Right on, Dom... so step one is figure out if the chart is wrong/right before wracking yer brain cells with some crazy-ass 3rd degree quadratic equations, yes? What if the chart is slightly off, and this is a while lot easier (linear) than we think? I.e, start at zero smithing with the console commands, and test the grindstone with an iron dagger, etc... Yeesh, that sounds tedious, doesn't it?

-Loth

So the warrior build could kill Aldiun on normal in 10 hits without enchanting or alchemy? Sounds like we've stumbled across a design decision, and not a coincidental arrangement of numbers... maybe.

The extra limitations weren't for difficulty; just immersion. It also made the game scale a lot better, and made many of the abilities suddenly make sense. I generally only do it once, just to see how the game feels, and it happened to work out ok for me this time. I also have a good memory though, so the lack of a map isn't totally ruining it for me. I did allow myself to level up though.

I was concerned about the Dremora Lord summon... but as a Mage, my only other option seems to be Paralyze + Bound Weaponry. Destruction is ok... but many of the complaints are right; it doesn't scale well, even with Alchemy. Frost is OP though.

Thanks for the feedback.

It is possible it's a lookup table, but this has the feeling of a nested equation set. there's a nice linear range in the center, but the endpoints taper in weird ways, and the 14 starting point, regardless of perks, should be a hint. Also, Flawless without perk just happens to align with 100 skill? The dif was lining up to be a clean 2nd order until that data point, and the switchover is too coincidental. Still working on it, but there are hints...

Sadly, I've done this, and the chart didn't appear to be wrong, although I may not have been 100% exhaustive. I'll do it again today, and see if I missed something the first time.

Edit; Hmm, seems sneak attack isn't quite that simple. Will be back with more numbers after some testing.

"
These perks enabled:

29% Fortify Enchanting enchantments
29% Fortify Smithing enchantments
32% Fortify Alchemy potions
130% Fortify Smithing potions"

Apologies about the informal means of quoting, but I believe you mean "Fortify Alchemy enchantments" and "Fortify Enchanting potions" if I'm not mistaken.

Thanks so much for all the work on this!

Haha, the chart IS wrong... but not by much. Luckily, it appears that this equation just got a little less annoying (sorta):

Tested on a char improving an unimproved steel sword, with one-armed skill at 100 for testing control, with the steel smithing perk

Smithing skill threshold -- Damage increase

0-13 Nothing, cannot improve anything
14-21 -- Fine +2
22-39 -- Superior +5
40-56 -- Exquisite +9
57-73 -- Flawless +12
74-90 -- Epic +15
91-107 -- Legendary +18
108-124 -- Legendary +22

And so on, with a 125 smithing giving +25... the point here is that this is looking more and more like a straight line at the end (where it matters): every +17 to skill is giving either an increase of +3 or +4 (occasionally), which is probably a rounding artifact, right?

The chart at UESP had flawless happening at 58 (off by one) and Epic happening at 77 (off by three)... but the truth of the matter is that after smithing level 40, you just add 17 to find the next jump in quality, which is going to be either +3 or +4 damage for steel swords. Now we just need to verify that these numbers hold true for other material types and weapons -- it might be a mistake to assume a daedric mace will have this same progression in damage as the steel sword.

-Loth

Edit: Ah, hell... I think my test char might have had 1 rank in Armsman, so that +20% might be contributing to the rounding artifact. I better go back and unperk and do a quick re-test...

The patern for skill increases starts from 22, it goes 18, 17, 17, 17, 17, 17, 18, 17 ,17 ,17 ,17 ,17 ,18 ,17 ,17 ,17 ,17 ,17 ,repeatedly

At 22 I get a +6 increase, it goes up in 3s and 4s, still working on the pattern.

Edit; This pattern starts from 14 and goes 4, 4, 3, 4, 3, 4, 4, 3, 4, 3, 4, 4, 3, 4, 3 repeatedly

Agh, that one rank in Armsman really messed up my initial testing! Even ONE rank in that perk will give fairly divergent numbers after a few iterations...

Dom, I'm matching your skill increases perfectly, 18,17,17, etc., but if you take a char with no perks except the steel smithing perk and a 100 one-handed, the damage shifts to:

Fine +2
Superior +4
Exq. +7
Flaw. +10
Epic +12
Leg. +15,+18,+20,+23,+26,+29,+31,+34

So the damage series is more like:
2,2,3,3,2,3,3,2,3,3,3,2,3

If THAT can be understood with my crappy communication skills...
-Loth

Edit: BTW, I have also verified that weapon type (sword, mace, axe) and material type (steel, elven, etc.) have no effect on the bonuses given from smithing. They are flat numbers for any weapon, i.e., all other things equal, your daedric mace improved to exquisite will have the same bonus applied as a steel sword improved to exquisite.

