Armor and Gloves both give you body armor. More expensive, heavier items of both types give you more armor. Unfortunately, you pay a penalty in upkeep and in decreased proficiency. Everyone knows that wearing Heavy Gauntlets with a Leather Apron, or Leather Gloves with Milanese Plate isn't optimal (though it can be funny!), but is it possible to figure out what combinations are optimal?
Yes! It's actually fairly simple to determine which gloves should be worn with any given armor so that you're not being wasteful with your proficiency.
For the match to be optimal, the cost of increasing your body armor by getting better armor should be equal to the cost of increasing it by getting better gloves. Otherwise, you could achieve the same armor result, with less wight penalty, by getting heavier equipment of one type and cheaper equipment of the other. Math incoming: the partial derivatives of cost with respect to the amount of body armor should be equal.
Note: I (and most others) min-max for performance, not gold. So, for the rest of this post when I say 'cost' I mean weight. Specifically, I mean the WPF penalty caused by the weight. This method would work to min-max for gold cost, I just didn't do it here.
What I did:
1) Develop equations for armor weight and glove weight as functions of the armor value that they provide
Plots are of fitted curves used to generate equations.
W = -0.5607 + -0.004811*B + 0.07181*L + 0.007091*B^2 + 0.004546*L^2
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loginW = 0.04838*B^2 + 0.3265*B - 0.06006
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login2) Differentiate the equations with respect to body armor to create functional forms of the partial differentials
You'll get things that look like this:
dW/dA_b = -0.0048109 + 0.014183 * A_b
dW/dG_b = 0.32654 + 0.096766 * G_b
3) Set the equations equal to each other and rearrange them. Now you're ready to plug in your BASE (+0) body armor value and solve for what gloves you should be wearing!
G_b = 0.1465 * A_b - 3.4242
Most likely, the result isn't going to exactly match any gloves. You need to round the value to the nearest pair of gloves. There's a table included in the how-to section below to help with this.
The following things are assumed to be true in this analysis. If any of them are untrue, or have become untrue since this was last edited, the conclusions may be erroneous.
- This is true:
Armor weight
Armor weight modified proficiency = base proficiency * (1 - 0.01 * effective armor weight)
Effective armor weight = 2*head armor weight + body armor weight + leg armor weight + 4*hand armor weight - 10
(Source: WaltF4, updated 31.7.2012 based on the new formula)
This means that every point of armor weight with helmet weight multiplied by 2 and glove weight multiplied by 4 over 10 reduces your wpf by 1%. Or the same put other way, any effective armor weight from the above equation reduces your wpf 1% per 1 point.
- Body Armor, Glove, and Heirloom stats haven't changed since October 23, 2012.
- Only body armors that provide at least 22 body armor were considered in this calculation. Conclusions are likely still valid for armors below this point. The Gothic Plate with Bevor was not considered because the Head Armor stat makes its pricing unique from the other armors.
- Item stats quoted on the website are correct.
1. Determine the BASE (non-heirloomed) amount of body armor provided by the armor type that you're wearing (i.e. if you're wearing a (+3) Heraldic Mail with 43 body armor, the BASE armor value is 38). This is
A_b.
2. Plug
A_b into:
G_b = 0.1465 *
A_b - 3.4242, and solve for
G_b. This is the BASE armor value of the gloves you should be wearing.
3. Determine which gloves BASE armor value is closest to
G_b:
G_b | | Gloves to wear |
x* | | No Gloves |
1 | | Leather Gloves |
3 | | Mail Mittens |
4 | | Mail Gauntlets |
5 | | Wisby / Red Wisby Gauntlets |
6 | | Scale / Lamellar Gauntlets |
7 | | Gilded Hourglass / Hourglass / Polished / Plain Gauntlets |
8 | | Plate Mittens |
9 | | Black Gauntlets |
10 | | Heavy Gauntlets |
* x is the negative of the armor bonus from your intended glove heirloom level; 0 for (+0), -1 for (+1), -3 for (+2), -5 for (+3). This accounts for the fact that, unlike all of the other gloves options, you can't heirloom your bare hands. If you're looking to wear heirloomed gloves it is very unlikely for bare hands to be better (i.e. can't beat 6 body armor for 0.4 effective weight from thrice-heirloomed leather gloves). Setting this negative value makes sure that if bare hands are the recommendation, it's only given when it's mathematically correct.
1. I wear (+3) Heraldic Mail With Tabard which provides 45 body armor. It's BASE (+0) body armor,
A_b, is 40.
2. I plug in
A_b = 40, and solve
G_b = 0.1465 *
A_b - 3.4242 to find
G_b = 2.4358.
3. I determine, from the table, that
G_b = 2.4358 is closest to:
Now I know that with my Heraldic Mail with Tabard, I should wear Mail Mittens. On a related note, does anyone want to trade their (+3) Mail Mittens for my (+3) Mail Gauntlets?
Notes:- Doing these calculations using the BASE (non-heirloomed) armor values is sufficient. Heirlooming armor items affects low tier and high tier items the same way (looms 1, 2, and 3 add 1, 3, and 5 armor points, respectively). This is a uniform shift of the armor-to-weight curve and so doesn't affect the derivatives necessary to match the items up. Justifying this mathematically with equations and what not is possible, but time consuming.
- It seems heavy gloves were nerfed pretty hard when the proficiency penalty formula was changed. If you are only concerned about WPF penalties, then there is no reason to wear anything heavier than Wisby Gauntlets unless you're wearing Milanese Plate.
- Obviously, this analysis shouldn't stop you from choosing equipment for cosmetic reasons. cRPG is boring when everyone uses the same stuff.
Edit 10/24/12: Modified Gloves Base Armor Values table to correctly draw the line between bare-hands and leather gloves of different heirloom levels.
Edit 10/25/12: Removed incorrect information from assumptions.
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