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Note: I refer to the swords as longswords as it is their proper designation and because they are listed as such in Elder Scrolls Oblivion.
Chillrend at level 46+ IIRC has the highest base damage of all swords in vanilla Skyrim. With Dragonborn it's Miraak's sword at level 61+. Highest _base damage_ output without Dragonborn would be Chillrend on main hand + Blade of Woe offhand (you get Blade of Woe either by killing Astrid at the beginning of the Destroy the Dark Brotherhood quest, or nearing the end of the Dark Brotherhood chain). Blade of Woe is the highest base damage dagger, and offhand daggers (but not dual daggers) speed up double power attacks enormously.
Thing is enchanting is so powerful here that any and all artifacts are outclassed by whatever weapon you want that you enchant (I've got all artifacts at max damage and am using a custom Blades sword just for the looks, heh).
If you've got Dragonborn, though, highest DPS weapon by a landslide is anything Stahlrim with chaos enchantment on it. Chaos benefits from any and all elemental damage boosting perks: all three from Enchantment tree, but also all three from Destruction tree as well, plus stahlrim gives it all an extra 25% because Chaos has a frost damage part too. With all those perks maxed out and proper enchanting gear Chaos damage has a 50% chance of dealing 280 damage of each elemental type (fire, frost, and electric) per hit, for an average extra damage of 420 per hit against non-resistant mobs - 280 average against single-element resistant mobs. All that with uskp installed - meaning no resto-loops or necromage exploits. All that factoring in just chaos damage of course; if you added fire damage (highest DPS enchant bar chaos) you'd have an extra ~142 fire damage per hit for an average 562 elemental damage per hit.
So, a main hand enchanted stahlrim sword and an offhand enchanted stahlrim dagger would yield maximum DPS. Even with you're a wizard with zero smithing, 15 one handed skill, and no Fortify one-handed gear whatsoever a dual strike would deal ~1.125 elemental damage on average, plus base damage from weapons. A lvl 46+ chillrend and blade of woe with maxed out one handed skill, four pieces of +54% Fortify one-handed gear, both weapons tempered with a 142% Fortify smithing potion and four pieces of +34% Fortify smithing gear, would deal ~1.350 damage on a dual strike. If you applied this same skill and gear setup to a dual stahlrim set you'd get over 2.3K damage.
Technically speaking, Mehrune's instakill chance is below 2%. The foremost practical use of Mehrune's (roleplaying reasons aside) is for non-hardcore gamers to shoot for an instakill on that big bad enemy that's very hard to beat otherwise. That usually takes a couple F9 presses.
On average, by the time you land an instakill with Mehrune's Razor on the highest hp enemy in the entire game (~4.3k hp) you would have killed it seven times with a fire-chaos enchanted stahlrim dagger, and that's just accounting for the elemental damage (double that for a full twinked stahlrim weapon). Though ofc if you can make that big a weapon you might as well choose weapons on their look alone (Blade of Woe looks amazing) because you'd be in your comfort zone against most enemies even on Legendary with any weapon / artifact you've twinked.
Daggers are FAST weapons. It may take you ten individual strikes to take out a bandit chief, but you can do those ten strikes in the time it takes to hit ONCE with with Volendrung, and ten strikes at 2% insta-kill means it's going to happen more often than you think. This makes it suitable for both an assassin's blade (for it's high base damage) and for a dodging knife-fighter (due to the 2%).
I also like Dawnbreaker on legendary. It's fun to use on drauger.
I dunno if Elemental Fury has been nerfed or not, but it was absolutely deadly in my experience.
Also, if one goes the dagger route, they can make use of Valdr's Lucky Dagger with its 25% critical rate. Put it in your off-hand for a 25% chance of doing bonus damage. It doesn't count as an enchanted weapon, so it's still boosted by Elemental Fury.
It's base damage is the same as a Daedric Dagger.
<2% = less than once per 50 strikes, regardless of what anyone thinks (random number generator deficiencies aside).
Comparing Volendrung against Mehrune's:
Volendrung = max stagger rate (1.25) + infinite stamina (absorbtion rate @ legendary = 50 stam / sec) + 1.3 range (longest) + best crit profile @ 0.7 attack speed (battle ax) + daedric battle ax damage (V is fully temperable with latest uskp). Daggers = min stagger rate (uesp says 0) + 0.7 range (shortest) + limited stamina (mehrune's) + worst crit profile @ lowest base damage weapon + 1.3 attack speed (fastest).
Actual in-game comparison with factual data and game mechanics, using Mehrune's instakill best case scenario (aka highest hp mob):
Damage output per hit of max uskp / "legit" twinked mehrune's = ~640 (158 on legendary against zero armor).
Hp of player, level 81 = ~750 (>2/3 of all levelups into health + 2*85 hp pieces of gear).
Damage output of max hp mob = 300 damage per hit (900 on legendary, 180* against capped armor).
Hp of said mobs = 4.3k.
Finishing move (aka "Kill cam") window = 4x single attack damage. Higher base damage weapon = bigger instakill window (which is why 2H weapon bandit bosses are so tough, as the OP says). Killcam = no dodge possible.
Said mob window for insta-killing the player = 2nd* hit onwards.
Up to you to decide what is more useful: a less-than-one-in-fifty chance to instakill a mob that otherwise takes >25 regular Mehrune's hits to die, but kills you in *2-to-5 hits (that against a lvl 81 character with capped armor, 2/3 of all lvlups into health and +170hp slotted in gear), or best possible stun rate, no stamina limitations.
* - corrections from 85% damage reduction (magic resist cap) to 80% (physical cap).
Everything is viable in a (relatively) easy game as Skyrim, of course. However, Blade of Woe has higher base damage than Mehrune's (its absorb health is rather weak though).
For the record, you can craft a +100 charges fire + chaos stahlrim weapon without wearing any destruction gear whatsoever (that's my current setup, btw). Such a weapon gets all 100 charges back with a single Grand soul (switch to a Chaos + Fiery Soul trap weapon once in a blue moon and you're golden - but you probably can keep charges up with whatever soul gems you find).
In Skyrim, either artifacts are weak, or enchanting is too powerful, or both. Volendrung and Azura's Star being exceptions because they offer useful features no amount of crafting can replace - AKA hammer stun ratio @ battle ax swinging speed and daedric battleax damage with no stamina limitations, and infinite soul gems.