I am putting this out here for what I have discovered and so that I don't forget about it later. TL:DR at bottom.

(credit to Crystalgate from a gamefaqs forum who figured out a weapon damage formula that was as close as one can get)

Damage = Weapon Damage ¤ (Character's Natural Damage + 30) / (Enemy Defense + 30) +- Random Variable (assumed to be around 10% or so of formula up to that point, or it could be as little as 1-2).

Needlers and Shots seem to go by a much simpler formula as they both ignore defense completely.

Damage = Weapon Damage +- Random Variable

From the research I have done, Fanbi is an additive bonus to the WEAPON DAMAGE. The amount of damage increased is based off what level Fanbi is at (so a Fanbi 1 will only increase the weapon damage by 1 whereas a Fanbi 20 will increase the weapon damage by 20). These effects do stack, so by casting it multiple times on the same character, it will just keep increasing the damage their weapon deals. Also keep in mind that one cast of Fanbi affects ALL weapons equipped by the target, so Fanbi is much better suited to be used on characters who dual wield, such as Mieu or Kara.

I assume Ner works in a similar way to the formula in that it just flat out increases defense. Haven't tested it yet since Ner isn't all that useful for a speedrun.

ALSO NOTE that the formula holds true for enemy attacks as well, except since they only have a base ATK, that number is put into the formula in both Weapon ATK and Natural ATK.

As far as Technique damage goes, it's a fairly simple formula. As one already knows, the more points you put into a technique, the more damage it will do.

In each of the formulas below, x = Technique Power

Foi Damage = Between 5x to 8x +- Random Variable Zan Damage = 4x +- Random Variable Gra Damage = 3x +- Random Variable Tsu Damage = 4x +- Random Variable Res Healing = 5x GiRes Healing = 2x

For example, if you have a Foi 10, then at max the technique will deal 80 damage.

NOTE that some enemies are resistant to certain techniques. In that case, damage dealt is equal to the power of the technique (a Foi 10 would just deal 10 HP damage). Technique damage cannot be changed by defense for your own characters (kinda unfair if you ask me), though I may test later to see if certain pieces of armor carry with it resistances.

-TL:DR- There is always a small random variable added or subtracted to the damage total.

Shots & Needlers: Damage = Weapon Damage + Fanbi Stacks

All other weapons: Damage = (Weapon Damage + Fanbi Stacks) ¤ (Natural Damage + 30) / (Enemy Defense + 30)

Fanbi increases Weapon damage equal to technique power of Fanbi. Can be stacked.

Techniques: Foi ¤ 5 to 8 Zan ¤ 4 Gra ¤ 3 Tsu ¤ 4 Res ¤ 5 GiRes ¤ 2

Also putting this here so that I don't forget as well. Could be helpful in determining stats for each character.

http://www.gamefaqs.com/genesis/586382-phantasy-star-iii-generations-of-doom/faqs/26809

HERO!

Do you know what I've been trying to get to the bottom of the PS3 damage formula for my remake since 2015. I've literally spent years googling and trying to get this worked out without much luck. Would you be interested in helping me out?

Do you know anything about the enemy damage formula or anything else?

Cannot believe someone's finally cracked this/

I didn't find the formula myself. I stumbled upon it (shown in the link) and basically just organized into one spot to hopefully read better.

as far as enemy damage formula, I don't recall off the top of my head. if it is anything like in Phantasy Star II (formulas are a bit similar), then the Weapon Damage in the first formula is just the enemy damage stat used again. don't quote me on that though.