On the Effectiveness of Various Threat Stats for Tankadins

No, I honestly haven't do0ne anything with this thread in a while...at a minimum I should run numbers for the T6 parses....hopefully a project for this weekend...
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Death and Taxes lates Teron kill sported a prot paladin MT.

I calculated up his TPS earlier for our warriors curiosity. He clocked in at 1187.25 TPS, making use of two Destro Potions and Stratholm Holy Water on cooldown.
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"Misunderstanding the Tankadin is forgivable.

In many ways we are still learning to understand ourselves."

www.joanadark.tankspot.com

E-Peen Parse.





This week's Teron Gorefiend kill:

http://wowwebstats.com/tgbm1q6oxsm3c?s=13439-13623&m

Note:

*I was using only an Adept's Elixer and Elixer of Major Fortitude, NOT a Flask of Blinding Light.

*I was wearing only partial threat gear which sat me at 147 +damage and 18 Spell Hit Rating lower than I would be wearing full threat gear.

*The ONLY group utility I had in my group was Windfury Totem.

*I did NOT have my Ret Paladin as I would normally.

*The fight was exactly 3 minutes and 1.9 seconds long, so I only was able to use Avenging Wrath once.


TPS: 1330.42

IF I had had the ret Paladin in my group that would have been:

TPS With Ret Pally: 1455.82
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"Misunderstanding the Tankadin is forgivable.

In many ways we are still learning to understand ourselves."

www.joanadark.tankspot.com

Joana provided us with lots of nice WWS stats and everyone's been too lazy too look at them until Dorvan did a few days ago and said 40% of our threat is affected by spell hit.

I took a closer look at Joana's parses, and did a double-take:

Consecration: 0% Missed, 6.4% Mitigated (partial resist)

Say what? I looked closer:
151 total dots, 30 partial resists, no full resists(misses). Total partial resist mitigation: 6.4%.

So then I looked at all the boss fights, minus the trash:

Consecration:

742 total dots, 109 partial resists, 6 full resists(misses). Total partial resist mitigation: 4.8%

So, over 742 consecration dots, there were 6 full misses. If we consider that each tick can be missed, that's <1% miss rate. If we consider that there were 6 dots/consecrate, and only the first tick could be missed, that's still only 4.8% miss rate. And in fact, it's lower than that, since there were definitely more than 742/6 ~ 124 casts of consecration.

However, if you look at the # of partial resists + full resists/(total # of dots), you get: 15.5%, which is awfully close to what you would expect from spell miss - precision.

Holy Shield was missed 0%, partial miss 0%.

Seal of Righteousness: 345 casts, full missed 0, partial miss 52.
Again, 52/345 = 15%

JoR: 40 casts, 5 full miss, 0 partial miss.
5/40 = 12.5%

Exorcism: 26 casts, 3 full miss, 3 partial miss
6/26 = 23%

Judgment of Vengeance: 39 casts, 5 full miss, 5 partial miss
10/39 = 19%

Holy Vengeance: 172 dots, 15 full miss, 15 partial miss
30/172 = 17.4%

Anyone wanna take any guesses as to what is actually going on?
At first glance, it seems that Consecration, SoR/JoR/Exorcism/JoV/Holy Vengeance all seem to be dependent fully on spell hit whether they hit FULLY or not.
If they fail the spell hit roll, then it seems to separate into 3 categories:
Almost all partial resists: Consecration/SoR
Almost all full resists: JoR
Half/Half: Exorcism/JoV/Holy Vengeance

But honestly the sample size for the half/half spells is small, though consistent.

For consecration, partial resists turned out as follows:
avg. dmg resisted: 53
avg. dmg unresisted: 193
Percent Resisted: 28%
All the other partial resist totals fall around there, as well.

What does this mean for threat?

For All Full resists(JoR), it's easy, exactly as we've always thought of it:
17% chance to miss, down to 14% from precision. 1% spell hit increases threat 1/86 (1.2%), then 1/87 (1.1%), up to 1/99 (1%).

For All Partial resists(consecration/SoR), we have the following breakdown:
17% chance to miss, down to 14%. Those 14% partially hit at 72% damage, dealing 10% more damage, resulting in 96% overall damage delivered. Each 1% spell hit increases threat 0.28/96 = 0.3%

For Half/Half resists, we have the following breakdown:
17% chance to miss, down to 14%. 7% of those hit at 72%, for 5% more damage, resulting in 91% overall damage delivered. Each 1% spell hit increases threat 0.64/91 = 0.7%

Using Joana's threat breakdown from the previous Teron fight:

All Full Resist Threat:
Judgement of Righteousness- 38974.7 (17.01%)
All Partial Resist Threat:
Consecration- 54163.3 (23.642%)
Seal of Righteousness- 45077.5 (19.676%)
Half/Half Resist Threat:
Exorcism- 21918.4 (9.567%)

Thus, 1% spell hit would have modified this fight by:
0.17*0.012 + 0.433*0.003 + 0.096*0.007 = .0040, or 0.40%.

LMAO. it matches exactly with Dorvan's 40% number. Any speculation as to the nature of all the weird partial resists(which occurred across all the bosses tanked) is welcome.
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Okay, that's really funny. And good analysis!

