Quantifying Gear Stats

[Digren]

I'm trying to quantify the value of gear based on its provided stats. This isn't easy, and I wanted input to see how valuable this seemed.

For test subjects, I'm looking at the helms on my Stage Three tank list. These are helms sought by tanks who want to gear up for raids.

Some assumptions have to be made to enhance the gear before comparison. If your assumptions differ from mine the comparisons may differ, but here's what I did:

1. All the helms have meta slots and support an enchant, so I ignored both for the purposes of comparison.
2. When I had an identical choice between dodge and parry rating, I picked dodge rating. It's arbitrary. It's probably better to pick some of each to keep the dr ratios about the same, so that it's always easy to compare gear by rating.
3. I matched good socket bonuses with parry/sta, and mastery/sta gems. I considered all of the socket bonuses good except the one for crit rating.
4. I followed the 55% rule for reforging for combat table coverage, meaning that I reforged the threat stat if it was 55% or more of the avoidance stat, and I reforged the avoidance stat if the threat was less than 55%.
5. In all cases reforging was to gain mastery, except where the piece already had mastery. Then I reforged to gain dodge rating as per my arbitrary choice above.
6. I used Theck's derivations thread to identify 7 armor as equivalent to 1 mastery rating, allowing me to account for armor differences.
7. I ignored the flooring effect when converting strength to parry rating. None of these pieces had agility to convert.

With that laundry list of assumptions, I then attempted to calculate three numbers for each piece:

1. Stamina (easy enough)
2. Mastery Rating Equivalent or MRE (including mastery and armor)
3. Avoidance Rating Equivalent or ARE (including dodge and parry rating, strength and agility)

The results are as follows:

Code: Select all

Item                                 S    MRE  ARE
Reinforced Bio-Optic Killshades      512  606  283
Grinning Fang Helm / Crown of Wings  484  438  341
Headcover of Fog                     484  458  321
Helm of Setesh (Heroic)              529  480  219
Helm of the Proud                    529  460  303
Helm of Easeful Death                484  595  146
Anomuran Helm                        514  585  126
Helm of Setesh                       476  446  193

The question that now arises is: Is this usable to guide gear selection? It's not easy to compare S to MRE; it's very encounter dependent. It's not easy to compare ARE to MRE; it depends on diminishing returns.

That said, I make a few observations:

• Helm of Setesh (Normal) has the lowest S, second lowest MRE, and lowest ARE, making it probably the worst piece in the set. This makes sense as a sanity check, because it is the lowest iLvl piece.
• The Grinning Fang Helm / Crown of Wings ties for second lowest S, has the lowest MRE, instead putting most of its iPts into ARE. Given diminishing returns, I would not recommend this piece. Pretty much the same argument applies to the Headcover of Fog.
• The Killshades probably are the best piece overall, despite the second-best S, due to the highest MRE and ARE.
• The DPS helms (Easeful Death and Anomuran) compare very favorably to the "default" tanking helms. I'd take Easeful Death over Grinning Fang any day (gaining 157 MRE at a cost of 195 ARE). Even versus Helm of Setesh (Heroic), the Helm of Easeful Death stacks up well (gaining 115 MRE at a cost of 15 S and 93 ARE).
• Helm of the Proud versus Helm of Easeful Death is the failsafe choice. Both cost the exact same amount from the same vendor (2200 Justice Points). Taking Easeful Death is a gain of 135 MRE at a cost of 45 S and 157 ARE. Rather than being a clear choice in favor of the tanking piece, I actually think this is a tossup, depending on whether you value Stamina or Mastery Rating higher.

Thoughts?

[Digren]

This post has been edited based on the conversation below.

Let's make a few blatant assumptions that ignore content and the scaling nature of DR.

1. Let's arbitrarily say that 1.5 S = 1 MRE
2. Let's arbitrarily say that 1.077 ARE = 1 MRE

The S to MRE ratio is based on Blizzard's weighting, where 15 stamina are equivalent to 10 mastery rating for gem itemization. The ARE to MRE weighting is based on Theck's calculations of mastery to armor and avoidance to armor, and are solely valid for the T11 avoidance assumptions he made.

With those assumptions I can boil the values down to a single stat, I call V. I've sorted the list below in descending order of V.

