4.3 Stamina Conversion Ratios

Fri Feb 10, 2012 7:57 am

4.3 Stamina Conversion Ratios

Some of you may remember that in past expansions, Meloree and I hammered out efficiency factors for certain gem trades (See Digren's 3.3 Gem and Enchant Guide, for example). I wrote a quick MATLAB script to perform this calculation for several Cataclysm gemming situations.

The idea here is to get the maximum bang for your buck. At high gear levels and/or heroic progression, many tanks are going with a "hit CTC cap, then stack Stamina" gearing strategy. So you would ideally want to gain as much stamina as possible while giving up the least CTC. This thought process is easily encompassed by a "Stamina Efficiency Ratio" of sorts:

Code: Select all: Efficiency = (Stamina Gained)/(CTC Lost)

This is what the MATLAB code calculates. "CTC Lost" is expressed in points of mastery, so changing a Puissant Dream Emerald to a Solid Ocean Sapphire in a blue slot would give you an efficiency of (30/20)=1.5. Avoidance is converted to an effective mastery value by a straightforward CTC conversion - the conversion factor in the gear set used is 3.2814 (so 3 avoidance rating is worth 3/3.2814=0.9143 mastery). Parry and dodge are assumed equivalent for this, so I've used parry throughout for consistency.

The efficiency ratios are listed on the table below. The labels describe the gem trade and any socket bonuses lost in the swap (i.e., "Gem1->Gem2, Socket Bonus Lost"). "EG" signifies that I'm converting one epic gem to another; otherwise blue gems are assumed. Blue to Epic gem conversions aren't considered.

Code: Select all: STA/CTC ratio (in STA per point of mastery) Gem Trade Socket Bonus Blue Epic Def->Sol 4.922 4.856 50 Dodge->40 STA (bracer ench) 2.625 Fin->Sol 2.299 2.299 Def->Sol 30 Parry 1.969 2.207 Fin->Sol 30 Parry 1.703 1.796 Def->Sol + Pui->Sol 30 Parry 1.703 1.796 Def->Sol + Fra->Sol 30 Parry 1.629 1.678 Fin->Sol + Pui->Sol 30 Parry 1.629 1.678 Fin->Sol + Fra->Sol 30 Parry 1.595 1.635 Pui->Sol 1.500 1.480 Fin->Def 1.500 1.480 Fra->Pui 1.500 1.480 Fra->Sol 1.500 1.500 Fra->Sol 10 Parry 1.394 1.414 Pui->Sol 10 Parry 1.302 1.319 Fra->Sol 30 Parry 1.221 1.268 Def->Sol 20 Mast 1.150 1.340 Pui->Sol 20 Parry 1.150 1.190 Fra->Sol 15 STA 1.125 1.200 Pui->Sol 30 Parry 1.029 1.084 Fin->Def 30 Parry 1.029 1.084 Pui->Sol 15 STA 0.750 0.880 Fin->Def 20 Mast 0.750 0.822 Fra->Sol 45 STA 0.375 0.600 Pui->Sol 45 STA -0.750 -0.320

It's a little surprising, but in fact it can be more efficient to forgo the 30 parry bonus in the tier legs/chest and gem stamina in the red/yellow slots (e=1.96+ for red and e=1.7+ for r+y) than it is to swap a Puissant to a Solid in a blue slot (e=1.5). Note however that changing just the yellow gem is worse (which should be obvious).

I've only included gem swaps here that show up in my current gear, so it's not an exhaustive list. If there are any I've left off, please suggest them and I'll add them to the code. Please limit this to gem situations that actually occur in gear - there's no point in adding a (X->Y, 30 mastery) option if there's no gear with a 30 mastery bonus.

Schroom

Fri Feb 10, 2012 8:20 am

Re: 4.3 Stamina Conversion Ratios

wow this is amazing, thank you very much and keep up the great work.