The odd thing to think of is the amount of threat that is not in any way affected by spell hit or melee hit. That appears to be all the reactive threat, all the threat from casting spells, gaining mana and healing. And (this is the big one) most of consecrate's ticks.The remainder is entirely affected by melee hit.

Also, why are there only 6 dots/consecrate?

As to the analysis, let's go through it again:

Spell damage -- increases the damage dealt by our spells

Spell hit rating -- reduces the frequency of "miss-resists" on spell abilities. The following abilities can be miss-resisted:

JoV 5-stack hit
JoR/JoV
Consecration (partial)

Hit rating -- reduces the frequency of melee attack misses, affecting both our white damage and seal damage (since misses do not proc seals). Averger's Shield and (as of 2.3) Righteous Defense misses are also reduces by hit rating.

Expertise rating -- reduces the chance for our melee attacks to be dodged/parried, having similar effects on our threat to hit rating. Does not affect AS/RD, but does reduce incoming damage slightly due to fewer parries.

Analysis of threat stats:

Spell damage: In a full threat rotation, 1 spell damage provides about .5 tps.

Spell hit: For a very rough look at spell hit I will make the following simplifications:

-- 34.4% of our threat comes from miss-resistable spells (why not 40%? see below)
-- These spells have a miss-resist rate of 17%
-- We have taken the 2.3 Precision talent

Given this set up, 1% spell hit will give us a .344*(.01/(1-.14)) ~= .40% increase in threat
Since 12.62 spell hit rating = 1% spell hit, a single point of spell hit rating would provide a ~.0317% increase in threat. Thus, under these assumptions 1 spell hit rating = 1 spell damage at a threat output of about 1830 tps

Hit rating: The main assumption here is that white damage + SoR account for 35% of overall threat generation. We also assume 6% miss, 6% dodge, and 15% parry by the mob,, which includes precision.

Thus, 1% hit provides a .35*(.01/(1-.27)) ~= .48% increase in threat generation. 15.76 hit rating = 1% hit, so each point of hit rating provides a ~.030% threat increase. In other words, 1 hit rating = 1 spell damage at about 1660 tps

Expertise rating: Here the same assumptions will be used as with hit rating.

1 expertise is -.25% dodge/parry (.5% combined), which provides a .35*(.005/(1-.27)) ~= .24% increase in threat generation. 3.94 expertise rating = 1 expertise, so each point of expertise rating provides a ~.061% threat increase. In other words, 1 expertise rating = 1 spell damage at about 825 tps

Conclusions:

Both hit and spell hit are worse than spell damage and expertise in terms of threat generation, by a large margin (and in reality, until well past gear levels in BT). Expertise compares reasonably to spelldamage once TPS is in the 800s, which is around T5 content levels typically. The order should be, still:

spelldamage > expertise >>>> hit rating > spell hit rating until 800TPS, then it switches to:

expertise > spelldamage >>>>> hit rating > spell hit rating

Some interesting notes to this: this doesn't take into account what getting more white damage (however you do it) would do to threat, which would be an interesting check as well and would improve hit/expertise even further.

Very nice summary.

A couple observations to add from this:

(1) Precision talent provides 0.40%(1% spell hit) + 0.48%(1% melee hit) increase to threat. I will fudge this number up a bit, since 1/83(pre-talented) is slightly larger than 1/86(post-talented). So let's say 0.90-0.92% threat for each point of precision. Thus, 3 talent points in precision is worth only about 2.7% more threat. However, IMO, reducing RD-miss and AS-miss is worth it over reckoning and other talents.

(2) After you pass 800 TPS, you have to move expertise with spelldam. Remember, each has diminishing returns. A point of expertise starts at (0.5%/73%) ratio, but after you get 12 points in expertise, you have (0.5%/79%), thereby diminishing it's effectiveness by almost 8%. Spelldamage based threat should increase by 8% then, too, to catch up.
Everything here is multiplicative, so 1.1*1.1 = 1.21 is marginally more effective than 1.2*1 = 1.20.

(3) Even still, the above considers 1 expertise rating to 1 spelldam @ 800 TPS as even. What matters in the real world is equipment on hand. If you can trade 12 expertise for 6 spelldam while you're only @ 700 TPS, it would be worthwhile, and vice versa.

(4) In the world of itemization points, spelldam = 0.855 points, so tankadins would only want pieces itemized specifically for expertise after 936 TPS, as those same item points spent on spelldam would give greater returns prior to reaching that TPS threshold.


PS> With regards to white damage, I realized today that Might is actually an overlooked blessing for tankadins. 220 AP = 16 DPS = 16 TPS = 2% more threat for 800 TPS tanks. If you're never mana-starved during a boss fight, it might be an option over wisdom, otherwise, if you have too many paladins, make sure you pick it up. 2% threat is still nothing to scoff at.
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This is just a jotting of notes looking over Cordelia's post:

-- Holy Shield does get resisted, it's just that the WoW combated log incorrectly records the event as you resisting the mob's HS instead of the other way around. BoSanc has the same bug.

-- 1 fight seems too small of a sample size for the spell hit data....Consecraation is probably enough, but JoR is definitely too small of a sample, and even for SoR a bigger sample would be nice feel more confident about those numbers.

-- Anyone want to tackle spell hit on SoV? As I recall, I'm not sure that SoV stack refresh resists are logged, so it's going to be a bit trickier...intuitively it seems like spell hit will be more useful for SoV than SoR
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