1 MRE = 1 V
1 ARE = 0.929 V
1 S = 0.667 V

Code: Select all

Item                                 V
Reinforced Bio-Optic Killshades      1210
Helm of the Proud                    1093
Headcover of Fog                     1079
Grinning Fang Helm / Crown of Wings  1077
Helm of Easeful Death                1053
Anomuran Helm                        1044
Helm of Setesh (Heroic)              1036
Helm of Setesh                        942

Assuming you could adjust your own ratios of S, MRE, and ARE, would you use such a value V to create a single list of pieces from best to worst? Would you use a list organized in that fashion?

The original edit of this post used a higher weight for S and a lower weight for ARE. In that form, the DPS helms (Anomuran and Easeful Death) did much better. They have the lowest ARE among the options. For iLvl 346 helms, only the Helm of Setesh is worse with the new ratings, likely because that helm has the next lowest ARE and derives most of its value from its high S.

[econ21]

My initial reaction is that I would use a value V to sort gear if I could figure out defensible weights. The problem at the moment is that, as you note, they are arbitrary. Given that, I don't find the composite V interesting or informative. I do think listing the three sub-indices is very useful and within the context of your guide, would find a "Digren says..." or "Digren's pick" comment very helpful. It would be subjective but that's where we are, whereas using a composite V gives an aura of objectivity that is unjustified. People could always use the sub-indices and their own weights to make their own Vs.

On the issue of the weighting, am I right to think that Blizzard is effectively budgeting for 1.5S=1MRE rather than 1:1? You can get 60 stamina or 40 mastery gems. If so, assuming 1:1 seems to be tilting rather heavily in the direction of effective health. Or is your comparison already adjusting for item points (i.e. you are assuming 15 stamina=10 mastery)? For comparison, Thelmiance's spreadsheet values S=0.37 and MR=0.527, although I am not quite clear where these numbers come from.

https://spreadsheets.google.com/ccc?key ... nI4F#gid=0

The point you make about combining armor and mastery is interesting though, as we did have rough and ready rules for comparing armor and stamina based on effective health for wotlk (I think it was often assumed 10AV=1S or thereabouts). Have you derived your 1:1 weighting from something similar?

Likewise, I wonder where 0.6ARE=1MRE came from? (You said the stamina/mastery weight was arbitrary but not this one). One common metric would be expected damage reduction. By this criterion, Thelmiance puts MR=0.502 and AR=0.461 for tanking at L85. Are you sure you are not still thinking in terms of L80 ratings, as your relative weights look rather similar to Thelmiance's at this level. Now, I admit damage reduction probably undervalues mastery relative to avoidance because it does not recognise that mastery leads to smoother damage which is good for survival and for healer mana.

One format I was thinking you might consider for your gearing guide is to provide "best for X" labels like you do in the gear enhancment guide. You could have "best EH", "best block cap", "best DR" and "best threat" with a "Digren's pick" tying it altogether.

[theothersteve7]

With that many "best" labels, they start to lose a bit of meaning, and there would be an awful lot of overlap.

Stat weights could work. You might want to calculate them based off a couple different EH:Mitigation ratios. Heck you could add in a Threat value as well, that would be easy to calculate since you could mostly rip the numbers from the matlab thread. Or just give each piece the three scores.

Also it's worth noting that reforging messes with those numbers a bit. You might want to assume proper reforging before you calculate the numbers.

[Digren]

Thanks for your replies.

I do think listing the three sub-indices is very useful and within the context of your guide, would find a "Digren says..." or "Digren's pick" comment very helpful. It would be subjective but that's where we are, whereas using a composite V gives an aura of objectivity that is unjustified. People could always use the sub-indices and their own weights to make their own Vs.

I do plan to add such suggestions, but I wasn't at a point yet where I was comfortable making them. This process helps me gain that comfort. Your concerns with the pseudo-objectivity of V are noted.