Lionizer

Fri Feb 10, 2012 11:22 am

Re: 4.3 Stamina Conversion Ratios

Lovely as always theck, thanks. I'll be using this a lot.

econ21

Mon Feb 13, 2012 4:21 am

Re: 4.3 Stamina Conversion Ratios

Any chance you chould include fine red gems in this table? I've been following Digren's guide, which recommends fine over defender's.

Dibdib

Mon Feb 13, 2012 5:32 am

Re: 4.3 Stamina Conversion Ratios

econ21 wrote:Any chance you chould include fine red gems in this table? I've been following Digren's guide, which recommends fine over defender's.

I've just quickly worked out the conversion for changing the fine gems in my tier legs and chest, I'll try to remember to do the others when I get home

Fine Ember Topaz --> Solid Ocean Sapphire, 30 Parry bonus = 1.703 stam per mastery

(in case I can't count as good as I think I can: 50 parry * 3.2814 works out to 15.2374 mastery, to give 60 stam / 35.2374 mastery = 1.7027. someone shout if I'm wrong.)

theckhd

Mon Feb 13, 2012 6:50 am

Re: 4.3 Stamina Conversion Ratios

That looks right, a Fine->Solid should be equivalent to a defender->solid + puissant->solid trade (in both cases, +60 stam -20 mast -20 parry). That's already on the list, but I'll add a few of the fine->x trades explicitly.

econ21

Mon Feb 13, 2012 9:06 am

Re: 4.3 Stamina Conversion Ratios

Thanks for the quick response. Looking at the table again, I just noticed there are no fractured gems in there - any chance of adding them, at least for the +30 parry calculations?

I've been following Digren's guide: fractured in yellow and prismatic; puissant in blue and fine in red. Having finally got to CTC cap, I've been making ad hoc 1.5 trades to avoid wasted mastery but it looks like I should change my wrist enchant and break up the +30 parry bonuses first.

theckhd

Mon Feb 13, 2012 10:53 am

Re: 4.3 Stamina Conversion Ratios

I think I covered all the fractured->x possibilities now, and added a few more fine->x options. Let me know if I've missed any.

Questions:
1) Would this be more readable if I split the two-gem conversions off into their own table? Or is it more useful to have everything in one sorted list?

2) Would it be easier to read if I used a fixed-width shorthand notation? For example:

Code: Select all: Def->Sol 4.922 50 Dodge->40 Stamina bracer enchant 2.625 Fin->Sol 2.299 Def->Sol, 30 Parry bonus, EG 2.207 Def->Sol, 30 Parry bonus 1.969 Fin->Sol, 30 Parry bonus, EG 1.796 Def->Sol + Pui->Sol, 30 Parry bonus, EG 1.796 Fin->Sol, 30 Parry bonus 1.703 Def->Sol + Pui->Sol, 30 Parry bonus 1.703 Def->Sol + Fra->Sol, 30 Parry bonus, EG 1.678 Fin->Sol + Pui->Sol, 30 Parry bonus, EG 1.678 Fin->Sol + Fra->Sol, 30 Parry bonus, EG 1.635 Def->Sol + Fra->Sol, 30 Parry bonus 1.629

Or, perhaps better yet, in a 4-column format:

Code: Select all: Gem Swap Socket Bonus Epic Ratio Def->Sol 4.922 50 Dodge->40 Stamina (bracer ench) 2.625 Fin->Sol 2.299 Def->Sol 30 Parry EG 2.207 Def->Sol 30 Parry 1.969 Fin->Sol 30 Parry EG 1.796 Def->Sol + Pui->Sol 30 Parry EG 1.796 Fin->Sol 30 Parry 1.703 Def->Sol + Pui->Sol 30 Parry 1.703 Def->Sol + Fra->Sol 30 Parry EG 1.678 Fin->Sol + Pui->Sol 30 Parry EG 1.678 Fin->Sol + Fra->Sol 30 Parry EG 1.635

I think I just answered my own question there, but I may as well get some confirmation of it before I go and spend half an hour prettying up the output.

theckhd

Mon Feb 13, 2012 12:24 pm

Re: 4.3 Stamina Conversion Ratios

Here are two versions of the four-column data. If anyone has a preference, let me know. I'll update the first post with whichever version is more readable later today.

