Armor cap and You - The definitive guide

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Just so that this doesn't get buried into the FMT thread..

What is Armor cap and why should I care?
The displayed armor rating in Skyrim isn't very informative, other than more being obviously better. However, there's a hard cap in how much armor you can have, and everything above this cap is wasted. The cap is at 567 displayed armor for 80% physical damage resistance, and the percentage works linearly in that every point of displayed armor equals 0.12% of resistance. Every piece of actual armor worn (ie. not clothes, circlets or such) also gives +25 hidden armor rating so that 567 displayed + 100 hidden (with all four armor pieces) = 667 times 0.12 = 80.04%, truncated to 80%.

Since the damage reduction increases linearly, the effect the armor has on YOUR effective health increases much faster, making every single point of armor more important than the previous all the way to the cap. For example, going from zero reduction (all clothes) to 25% reduction (208 armor) increases your effective health by just 33% (1 divided by 0.75=1.33), but if you're already at 50% reduction and get the same 25% added from there, you just effectively doubled your health (0.5 divided by 0.25=2) and compared to having zero reduction, you now endure FOUR times as much damage before dying. Thus at 80% reduction, your health points are FIVE times as durable against physical attacks, compared to wearing clothes all around. That is quite a difference!

Any other damage type is unaffected by your armor rating, requiring either Fire, Frost, Lightning or Poison resistance to counter. Magic Resistance covers the first three as well. Finally, you can get resistance all the way up to immunity (100%) against Diseases, of which Vampirism is potentially the most difficult to counter unless you cure it in time. But of all damage types in Skyrim, physical is by far the most common and usually the most dangerous.

So what do I actually need to get there?
To set a benchmark and a starting point, take the Daedric armor set (including shield) with maxed Juggernaut, Well Fitted and Matching set perks from Heavy armor tree together with maxed skill in Heavy Armor and all armor pieces improved with maxed Smithing and Daedric Smithing perk. This puts you at 856 displayed armor, ie. quite a bit over what you need. Therefore, there's quite a bit of slack in what you could use, down to using Steel set (655) with Heavy armors or if you want Light Armors (with corresponding perks & skill), Elven (or better) set is all you need as it tops at 583.

For the record, the actual armor formula is as follows (from UESPWiki):
Displayed armor rating = (worn armor rating + item quality) * (1 + 0.4 * (skill + skill effect)/100) * (1 + Custom Fit or Well Fitted + Matching Set) * (1 + Agile Defender or Juggernaut)
+ (shield armor rating + item quality) * (1 + 0.4 * (skill + skill effect)/100) * (1 + Custom Fit or Well Fitted + Matching Set)
+ armor effects

The important value here being 1.4 (skill) x 1.5 (matching set et al) x 2 (the first five perks) = 4.2 times base value when everything relevant is maxed.

So, I NEED maxed armor perks AND a shield to enjoy the benefits?
Not at all. There's quite a bit of other means of attaining the armor cap, although the most powerful means revolve around pushing Smithing to its limits with a bit of help from Enchanting and Alchemy. At the extreme end, all you need is just one (1) perk, total, in all of Smithing and Armor trees, without shield. Nice, eh?

With the introductions out of the way, let's get to business.

Part one: Smithing improvements
Maxed Smithing skill without any perks enables you to improve (upgrade) any non-enchanted base item to Flawless quality, ie. +13/+7. The first number is ONLY used to calculate the amount of base armor added to a body armor, all the remaining armor pieces (helm, gauntlets and boots) only get the latter as base armor. For the record, weapons also get the latter value added to their base damage, prior to any skill modifiers, perks, enchants or various temporary effects, when improving them. With the five armor slots available (including shield), this translates to +41 base armor, regardless of material, or +34 without a shield.

When you're upgrading a material you have a Smithing perk for, the base improvement at 100 Smithing skill becomes Legendary (+20/+10) instead. This gives +60 base armor to any set you have a perk for with shield and +50 without. Worth noting that the first available armor types that you CAN get a perk for is Steel for Heavy armor and Elven for Light. All types of Leather, Hide, Iron and most non-standard types can only be improved without a perk.

Both perked and unperked Smithing improvements keep on improving past 100 skill, which you can get via enchanted items and/or using a potion. But perked improvement has always slightly less than double the effect of corresponding unperked one. As the skill uses a tiered table lookup table instead of a straight formula, you could need rather sizeable increments to your skill to get to the next breakpoint, depending on how close to it you were to begin with.

Part two: Alchemy and Enchanting
To get the most out of Smithing improvements, you should consider maxing and putting perks into Alchemy and Enchanting to boost it. Here's why.

