adjustment Hot Fixes - MMO-Champion BlueTracker, there are some fairly significant changes.

Holy Wrath now deals 100% more damage.
Avenger's Shield now deals 50% more damage.
Seal of Truth and Censure now deal 80% less damage for Protection Paladins only.

It's looking like AS and HW will be our heaviest-hitting abilities once those changes take place.

This also brings up another point: With SoI intended to be our seal for best survival, expertise, haste, and hit would seem to have added value since SoI is dependent on melee swings after all. Last we checked it was 15ppm, so hitting more often would increase the procs.

Finally, on Patch 5.0.5 Hotfixes - MMO-Champion BlueTracker Blizz has changed Symbiosis so that tanks no longer get a tanking cooldown from it. Wrath is replacing Barkskin for us. It might have use in niche cases where we're stuck at range with a target and have AS and J on CD but that's about it.