Code: Select all: Gem Trade Socket Bonus Epic? Ratio Def->Sol 4.922 50 Dodge->40 STA (bracer ench) 2.625 Fin->Sol 2.299 Def->Sol 30 Parry EG 2.207 Def->Sol 30 Parry 1.969 Fin->Sol 30 Parry EG 1.796 Def->Sol + Pui->Sol 30 Parry EG 1.796 Fin->Sol 30 Parry 1.703 Def->Sol + Pui->Sol 30 Parry 1.703 Def->Sol + Fra->Sol 30 Parry EG 1.678 Fin->Sol + Pui->Sol 30 Parry EG 1.678 Fin->Sol + Fra->Sol 30 Parry EG 1.635 Def->Sol + Fra->Sol 30 Parry 1.629 Fin->Sol + Pui->Sol 30 Parry 1.629 Fin->Sol + Fra->Sol 30 Parry 1.595 Pui->Sol 1.500 Fin->Def 1.500 Fra->Pui 1.500 Fra->Sol 1.500 Fra->Sol 10 Parry EG 1.414 Fra->Sol 10 Parry 1.394 Def->Sol 20 Mast EG 1.340 Pui->Sol 10 Parry EG 1.319 Pui->Sol 10 Parry 1.302 Fra->Sol 30 Parry EG 1.268 Fra->Sol 30 Parry 1.221 Fra->Sol 15 STA EG 1.200 Pui->Sol 20 Parry EG 1.190 Def->Sol 20 Mast 1.150 Pui->Sol 20 Parry 1.150 Fra->Sol 15 STA 1.125 Pui->Sol 30 Parry EG 1.084 Fin->Def 30 Parry EG 1.084 Pui->Sol 30 Parry 1.029 Fin->Def 30 Parry 1.029 Pui->Sol 15 STA EG 0.880 Fin->Def 20 Mast EG 0.822 Pui->Sol 15 STA 0.750 Fin->Def 20 Mast 0.750 Fra->Sol 45 STA EG 0.600 Fra->Sol 45 STA 0.375 Pui->Sol 45 STA EG -0.320 Pui->Sol 45 STA -0.750

Code: Select all: Gem Type (empty = unchanged or n/a) Gem Trade Socket Bonus Blue Epic Def->Sol 4.922 50 Dodge->40 STA (bracer ench) 2.625 Fin->Sol 2.299 Def->Sol 30 Parry 1.969 2.207 Fin->Sol 30 Parry 1.703 1.796 Def->Sol + Pui->Sol 30 Parry 1.703 1.796 Def->Sol + Fra->Sol 30 Parry 1.629 1.678 Fin->Sol + Pui->Sol 30 Parry 1.629 1.678 Fin->Sol + Fra->Sol 30 Parry 1.595 1.635 Pui->Sol 1.500 Fin->Def 1.500 Fra->Pui 1.500 Fra->Sol 1.500 Fra->Sol 10 Parry 1.394 1.414 Pui->Sol 10 Parry 1.302 1.319 Fra->Sol 30 Parry 1.221 1.268 Def->Sol 20 Mast 1.150 1.340 Pui->Sol 20 Parry 1.150 1.190 Fra->Sol 15 STA 1.125 1.200 Pui->Sol 30 Parry 1.029 1.084 Fin->Def 30 Parry 1.029 1.084 Pui->Sol 15 STA 0.750 0.880 Fin->Def 20 Mast 0.750 0.822 Fra->Sol 45 STA 0.375 0.600 Pui->Sol 45 STA -0.750 -0.320

L'ombra

Mon Feb 13, 2012 7:31 pm

Re: 4.3 Stamina Conversion Ratios

I like the latter, so that you don't have to look for the other quality gem value elsewhere.