On the issue of the weighting, am I right to think that Blizzard is effectively budgeting for 1.5S=1MRE rather than 1:1? You can get 60 stamina or 40 mastery gems. If so, assuming 1:1 seems to be tilting rather heavily in the direction of effective health. Or is your comparison already adjusting for item points (i.e. you are assuming 15 stamina=10 mastery)? For comparison, Thelmiance's spreadsheet values S=0.37 and MR=0.527, although I am not quite clear where these numbers come from.

https://spreadsheets.google.com/ccc?key ... nI4F#gid=0

I was indeed assigning 1 stamina = 1 mastery rating. I did not go back and check to see if this assumption, made to calculate V, meant that my initial assumption to match socket bonuses was in conflict. However, when I was making my observations in the first post, I found myself continuously equating S to MRE. This is likely a bias on my part. Not stacking stamina in gem slots makes me feel like I have moved sufficiently away from effective health. Pushing down the weight of stamina compared to mastery rating seems like overkill. Again, I don't think there's one true answer yet.

Likewise, I wonder where 0.6ARE=1MRE came from? (You said the stamina/mastery weight was arbitrary but not this one). One common metric would be expected damage reduction. By this criterion, Thelmiance puts MR=0.502 and AR=0.461 for tanking at L85. Are you sure you are not still thinking in terms of L80 ratings, as your relative weights look rather similar to Thelmiance's at this level.

Both statements were blatant assumptions. I just left the word "arbitrary" off the second. I haven't reviewed Thelmiance's numbers. Theck's numbers in the Derivations thread equate 7 armor to 1 mastery rating, but he also approximates 6.5 armor for 1 mastery rating using avoidance levels assumed for a T11 tank (aka a stage four or stage five tank on my scale). I don't know how well that compares to a stage three tank, but using both numbers then 1.077 ARE ~ 1 MRE. Oops! I meant to give ARE a lower value than MRE. My text is wrong. My original assumptions were:
1 S = 1 MRE = 1 V
1 ARE = 0.6 V

As you can see, these assumptions make 1 ARE of lower value than 1 MRE. This is what I used in the math, but not what I printed in the post.

Also it's worth noting that reforging messes with those numbers a bit. You might want to assume proper reforging before you calculate the numbers.

All of the above assume reforging already, using the stated methods.

I'm going to edit my second post to correct the typo and adjust the weights.

[Digren]

I think that the revised post two above is now a good starting point. I wanted to post another set of V weights though and see what that does to the recommendation order.

1.5 S = MRE seems to undervalue stamina to me. Yes, it's probably EH bias, but it also ignores a few concrete items, such as the fact that almost every encounter has some amount of unblockable damage. I'm going to increase the value of stamina by arbitrarily changing this ratio to 1.2 S = 1 MRE.

Likewise, 1.077 ARE = 1 MRE means that avoidance is 93% as good as mastery rating. That may be true for damage taken at T11, which was Theck's calculation, but it's not as good for combat table coverage, which acts to smooth damage taken and ease the healing burden. I am going to lower the value of avoidance relative to mastery by arbitrarily changing this ratio to 1.2 ARE = 1 MRE.

My new values for V are thus

1 MRE = 1 V
1 ARE = 0.833 V
1 S = 0.833 V

Code: Select all

Item                                 V
Reinforced Bio-Optic Killshades      1268
Helm of the Proud                    1153
Headcover of Fog                     1129
Grinning Fang Helm / Crown of Wings  1125
Helm of Easeful Death                1119
Anomuran Helm                        1118
Helm of Setesh (Heroic)              1103
Helm of Setesh                       1003

Interestingly, that didn't change the value order at all, though it did reduce the differences between individual pieces.

[yappo]

I'd split it into two types.

Spiked to death and pummeled to death.

In the first case stamina wins hands down (possibly augumented by armour if the spike comes in the form of a two ton brick dropped on the tank)

In the second case stamina is of (almost) no concern. The tank will stay alive until the healer runs out of juice, or tank health will slowly deteriorate along a linear curve until either healer runs out of juice or tank runs out of health.


Assuming that armour is, in the long run, constant (your helmets would indicate that armour is only a function of ilevel), we can disregard it for any item not splashing armour as a gimmick (read armour trinket).

This makes calculations a LOT easier. Misses (avoidance), blocks and in-your-face -attacks all damage the target for the same amount no matter what TYPE of gear the tank is wearing.

All misses do zero damage per second.
All blocks do K damage per second.
All in-your-face do 1.7 X K damage per second.

Assign a value to K.
Assign a swingtimer and calculate N, the blocked damage taken per swing.

Compare 2 X 1.7 X N (two hits in a row) with M% of tank health. M basically giving the lowest amount of health a tank experiencing spiky damage will ever see during the course of a fight. You now see if the gear-set is sufficient for bad luck in a fight where tank-health resembles the ICC-tanking rollercoaster.