Neither Alchemy nor Enchanting: The best you can get is 3 x <Apparel> of Peerless Smithing, not four since Fortify Smithing is not available on a chest piece as random loot, only by enchanting yourself. However, you can get +12% improvement on chest without any enchanting perks (just Enchanter's Elixir) if you have the Enchanting skill itself maxed. That's +87% improvement total. Combined with a Blacksmith's Elixir for +50% improvement for a combined effect of +180% increase in Smithing skill. Also, actually finding all three enchanted items at maximum quality requires at least level 47 and a fair bit of luck.

Only Alchemy: You still only get +87% from your smithing set (see above), but can instead create more powerful +smithing potions. Note that even if you can also create better +enchanting potions, the additional effect past Enchanter's Elixir is negligible and applies to unperked enchant in just one piece. The same limitation of only being able to find three different <Apparel> of Peerless Alchemy as helm, necklace and gauntlets applies. Ring is only available via enchanting, thus 87% improvement max, which allows the creation of a +112% smithing potion. Combined, these two give +296% to your Smithing. And, you need to find SIX instead of just three enchantments at maximum quality to be able to do it.

Only Enchanting: Now you can get 4 x 28 = 112% improvements for both Smithing and Alchemy, as long as you can get enough Enchanter's Elixirs to create them. However, this only allows the creation of a +51% smithing potion since the Alchemy perks are now missing. Combined effect becomes thus only +220%.

Both Enchanting and Alchemy: You get maxed everything, ie. 4 x 29 = 116% improvement from enchants and +130% from a potion for a combined effect of +397% in your Smithing skill. This translates into the infamous +92/+46 Smithing improvement value.

Part three: Other notable effects
Ancient Knowledge: I've finally confirmed myself that this permanent buff you get as a quest reward by completing "Unfathomable Depths" STILL fails to do what its description says. Instead, you get +25% armor bonus to ALL types of armor (not just Dwarven), although you need to re-equip one of your armor pieces to update the displayed values. It's worth noting that the percentage is supposedly additive (rather than multiplicative) with whatever you get from Agile Defender and/or Juggernaut, if you have points in those perks, according to UESPWiki. Also, you get yet another bonus to how much you can improve stuff by Smithing. The most interesting part is that instead of doing +92/+46 improvements with triple crafts, you can instead get +100/+50, ie. and additional +8/+4 on top of everything else.
Lord Stone: Gives you +50 armor (and Magic Resist) as straight addition after everything else is accounted for.
Oakflesh/Stoneflesh/Ironflesh/Ebonyflesh: Alteration spells that give anywhere from 40 to 100 armor for a full 60 seconds. Stoneflesh at +60 armor is especially noteworthy as it becomes useful with base magicka with the Apprentice Alteration perk many builds pick on their way to get Magic Resistance perks in the Alteration tree.
Potions and enchants: Both types apply directly to the armor skills themselves, gaining an additional 0.4% bonus to the "Skill" part of the armor equation per skill point. Since 100 skill for a 1.4 armor multiplier is what you ultimately end up with, these can be used to push this part beyond that limit. However, potions only last for a short while and enchants tie up slots that are usually much better used for something else, so both are to be seen as last ditch minor temporary tweaks.

Part four: Constraint limits
So, what does this all mean in practice? Generally what you do when planning your character is to start with the armor cap value (567), divide it with the known multiplier(s) for your projected build and check how much base armor you need to be able to reach the cap.

Since most armor cap calculations assume maxed Armor skill, eliminating it first is usually the best bet. Thus you need 567/1.4 = 405 armor without skill bonus accounted for. This also removes the weakest effect, potions and direct +armor skill enchants from the picture.

Second, since Ancient Knowledge is a quest reward, there's absolutely no reason whatsoever to not include it into your plan. The effect on Smithing improvements cannot be included at this step, but just make a note that you have it for later. Since it's an additive effect together with your points in either Juggernaut or Agile Defender, you need to divide by a variable value anywhere from 1.25 for no armor perks whatsoever to 2.25 for full 5/5. Hence, you have a range of values between 405/2.25 = 180 (5/5) to 405/1.25 = 324 (0/5) that you need to meet without any influence from the effects listed so far. For those interested only in later perks in the tree, 1/5 perk here puts us at a reasonable 405/1.45 = 279.

Third, you divide out the effects you get from Matching set plus Custom Fit/Well Fitted, if you plan to have any of those. Skip this step if you have none of those, divide by 1.25 for just one and 1.5 if you get two. Note that if you plan on going with zero armor perks, you can't qualify for any of these either. Thus you have a value ranging from 180/1.5 = 120 to 324 remaining. For the ones taking prereqs only, 279/1.25 = 223.

