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Weapon and Skills

Some useful info not directly related to the damage formula:

• For working out the relative value of skills with differing BP costs, looking at SkillPower per BP is not accurate. Turns where you are 'charging up' for more expensive skills would still be contributing damage from auto-attack. Try the sim for spamming strategies, and romsaga has a complete auto-battle sim.
• For S weapons, going from unevolved level 1 to max evolved max level increases WP/SP by 11. This holds true for every S drop in JPN so far.
• SS Weapons start at ~22 WP, max evolve gives 14 to arrive at ~36.
• Usually (not always) a new story drop for a S weapon type has 1 WP above the previous. For the next while, the next weapon for a type is added 3 story updates after the previous.
• To rank up more expensive skills on Auto: Easiest way is to get the skill to 10BP to ensure it is cast once per battle. If that is not an option, but you can get the skill cost to at most 13, setup the character to be as slow as possible (EQ with -AGI, styles with lower mods and inherit the skill, low AGI Formation slots), and setup the rest of your squad to wipe the the first wave with their opening burst before the character can act. The character will have 13bp in the second round. It is slow going, but depending on the setup you could also Rank up multiple characters this way.

Now for the formula. Substitute SP for WP when looking at spells (When is it a spell?):

• [WP*1.5 eSkillPower]

Note that for Martial Arts, WP is multiplied by 1 instead of 1.5. IE, Weapons have a smaller impact on Fist damage than for other weapon types. For Guns the WP Multiplier is higher, 1.9.

The 'eSkillPower' part is a bit more complicated but I was trying to avoid scaring you off :P.

• eSkillPower = BaseSkillPower (BaseSkillPower - 5) * (1 SkillRank/100)

You can look up every skill's damage here, or by character here. Auto attack has a skill power of 7.

So, the stronger the skill, the more % damage increase Ranking up gives (because the higher BaseSkillPower, the more negligible that -5). But even with the strongest skills, 1 SkillRank won't result in a 1% increase in damage, because the factor involved also adds your WP (Weapon power) to it, or SP (Spell power) in the case of spells of the correct Affinity.

In fact, the stronger your weapon, the smaller the contribution of SkillPower to total damage. Stronger skills will always do more damage per cast than weaker skills, but the stronger your weapon, the smaller the difference. Put another way, weaker skills benefit more from better weapons, and gain more bp efficiency, than stronger skills do (this does not necessarily mean they will end up more BP efficient overall).

I made a small chart that illustrates both the points above, you can check it out here.

If you can't be bothered with the link, here are more condensed tables of the same info, for skills that aren't MA or Gun.

For WP/SP 27 (Strongest weapon at game launch):

* The strongest at global launch also happens to be the start of SSS Rank, Ellen's Dynamic Chop.

For WP/SP 36 (WP for most SS Rank weapons in JPN currently):

You can see that the stronger the weapon, the less percentage increase Rank has on damage. Conversely, the stronger the Skill, the more strongly influenced damage is by Rank. Max Skill Rank increases damage anywhere from ~10% to ~40% with S Rank weapons, this will be lessened further with stronger weapons such as SS Rank or future S Ranks. But power creep also means we get stronger skills over time.

Overall, given the small impact of Rank on weak skills, and the difficulty ranking up high cost skills, its small wonder that the medium power, medium cost skills tend to be the more popular (being more likely to be auto-able helps too). In general, a mid power/cost skill at high rank will do more average Damage per turn than a high power/cost at low rank, after accounting for turns spent auto attacking. While you will generally get overall better average DPT from spamming high power skills of high Rank, it takes a lot of time investment to make the most of it, and you have to be careful of overkill.