ALSO

The numbers for un-perked smithing on UESP are wrong as well. This is what I found by testing:

Skill req -- Level
14 -- Fine
31 -- Superior
65 -- Exquisite
100 -- Flawless
134 -- Epic
168 -- Legendary
203 -- Legendary

So the skill progression to hit new bonuses is roughly doubled for unperked materials:
17,34,35,34,34,35

I suppose this is what the description in-game meant by being able to improve stuff twice as much?

Edit2: Maybe we should be trying to get these numbers with a ZERO skill in one-handed instead of a 100? If we are trying to distill the formula from all this data, maybe removing as many modifiers as possible could help? But then again, it might end up being a bunch of ones and twos... jeez, let's set one-handed to 10000 instead.

The 100 one handed might throwing your numbers off as well. Check with 0 in all skills except smithing.

To figure out what skill 'step' you're on, this calculation works;

17 * ROUNDDOWN((SKILL-22)/(17+1/6)) + ROUNDUP((SKILL-22)/(17+1/6)/6) + 22

And then to figure out how much that will boost your skill you can use this calculation;

ROUND(ROUNDDOWN((SKILL-22)/(17+1/6)) * 3.6 + 6)

Don't know if anyone can tidy those up a bit, but I've tested a bunch of different numbers up to 300 and they came out correct

This is with perks and for armor, doing more testing to see how unperked effects it and how the non-armor calulcations are done

Okay, finally found the repeat in weapon improvements.
Test character has no perks in anything except for steel smithing, and zero skill in one-handed as a base for measurement. Assuming y'all know the 18,17,17, etc. pattern with the smithing skill by now, this is the weapon damage progression, starting at "Fine" and going on well into legendary and beyond... the numbers are additive with each other, meaning that you continue to add each number to the last sum to get the final damage bonus depending on how smithed-out you are making your gear:
Fine starts at +1, and then the next levels are: 2,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,1

After this point, you are over 314 in smithing skill, but you can see the pattern, yes? Four 2's and then a 1, four 2's and then a one, etc.
Wish I had started off testing the right way in the first place... might have saved a few posts (and an hour or two).

-Loth

Here's the calculation for working out what 'step' you're on without the correct perk;

34*ROUND((SKILL-31)/(34+1/3))+ROUND((SKILL-31)/(34+1/3)/3)+31

Again, probably untidy and could probably be merged into the other step calculation, but I'm lazy and not too good at simultaneous equations.

And for how much you can improve your armor without the perk;

ROUNDDOWN((E11-31)/(34+1/3)+0.01)*3.6+6

Now just need someone to swoop on down and merge all those formulae into one

This would be so much easier if the 14 was out of the equation. It's not in the same pattern as everything else

Edit: I think my second formula is off, gotta re-test and tweak it

Had to add a 0.01 in there because the 1/3 was putting it slightly off count.

This has become.. confusing. Can you guys just post the numbers again quick? :-p Like, (Smithing Skill:Improvement)

Is it possible that weapon and armor improvements share some Grand Unified Formula of Smithing? I wouldn't know how to go about solving such a thing, given all the data we've collected... I was more of a biology major in college than a math wizard. Where's all my nerds at?

-Loth

Edit: Yeah, sorry Ches... this is a little confusing isn't it? For weapon improvements:

Minimum Smithing skill of perked material : Improvement to Base unmodified weapon, given zero skill and no perks to increase damage

14 : +1
22 : +3
40 : +5
57 : +6
74 : +8
91 : +10
108: +12
125: +14
143: +15
160: +17
177: +19
194: +21
211: +23
228: +24
246: +26
263: +28
280: +30
297: +32
314: +33

And so on... basically, every 17 skill points equals a damage boost, except every sixth step is eighteen, not seventeen (yeesh), and every damage boost is +2, except every fifth step is only +1.
If that makes any sense.

I'm your math nerd, but I need raw data, not the derivative stuff you've been posting. :-p Although, Dom has been doing a decent job too.

Speaking of which.. post 188? wow. Time for thread 7 soon. I'll get it started, and we can move over at your guys leisure. Damage section still going to be blank until we get a bit more data on the various damage levels we want to explore.

Cheshyr: Please see raw data as requested in my previous edited post. I hope you have a bunch of leaky pens in your pocket protector and some tape on your glasses, because this is gonna be a mess, sir. I think that you might have to nerd very hard to figure this one out.

But as an aside, I'm still leery about how "conveniently" unperked smithing just happened to land squarely on 100 as one of the limits.

