I'm not sure about the exact equations, but here is a general guide:

http://wiki.ultimacodex.com/wiki/Character_attributes

You'll want a high STR, giving you the ability to carry many items. Forget the other attributes. They can be substituted by skills.

^This.

I'm not sure about UW1, but I do recall that in UW2 a character with very high Dex seemed to have faster movement, albeit not to a game-changing extent.

Strength and Intelligence do affect both initial and per-level Vitality/Mana.

All of them also affect the number of points you gain in skills that use them when you train. This applies to both but is more easily seen in UW2 since you have direct control over what you train in. Essentially, you have the greatest gain up to 1/2 the stat, moderate gain up to the stat, and slow. It isn't strictly 3/2/1 but often hovers around that.

Beside of the things that were already mentioned the attributes have a hugh impact on your starting skills during character creation.

Some examples:

A fighter with 30 STR that chooses Attack can start with an attack skill around 19
if the same fighter had only 20 STR he would never get around 19.

A Tinker with 27 DEX that chooses Repair can get a repair skill around 17.
With significant lower DEX you want score a 17 in repair.

A Shepard with 29 INT that chooses Lore two times can get a lore skill around 17.
Compared to that a Shepard with 14 INT might only get 6 lore.

There is some randomness to this but generally it is advisable to get very high nummers in the attributes
that are related to the skills you are planning to use the most.

Hi.

Sorry if this is a necro. This was posted only a while ago 2020 so I figure wouldn't hurt to add my findings. I did a bit of extensive testing sampling various characters, classes and the resulting stats values and trying to reverse engineer and figure out the formulas. I filled in some of these details in the codex wiki as well.

STR = carry weight, damage with weapon skills, vitality and hit points gained per level.

Carry Weight
UW1 (2 * STR)
UW2 (1.35 * STR + 29)
This means in UW1 STR is hugely important where as in UW2 has higher base value but you gain less per point of STR .

Vitality
UW1 (0.24 * STR + 29)
is been suggested INT plays a role in Vitality in UW2 formula may be different

Hit Points per level
UW1 (STR / 5) rounded down
i think is same for UW2

DEX = evade chance with Defense, attack chance with Attack and weapon skills

DEX 25 or higher seem to give +1 speed

Speed 2 tiles / sec
Jump height 0.5 tiles

Acrobatics seem to only affect fall damage and not jump height or speed.
Swimming seem to affect swim speed.

Most modern FPS games you always hit but in Ultima Underworld you can completely miss and deal zero damage since it features this oldschool attack miss mechanic. This means having high DEX you can hit more often and be hit less often makes it quite useful stat if you plan to do lots of combat.

INT = chance of casting spells along with Casting skill, mana and mana gained per level

Mana
(INT / 8 * mana skill + INT / 12).
I verified this multiple times and is consistent with both UW1 and UW2

Looking though the decompile code is quite close it actually does (INT * mana) / 8 but at level 1 you have INT / 8 starting mana.

Mana per level likely similar to Vitality (INT / 5) rounded down

Note that spell costs 3 * spell circle so is not INT based. But spell success chance is.

It seems to me like the game was meant to be played by balancing out stats right from the start in various ways

Dominant > Secondary > Dump
STR > DEX > INT fighter
INT > DEX > STR mage

Dominant > Balance
DEX > STR = INT bard
STR = INT > DEX druid
DEX = INT > STR paladin
STR = DEX > INT tinker

Balance all 3
all high STR = INT = DEX ranger
all low STR = INT = DEX shepherd

So you notice something interesting. Each category you have a kind of opposite: Fighter is opposite of mage both are highly specialized in the exact reverse, Bard is the opposite of druid and paladin the opposite of tinker, Finally ranger is the more specialized version of shepherd.

For Ultima Underworld 1 STR > INT > DEX is probably the best stat selection.

For Ultima Underworld 2 STR is still important but can be lower due to being naturally higher base value so you could go with either STR = INT > DEX or STR = INT = DEX

Magic is important in both games so INT is second most important stat. Having DEX helps you in combat a lot so if you wanna prevail you need some DEX.

Probably best character class is Druid (since naturally focuses on most important STR and INT stats) or you can go with Ranger/Shepherd since they have above average rolls for all stats.

I agree. I usually pick a Druid with the highest Str for both games, as I like to wear plate armor and carry many items. The spells are nice, but having high Mana and Casting can make up for a low INT.

Druid is like the obvious choice, at least in the first game.
The game also favours the melee + magic support play style, while stealth, archery and offensive magic is just too frustrating.

Druid is definitely the top class in the first game, but Paladin is just a hair better in the second.

Hey guys I been doing some decompiling of Ultima code to extract some more stats seems Unarmed is not too shabby

According to the assembly based on what I understand is something like this for Unarmed Damage

base damage / 6 + Unarmed / 5 + 4

base damage is a lookup table and seems to be grabbing STR 5 which is 0 but I think it does a bit more math. I think might be a STR based formula like STR / 2 - 5

So if my understanding is correct a char with 30 STR and 30 Unarmed would deal (30 STR / 2 - 5) / 6 + 30 Unarmed / 5 + 4 = 12 damage which is halfway between a Longsword and a Broadsword or Axe and Battle Axe.

A low STR character would probably not progress too much and be stunted if my formula is indeed correct.

A low Unarmed starts around 6 or 7 damage which is about same as a sword or hand axe.

According to the rulebook an Unarmed skill of 30 should give +7 bonus but my calculations give +6 seems pretty close.

someday i'd like to mod in reporting (on the in-game message log) of each damage done, including points of damage, whether poison or any other effects are applied, maybe what part of the body was hit, and the identity of attacker and receiver, if possible. able to be toggled by the player.

Hey wisdomelemental how far did you get into ripping those functions out? Right now I'm working to import UW1 into the GZDoom engine, I'd love to know any of the behind-the-scenes functionality you know of.
That would be a great mod, as well as a function to scroll back the message buffer to see all the stuff that flew by too fast.

yes, i would like to do this when i get some time to.

i would also like to add this sort of text logging to Ultima 7. (6 had a message log, why shouldn't 7?)

any other ideas of things that ought to be logged, but aren't?