Skye1013

Tue Feb 14, 2012 4:13 am

Re: 4.3 Stamina Conversion Ratios

L'ombra wrote:I like the latter, so that you don't have to look for the other quality gem value elsewhere.

Aye, let's you compare the blue/epic (though obviously the epic will be an upgrade to an equiv blue) and makes it so I don't have to make sure I'm reading "EG" on the correct line.

poptart

Tue Feb 14, 2012 6:24 am

Re: 4.3 Stamina Conversion Ratios

First of all, Theck, strong work, as always.

So, for an up and coming Prot Warrior Alt, is this different because any rating over CTC cap for me turns into "Critical Block" chance instead of just being "wasted" as on a Prot Pally?

What is your thought on the relative worth of Critical Block vs more Stamina for Prot Warriors?

Poptart

theckhd

Tue Feb 14, 2012 6:37 am

Re: 4.3 Stamina Conversion Ratios

Honestly, I can't really answer that with much certainty. My guess is that the mastery->crit block conversion rate is low enough that it isn't worth keeping mastery over the cap, so the same methodology should apply. However, the mastery->CTC conversion is different for warriors (1.5 instead of 2.25). That means that trading dodge/parry for Stamina won't be as large an efficiency boost. For a rough estimate, you should be able to take any of the straight parry->stam factors and multiply by a factor of (1.5/2.25) to get the adjusted value for warriors. The mixed mastery+parry->Stam trades will be more complicated though.

I can easily crank out correct ratios for warriors, if that will be useful.

theckhd

Tue Feb 14, 2012 9:37 am

Re: 4.3 Stamina Conversion Ratios

Including numbers for warriors:

Code: Select all: Paladin Ratio Warrior Ratio Gem trade Socket Bonus Blue Epic Blue Epic Def->Sol 4.922 4.856 3.281 3.238 50 Dodge->40 STA (bracer ench) 2.625 1.750 Fin->Sol 2.299 2.299 2.059 2.059 Def->Sol 30 Parry 1.969 2.207 1.313 1.472 Fin->Sol 30 Parry 1.703 1.796 1.400 1.496 Def->Sol + Pui->Sol 30 Parry 1.703 1.796 1.400 1.496 Def->Sol + Fra->Sol 30 Parry 1.629 1.678 1.432 1.491 Fin->Sol + Pui->Sol 30 Parry 1.629 1.678 1.432 1.491 Fin->Sol + Fra->Sol 30 Parry 1.595 1.635 1.448 1.498 Pui->Sol 1.500 1.480 1.500 1.480 Fin->Def 1.500 1.480 1.500 1.480 Fra->Pui 1.500 1.480 1.500 1.480 Fra->Sol 1.500 1.500 1.500 1.500 Fra->Sol 10 Parry 1.394 1.414 1.346 1.374 Pui->Sol 10 Parry 1.302 1.319 1.221 1.251 Fra->Sol 30 Parry 1.221 1.268 1.117 1.177 Def->Sol 20 Mast 1.150 1.340 1.029 1.177 Pui->Sol 20 Parry 1.150 1.190 1.029 1.084 Fra->Sol 15 STA 1.125 1.200 1.125 1.200 Pui->Sol 30 Parry 1.029 1.084 0.890 0.956 Fin->Def 30 Parry 1.029 1.084 0.890 0.956 Pui->Sol 15 STA 0.750 0.880 0.750 0.880 Fin->Def 20 Mast 0.750 0.822 0.750 0.822 Fra->Sol 45 STA 0.375 0.600 0.375 0.600 Pui->Sol 45 STA -0.750 -0.320 -0.750 -0.320

poptart

Wed Feb 15, 2012 5:14 am

Re: 4.3 Stamina Conversion Ratios

Thank you, Dr. Theck! Excellent work.

Now, if only your ring would become available on my AH for my alt Prot Warrior. Hitting level 85 and putting on your 378 plus the crafted 346 would be much better than putting on the crafted 346 plus the Therazane rep 346 which is the current plan.

But, alas, none have been available for ages on the AH!