At this point, all calculations are done with straight base values, simplifying things greatly. If you had all the relevant perks along the way, reaching just 120 base armor can be done with UNIMPROVED Orcish set or better, while Dragonscale (Light) is only 9 points short at 111. While no powergamer would willfully skip improving their armor, it's nice that there's still hope for the roleplayers wanting to go strictly with what they find themselves.

Part five: The what ifs
If we assume just basic Flawless improvement level (no trade skills whatsoever, no potions, just 100 Smithing), you get +41/+34 armor for free with/without shield, respectively. This allows dropping armor quality all the way down to Elven, or keeping it at Orcish+ but dropping the shield, assuming you still qualify for both Matched set bonus. With just one Matched Set, Glass+ is required, and Daedric is just two points short of making it without the shield.

With Legendary improvements, the freebie bonus is at +60/+50. This makes Scaled+ qualify with just one Matching set, or Ebony+ if you also lack the shield. Orcish+ with shield makes it without needing any Matched set bonus.

If also add the lazy crafter's +100% Smithing set, freebie bonus is at +120/+100. (For the odd case of NOT having the Smithing perk for what you improve, just check the previous point as you still end up at Legendary.) Anything Elven+ makes it without shield and just one Matched Set, Dragonscale+ with neither of them. Also, if you just went with the prereqs in either armor tree, ie. only 1/5 in either Agile Defender or Juggernaut, Steel+ is enough with shield + Matched Set but is not doable without either.

Triple tradeskills provide a hefty +276/+230 bonus from improvement alone. Just as before, check the previous point if you lack the Smithing perk on what you're improving, although it'd be strange if you did that. Any armor type that you can put a Smithing perk on easily meets the requirements with just one perk in the corresponding armor skill without shield, and you don't even need that if you do carry a shield. With neither shield nor perks in either Armor skill, you need to come up with a total of 94 base armor points from the pieces you wear, meaning Ebony+ in most item slots. Or, since there no longer is many percentual armor increases remaining, just skill and Ancient Knowledge, adding the Lord Stone drops this by 50/1.4/1.25 = 28 points down to 66, which makes even Steel qualify with flying honors.

Finally, if we add the extra effect from Ancient Knowledge, you can get all the way up to +300/+250 from Smithing alone, without even going into Vampires with Necromage, Fortify Restoration potion exploits or Falmer helm glitches. That reduces the base requirement to just 74 with no shield and no perks. Steel items plus Elven Gilded Armor is already 76 but requires two perks in Smithing, while Steel everything is just two (!!) points short of the goal, leaving the total at 563, ie. 79.56% damage reduction. That's within rounding error from 80%, so yes, all you need is just Steel Armor even if you want to use other Standing Stones besides the Lord Stone.

 

Wow Rechet - that is comprehensive. I do have one question - do enchantments that raise your light/heavy armor skill beyond 100 count? I believe you can enchant up to +8 in the skill, and find it up to +12. When you state:

It says to me that anything beyond 100 is wasted. I guess an ancillary question not directly pertaining to armor would be which effects/enchatments that add to skill have any effects beyond 100? It would appear that smithing does, as does alchemy and enchanting, which is why triple crafts are possible. Anything else?

 

Unless there's a reason to assume otherwise, I'd say that ALL skills scale past 100.

However, some effects aren't actual skill bonuses but direct percentage effects after skill has been taken into account. This is especially notable with Pickpocketing - even if you get +100% Pickpocket as enchants, your chances to keep pickpocket training past 51 skill isn't improved by much. (50 to 51 is still doable as it costs just 550 gold, the jump in cost comes after that.) Say that your chance to pickpocket without any enchants sits at 20% - after the +100% bonus, you'd still only get double that, ie. 40% chance. However, the perks give direct addition to your chances, Cutpurse being the big one as it could take you from a mere 1% chance to 51% since it's additional. Likewise, Night Thief on sleeping trainers (College of Winterhold, anyone?) gives an additional 25%, which directly translates into being able to pickpocket 250 more gold with the exact same chance.

Bonus to armor skills from enchanting and potions is direct +skill addition, and has the same numerical magnitude as -magicka cost, +alchemy and +smithing, ie. you can get up to +29 skill per enchant slot. The difference to, say, Smithing is that it's just additive, while Smithing bonus is multiplicative. To make it even more complicated, even if you have "+50% to smithing" total from enchants, this doesn't necessarily translate to exactly +50% to the amount you can improve stuff. Instead, you multiply the Smithing skill you have by 1.5 and check from Smithing skill table where you end up at. Thus, 67 Smithing skill + 50% from enchants = 100 effective skill = Legendary level with perk, rather than whatever you get at 67 skill plus 50%.