Unperked smithing required : Level of improvement

14 : Fine
31 : Superior
65 : Exquisite
100 : Flawless
134 : Epic
168 : Legendary

Somehow, I have the feeling that the root of the Grand Unified Formula of Smithing lies in unperked territory, like they based everything off of that "100 : Flawless" mechanic, and everything else is just derived from that one point according to the mysterious formula we don't know yet (if it even exists).

-Loth

Skill needed With Perk - Without Perk - Armor Boost - Non Armor Boost

The fourth column I just copied from Lothario, so if it's wrong shout at him

14 - 14 - 2 - 1
22 - 31 - 6 - 3
40 - 65 - 10 - 5
57 - 100 - 13 - 6
74 - 134 - 17 - 8
91 - 168 - 20 - 10
108 - 203 - 24 - 12
126 - 237 - 28 - 14
143 - 271 - 31 - 15
160 - 306 - 35 - 17
177 - 340 - 38 - 19
194 - 374 - 42 - 21
211 - 409 - 46 - 23
229 - 443 - 49 - 24
246 - 477 - 53 - 26

You two are awesome. Working on it now, between 'Boss Interventions'.

Re: 100 Flawless... I think that's an arbitrary data point, independent of the equation, but I have no proof as of yet. I do R&D for a living.. a little math wont hurt me. :-p

At some point, I want to get into the blocking mechanic some more. There was a whole different thread about it a while ago, but blocking with weapons was never truly explored IIRC, which is a shame if you use 2H swords and such. Dom, you did a bunch of testing in that thread, didn't you? Seeing as how the focus on weaponry lately has settled on "let's do less than a million pts of damage per hit", the 2H weapons and sword+shield styles might come into play again, and the ability to block is what sets these styles apart from our usual dual wielding stuff. I might have to look into this in the near future... maybe I'll actually do the testing correctly this time.

-Loth

The problem with blocking is you're already reducing damage by 80%, and your block is multiplicative with your armor reduction, so if you do manage to block an attack you're blocking 85% of 20% of the damage. Same reason using elemental resist is overkill, they're only resisting 85% of 15% of the damage. Even if you don't want to go overkill, Dropping over half your damage for a chance to absorb an extra 17% damage just seems silly

Two Handed blocking might be viable depending on how the numbers go, I'll run some tests.

I'll see if I can pull up my numbers from before as well, but this forum has a terrible post finding function

Edit; I lied, the search is okay id you use the advanced bit;

http://www.gamesas.com/index.php?/topic/1294892-max-block-absorb/#entry19589131

The 'dropping half your damage' argument gets a bit thin when we're one-shotting alduin. Oh NOES! 2 SWINGS NOW? Whatever will I do? And Blocking does make combat a bit more engaging... My question is, do you get the same amount of block from a shield as you do from a weapon?

Yeah, I agree that with capped armor, having a shield/ability to block with a weapon is kinda going overboard, but this just means that we can use the blocking mechanic to supplement damage mitigation earlier, without actually hitting the passive armor cap. In other words, when does it pay off to be a good blocker in terms of having an active defense vs. a passive one? Could someone with only 40% passive mitigation use blocking to mimic having 80%? Maybe... but what would that take? Is it even worth it? For someone using a 2H sword, if we discover that they can "fake" having a really high armor rating by simply blocking skillfully, wouldn't that be good to know? Might even make the game more interesting...

-Loth

I might miss the second swing! OMG WHAT NAO!

A daedric warhammer blocks less than a glass shield but more than a hide shield. About 55% unperked.

Edit; And why are you making fun of me when that formula isn't done? Get to it!

Rofl.. the formula is hard! I think i'm close though. And I'm making fun of myself as much as you. I one-shotted Alduin too.

Well, yes - you only block part of the remaining incoming damage, true - but nonetheless it's the highest portion of any damage taken whatsoever. Since DPS is not much of a factor you could say. You will deal 50% damage less but receiver 85% damage less while blocking (given maxed armor). So it's not really a bad tradeoff - especially not, when considering you can use the "shield wall" to get close to archers etc while you would not be able to deal any damage whatsoever.

If I could change the game mechanics a little, I would make absorb health and stamina shield enchants(triggered by the shield being hit) and remove them from weapons...

But on the other hand I'd change a lot of things in the game balance if I could...

... And I'm guessing that weapon material affects block effectiveness, just like shield material does? Daedric weapons make better "shields" than steel weapons, yes? So now we are left with the questions "how much", and "should I be bothering to level-up block vs. leveling up armor for defense". If you got 55% damage mitigation from blocking with a daedric warhammer, that's like a pretty high armor rating without spending any perks in the Blocking tree -- why the hell hasn't this been brought up a long time ago?

-Loth

This is probably where fortify block would finally make sense - unless it does not work on weapons either. Maximizing Block while still swinging for a higher damage than Sword/Shield Combos...