Why should I wear robes instead of armor in Skyrim?
Robes have very few advantages over armor. They are completely silent so it is easier to sneak in them and if you are using an alteration spell for armor rating that is affected by the perk Mage Armor then the alteration spells will provide much more defense as long as you are only wearing robes/clothes. It is much easier to have armor buffed with smithing that provides more defense than even the most powerful alteration armor spells though so if you want damage resistance you need to have armor.
Ok, so there's 3 options here: Heavy Armor, Light Armor, and no armor/robes. And I'm assuming you're going for a mage-type character.
I think Heavy would be out of the question, because personally I don't find the perks in the Heavy Armor skilltree to be as useful. Additionally, Light Armor/no armor lets you move faster and be more quiet than Heavy does, and Heavy doesn't really fit the mage's role anyway.
Then, we have the option of no armor. The catch to this is the Mage Armor perk, which multiplies the effect of the protective Oakflesh, Stoneflesh, Ironflesh, Ebonyflesh, and Dragonhide spells if no armor is equipped whatsoever. This perk multiplies by 2x with one skillpoint, 2.5x with two points, and 3x with three points.
The Oakflesh, Stoneflesh, Ironflesh, and Ebonyflesh spells affect armor rating directly, so here is what your armor rating would be depending on which spell you're using and the level of the perk.
- Mage Armor (x2) w/ Oak: 80
- Mage Armor (x2) w/ Stone: 120
- Mage Armor (x2) w/ Iron: 160
- Mage Armor (x2) w/ Ebony: 200
- Mage Armor (x2.5) w/ Oak: 100
- Mage Armor (x2.5) w/ Stone: 150
- Mage Armor (x2.5) w/ Iron: 200
- Mage Armor (x2.5) w/ Ebony: 250
- Mage Armor (x3) w/ Oak: 120
- Mage Armor (x3) w/ Stone: 180
- Mage Armor (x3) w/ Iron: 240
- Mage Armor (x3) w/ Ebony: 300
As you can see, it's possible to obtain an armor rating of 300 with no armor. The downside is that it still costs Magicka to use the protection spell of choice, which takes away from how much you have left to use to attack.
Also, since these spells all last for one minute, you will have to remember to do this every 60 seconds, every time you want to have armor. This adds up to a lot of Magicka being used during a fight that could be used on damaging the opponent.
On the other hand, Light Armor will give you a permanent armor rating, and with the Unhindered perk, it too does not weigh anything.
If we assume that Dragonscale armor is being used, there is a base armor rating of 82 (not including the shield of course, because we are a mage).
This can be further improved through the Agile Defender, Custom Fit, and Matching Set perks in the Light Armor tree. Maxing these perks out requires 7 skillpoints and a Light Armor skill of 70, but it will bring this base rating up 150% to 205.
Or, even better, if all four pieces of armor had been improved to Legendary on a workbench, they normally get +20 armor per piece for the improvement, which brings base armor rating up to 162. Now apply the 150% increase from the perks, and you have an armor rating of 405. Note that this is without the use of Fortify Smithing potions or any other effects.
This already surpasses the Mage Armor trick by far in terms of armor rating, but you can still improve. If you were able to use the previously mentioned spells and still have Magicka left over for other spells you need to attack, then the armor ratings would go as follows:
- Oak w/ perks & improved armor: 445
- Stone w/ perks & improved armor: 465
- Iron w/ perks & improved armor: 485
- Ebony w/ perks & improved armor: 505
Using Light Armor, you can reach armor ratings suitable for a fighter-class character despite still being a "mage." The downside is the immense skill and skillpoints needed for this method. Altogether, you will need a Light Armor skill of 70, a Smithing skill of 100, and 13 skill points, on top of the skill/skillpoints needed in Alteration if you want to use the protection spells to further buff your armor rating.
So to answer the question, I'm basically going to agree with Grim Wrath's response that the "no armor" method is better early-game, as long as you have enough Magicka potions to restore the Magicka you use on protective spells.
But once you acquire skill and levels as the game goes on, Light Armor will become the better way to go, with no major differences except for the fact that you will have a much better armor rating.
Long comment short, there's no real gain stat wise, only in terms of RP and all advantages that come with making it viable can be applied to armor.
To make robes/clothes more viable it kind of pushes you towards using Enchanting, but more so Alteration. Robes themselves have no inherit advantage over armor, but with the use of Alteration you can get yourself some good protection without needing to invest into Light/Heavy Armor, Smithing and Enchanting as Alteration to some degree covers all of that. Early game I'd say it's useful if you get Mage Armor(Alt 30, 3 perks) early on as it will beat out most(I think all and without smithing armor on it's own even with a high Heavy Armor skill ends weaker than Mage Armor) early armors and in terms of weight to defense pretty much always wins until you get to Heavy Armor 70 and grab Conditioning(4 perks) or Light Armor 50 for Unhindered(3 perks). It's easier to raise as well in comparison to the armor skills as it has other uses. The Magic Resistance and Atronach perks also help but these can go with armor and Enchantments making Mage Armor worth skipping for better stats.