By "removing enchants and potions from the picture" I mean that since their effect is both rather minor and in the case of potions temporary as well, it's quite fine to ignore them from the calculations to remove clutter. The effects are still available for temporary boosting along your way to 100 in Armor skill(s), should you need to come past some extra tough fights. Just that neither potions nor enchants figure into your long time plan, as I'm assuming you'll ultimately want to be able to reach cap without either.

---------- Added 1 hours, 29 minutes and 20 seconds later... ----------

For shits and giggles, I tested what happens when I fully improve Hide armor with all the boosts, including Ancient Knowledge. It seems improvements without perk cap at +48/+24, as that's what my Hide set got improved by - after deductions for my armor skill and Ancient Knowledge, of course. It's quite nearly half of what you get with a perk, just as expected.

In other words, Hide set without shield can be made to have as much as 160 base armor. Combine that with just 4/5 Agile Defender and Custom Fit and you're already over armor cap, at 574 to be more exact. Together with shield, you only need 2/5. And since Fur armor is actually an upgrade to Hide, this means that you can prance around in Fur Bikini and still be at armor cap!

---------- Added 0 hours, 42 minutes and 37 seconds later... ----------

Speaking of style points: Just as long as you wear body armor, Scaled+ is enough if you combine it with the set's helm or Dwarven+ if you only want boots or gauntlets together with it. All three remaining pieces are needed if you want to forgo wearing body armor, as long as the pieces are at least of Glass quality. All of these without shield and with appropriate armor perks maxed, obviously without Matched Set bonus since you're missing parts now. Remember also that your displayed armor needs to cover for the missing "hidden armor" bonus so your target value becomes either 592 or 617.

This could be utilized to make it to the armor cap while wearing Archmage's Robes, together with almost any Dragon Priest Mask (improved via Daedric Smithing) as normal helmets cannot be equipped at the same time due to the hood on it.

Another alternative is to wear a circlet to show the nice facial features you selected at the very start of the game, together with either Shoes or Gloves of your choice.

 

Hallelujah! The almighty modding community has solved this abomination Bethesda CLAIMS to be their "armor scaling solution".

Improved Armor Formula is everything the armor scaling SHOULD have been at game launch. Instead of having a linearly growing damage reduction percentage, it switches over into an effective health calculation model, such as in World of Warcraft.

Not only is this mod lore-friendly, it is actually an improvement over the game's very own system in terms of lore. Otherwise, you'd have to concede the following points as being "lore" friendly, when they're everything but.
- The plain fact of wearing ANY armor makes bigger difference than the difference between wearing Leather or Daedric Armor, due to the hidden armor bonus.
- The first 467 armor points on your way to the armor cap matter LESS than the last 100 armor right before it.
- There no longer is an arbitrary armor cap, since it's no longer needed. No more wasted perks in armor and/or tradeskills, everything counts.

For the mathematically inclined, here are some key values for comparison:
Armor rating - Vanilla damage reduction - IAF damage reduction
0 - 0% - 0%
100 - 24% (incl. hidden armor) - 33%
200 - 36% - 50%
300 - 48% - 60%
400 - 60% - 67%
500 - 72% - 71%
...
800 - 80% (same as with 567 armor, capped) - 80%
...
2000 - 80% - 91%

Now, that's looking at from the (IMHO) wrong angle. Let's see how much more damage you can actually take, compared to zero armor:
Armor rating - Vanilla (effective health multiplier) - IAF
0 - 1.00 - 1.00
100 - 1.32 - 1.50
200 - 1.56 - 2.00
300 - 1.92 - 2.50
400 - 2.50 - 3.00
500 - 3.57 - 3.50
...
800 - 5.00 (same as with 567 armor, capped) - 5.00
...
2000 - 5.00 - 11.00

With the new formula, you can easily see that for every 100 additional armor, you get an additional 50% effective health. Rather than the hyperbolical function with an arbitrary and extremely sharp cap, like in vanilla!

Edit: For the record, you can reach 1893 armor rating using Dwemer armor (due to Ancient Knowledge) in standard DLC game, using 35% skill enchants which allow the creation of 144% smithing potions and maxed Heavy armor perks. Pushing over 2k is possible by using Fortify Heavy Armor enchants, spells and Lord Stone. Having the cap at 567 visible armor was just stupid to begin with.