If M is very low (under 50%) and the tank would STILL survive a double in-your-face, then this is not a fight with spiky damage. Proceed to pummeling calculations.

For pummeling calculations you need to invent a healing-received-per-second number, A. Make A a sustainable number for healers.

Calculate damage-taken-per-second from K and the percentages from misses, blocks and in-your-face. Call it B.

Calculate B - A = C. This is the loss of health per second.

Lowest C is the best gear for pummeling fights. Remains to see if it's good enough.
If A is unknown, lowest B is probably still the best gear.


This has some results as well.

If C is negative you're home free. Start regemming for threat, cute colours or whatever makes your raid happy.

If C is positive, but multiplied with the number of seconds for a given fight still is lower than starting tank health, you're still good to go.

If C is positive and multiplied with the number of seconds for a given fight is higher than starting tank health (which is likely), then you have a problem that can only be solved by increasing A (likely running your healer out of mana), increasing starting tank health or start doing funky math involving the use of cooldowns and other gimmicky lifesavers. This is part of raidplanning, and I don't know squat about running numbers for raids.
Still, lowest B is best for a pummeling fight.


All in all, two sets of easily quantified gear stats. Should probably include frantic gemming and enchanting in order to draw one of the below as extreme as possible.

1) Highest health wins.
2) Lowest damage-per-second wins.

[yappo]

Short addendum on pummeling:

You can do this per gear-slot as well.

By arbitrarily assigning a baseline avoidance and block to a gear-set representing the tierlevel the specific item (gemmed, enchanted and reforged for maximizing the lowering of damage taken per second) you will get a contribution value for the item in question.

Say 27% avoidance and 50% block for the typical level 3 tank. This allows you to handle DR on avoidance.

To make it even easier, always assume 1000 blocked damage taken per second. After all the numbers will scale linearily with actual damage, and you can leave the healer-calculations to actual encounters.

[Maelsstrom]

For mitigation and avoidance calculations, you can take averages and determine the relative values (for mitigation/avoidance) of strength, dodge, parry, agility, armor and mastery. If parry-haste is turned on, you need to make some other assumptions to work expertise into the picture but as of today it's reasonable to assume it has no damage reduction benefit.

The challenge is to mate this with stamina. If you take the WOTLK-era EH calcs, you can make an assumption about how many damage in the fight is physical and how much is magical or bleed and calculate a time-to-live value of stamina in terms of armor. Since you worked out armor's relative value already, now you've linked stamina to all mitigation/avoidance. Blizz has said that standard dragons are intended to be 60% physical, 40% magic, so that's what I use in that calculation. It's possible that the majority of fights are more than 60% physical but I've not seen any data to support one way or the other. After a few raid fights I'll have some better info. The only data point I have today is that Argaloth is around 70% physical.

The problem with that is that it reflects only the spike damage cases and generally will result in overvaluing stamina -- which was fine in WOTLK, not sure if that's appropriate in Cata. I do this calc this way and then weight the stamina by only 75% of what I calculate. It still results in favoring stamina heavily. Personally I also factor in threat because while threat is not a critical stat these days, it would be wrong to discount it entirely lest we have a gear set with 0 hit and 0 expertise. The intent is really to find the most favorable and efficient gear pieces...these weightings will result in favoring pieces that have underbudget strength and, in some cases, rings/necklaces/etc that have agility rather than strength.

Intuitively and at risk of stating the obvious, one should stack stamina until they're convinced they are not dying of spike damage...and then, and only then, should one trade back stamina in favor of damage reduction stats. I plan to review each and every death and assess whether it was because healers were gassed on mana or whether it was truly a situation of inadequate EH and adjust from there.

[econ21]

Thinking about it a bit more, if I were to compute a V it would be based around changes in H/(1-EDR) where H is hitpoints and EDR is expected damage reduction, incorporating % avoidance, A, % damage reduction from armor, Av, and % block, B. For physical damage:

EDR=(A+0.4B)(1-Av).

