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4.3 Stamina Conversion Ratios

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4.3 Stamina Conversion Ratios

Postby theckhd » Fri Feb 10, 2012 7:57 am

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.
Last edited by theckhd on Tue Feb 14, 2012 6:31 am, edited 3 times in total.
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Re: 4.3 Stamina Conversion Ratios

Postby Schroom » Fri Feb 10, 2012 8:20 am

wow this is amazing, thank you very much and keep up the great work.
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Re: 4.3 Stamina Conversion Ratios

Postby Lionizer » Fri Feb 10, 2012 11:22 am

Lovely as always theck, thanks. I'll be using this a lot.
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Re: 4.3 Stamina Conversion Ratios

Postby econ21 » Mon Feb 13, 2012 4:21 am

Any chance you chould include fine red gems in this table? I've been following Digren's guide, which recommends fine over defender's.
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Re: 4.3 Stamina Conversion Ratios

Postby Dibdib » Mon Feb 13, 2012 5:32 am

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.)
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Re: 4.3 Stamina Conversion Ratios

Postby theckhd » Mon Feb 13, 2012 6:50 am

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.
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Re: 4.3 Stamina Conversion Ratios

Postby econ21 » Mon Feb 13, 2012 9:06 am

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.
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Re: 4.3 Stamina Conversion Ratios

Postby theckhd » Mon Feb 13, 2012 10:53 am

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.
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Re: 4.3 Stamina Conversion Ratios

Postby theckhd » Mon Feb 13, 2012 12:24 pm

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
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Re: 4.3 Stamina Conversion Ratios

Postby L'ombra » Mon Feb 13, 2012 7:31 pm

I like the latter, so that you don't have to look for the other quality gem value elsewhere.
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Re: 4.3 Stamina Conversion Ratios

Postby Skye1013 » Tue Feb 14, 2012 4:13 am

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.
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Re: 4.3 Stamina Conversion Ratios

Postby poptart » Tue Feb 14, 2012 6:24 am

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?

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Re: 4.3 Stamina Conversion Ratios

Postby theckhd » Tue Feb 14, 2012 6:37 am

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.
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Re: 4.3 Stamina Conversion Ratios

Postby theckhd » Tue Feb 14, 2012 9:37 am

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
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Re: 4.3 Stamina Conversion Ratios

Postby poptart » Wed Feb 15, 2012 5:14 am

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
poptart
 
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