Poptart

Maklesh

Thu Feb 16, 2012 4:59 am

Re: 4.3 Stamina Conversion Ratios

I've never been much of a math-head so hope it's not a silly question but; if avg gear (or ilvl) goes up, how does that affect these conversion rates?

Dibdib

Thu Feb 16, 2012 5:22 am

Re: 4.3 Stamina Conversion Ratios

Maklesh wrote:I've never been much of a math-head so hope it's not a silly question but; if avg gear (or ilvl) goes up, how does that affect these conversion rates?

DR would suggest that with better gear (and therefore more overall dodge/parry), the net effect (in terms of actual avoidance lost) of replacing x dodge or parry with stamina would move more in stam's favour. The same wouldn't apply for replacing mastery with stamina as it's not subject to DR.

As for how big a change, well.. smarter brains than mine will have to get their abacuses out.

theckhd

Thu Feb 16, 2012 8:17 am

Re: 4.3 Stamina Conversion Ratios

It's not that large a change within a tier. These ratios were calculated using full T13N gear, so the ratios will be slightly better for parry->stam conversions as you get better gear, and slightly worse if you're in sub-397 gear.

<edit> For example, the conversion factor in T13N is 3.2814, as mentioned in the OP. If you use T13H gear, it goes up to 3.5413. Here's what the results look like for the T13H gear set:

Code: Select all: Gem trade Socket Bonus Blue Epic Blue Epic Def->Sol 5.312 5.241 3.541 3.494 50 Dodge->40 STA (bracer ench) 2.833 1.889 Fin->Sol 2.339 2.339 2.107 2.107 Def->Sol 30 Parry 2.125 2.382 1.417 1.588 Fin->Sol 30 Parry 1.759 1.850 1.457 1.553 Def->Sol + Pui->Sol 30 Parry 1.759 1.850 1.457 1.553 Def->Sol + Fra->Sol 30 Parry 1.663 1.709 1.471 1.528 Fin->Sol + Pui->Sol 30 Parry 1.663 1.709 1.471 1.528 Fin->Sol + Fra->Sol 30 Parry 1.619 1.657 1.478 1.526 Pui->Sol 1.500 1.480 1.500 1.480 Fin->Def 1.500 1.480 1.500 1.480 Fra->Pui 1.500 1.480 1.500 1.480 Fra->Sol 1.500 1.500 1.500 1.500 Fra->Sol 10 Parry 1.401 1.420 1.356 1.383 Pui->Sol 10 Parry 1.314 1.330 1.238 1.266 Fra->Sol 30 Parry 1.238 1.283 1.138 1.196 Def->Sol 20 Mast 1.170 1.367 1.054 1.210 Pui->Sol 20 Parry 1.170 1.207 1.054 1.105 Fra->Sol 15 STA 1.125 1.200 1.125 1.200 Pui->Sol 30 Parry 1.054 1.105 0.917 0.981 Fin->Def 30 Parry 1.054 1.105 0.917 0.981 Pui->Sol 15 STA 0.750 0.880 0.750 0.880 Fin->Def 20 Mast 0.750 0.822 0.750 0.822 Fra->Sol 45 STA 0.375 0.600 0.375 0.600 Pui->Sol 45 STA -0.750 -0.320 -0.750 -0.320

Hespherus

Tue Oct 02, 2012 3:29 am

Re: 4.3 Stamina Conversion Ratios

Will we ever get a MoP version of this?

theckhd

Wed Oct 03, 2012 5:58 am

Re: 4.3 Stamina Conversion Ratios

Maybe? We no longer care about efficiently trading mastery for stamina though, as there's no block cap to dance around. So I'm not sure an updated set of ratios would be all that useful.

econ21

Wed Oct 03, 2012 6:37 am

Re: 4.3 Stamina Conversion Ratios

With secondary stats getting double itemization on gems, I would look at your trinket choices first before deciding to gem stamina. Stamina trinkets are presumably twice as efficient as gems as ways of bulking up.