I don't know what we should call this - I'd like to call it effective health, but that term is already taken so something like DR adjusted health would have to do. It's a measure of how much damage output you could face before dying (absent healing).This is the kind of calculation I was doing to compare stat vs mastery gemming:

http://maintankadin.failsafedesign.com/ ... 90#p635592

I think Theckhd has already done the heavy work required to implement this kind of approach. His recent armor vs mastery/avoidance thread linked to in the OP essentially covers the EDR part. To trade off that with stamina, we could use the armor vs stamina trade-offs he derives in his effective health done right thread:

http://maintankadin.failsafedesign.com/ ... =viewtopic

As Maelsstrom says, it will depend on how much damage is physical. If it is all physical, 1 stamina=8.59 AV. The 40% magical figure seems a little high to me, but if it were true, theckhd's figures imply 1 stamina=14.31AV. Personally, I tend to go with 1stamina=10AV (about 15% magic damage) and so if 1 mastery=7AV by Theckhd's calculations, we are pretty close to Blizzard's weighting of 1mastery=1.5 stamina.

Maelsstrom and Yappo are right, this will overvalue effective health relative to damage reduction if Cataclysm raids do tend to be more "death by pummelling" than "death by spike". But for a gear guide, a presentation of the value of gear in terms of (a) effective health; (b) expected damage reduction; and (c) a composite V along the above lines would be informative.

[theckhd]

I think that EH-like metrics are of fairly limited usefulness right now. For the most part, bosses are not slamming you for 80k+ hits, and if they are, you're supposed to be using cooldowns to prevent it from happening.

The other problem with EH or TTL metrics is that they neglect healing. If we learned anything from the Armor vs. Stam debate, it's that healing grossly inflates the value of mitigation effects like armor or block. This effect is magnified even further by the way Cataclysm tanking is designed (generally slow whittle-down deaths over 5-10 seconds rather than damage spike deaths in 2-3 seconds).

I've been wary of making a direct Stamina->Armor/Mastery comparison in the derivation thread for this very reason (also, I'm a bit gun-shy given what happened last time we naively wandered into this territory). My impression is that the relationship varies significantly enough that a single value really won't suffice; if your stamina is low enough that you're vulnerable to bursts (completely possible in blue 346 gear), you'll value stamina more than someone in full 359 gear who's above the burst EH threshold.

[inthedrops]

I would not use a "single value list" to pick a piece of gear. What I would find useful however is a list that tells me of all the pieces, which has the largest gain in X and at what costs to Y and Z. X, Y, and Z usually being stamina/armor, mastery, and avoidance.

[yappo]

I would not use a "single value list" to pick a piece of gear. What I would find useful however is a list that tells me of all the pieces, which has the largest gain in X and at what costs to Y and Z. X, Y, and Z usually being stamina/armor, mastery, and avoidance.

We'll likely be forced to tweak this type of list for each content-patch.

For the current one overall comments would suggest we can focus on two types of gear. Unavoidable damage (or huge spikes of avoidable damage) corresponding to a stamina-centric gear-set. Avoidable damage portioned out to allow statistics to work in reality, corresponding to a mastery/avoidance-centric gear-set.

If I've read things correctly there are zero encounters favouring a threat-centric gear-set, so we can proably leave that aside for the time being.

If, and only if, the community here comes the the conclusion that there are currently zero encounters favouring a stamina-centric set (given a tank in mostly T11 quality gear), then we can pretty much give a single digit for a piece of gear that only takes into consideration its contribution to mastery/avoidance.

[Digren]

I think the huge spikes are supposed to be addressed now with cooldowns, leaving only the (minimum stamina threshold plus) mastery / avoidance set as the only required gear set.

[econ21]

In practice, perhaps the stamina vs mastery issue is not so important for a gear list? The 246 helm with the +45 stamina bonus seems something of an exception: most gear of the same ilevel has the same stamina and we choose based on the secondary stats. Stamina vs mastery/avoidance trade-offs seem to arise mainly with gemming and with trinkets, which have always been treated differently from a one dimensional "best in slot" gear list.

Personally, what I would find useful in a gear list would be a single measure of expected damage reduction: combining the mastery and avoidance stats, after reforging. That's not easy to eye ball from the wowhead item tool tip (given the conversion factors, diminishing returns, reforging etc) so having consistent formal calculations provided in a guide would be useful. It is not definitive - people are likely to prefer mastery to avoidance, for similar levels of damage reduction, because it smoothes out damage. But it is an important stat to know and is intuitive, not based on an arbitrary weighting.