Last week I talked a bit about agility in Final Fantasy X and how if I spent 18 levels worth of stats on Rikku that I could get her to take 33% more actions in the same span of time. I mused a bit about how I could probably take 18 levels worth of strength and probably do more than 33% more damage for the level investment. So I went to look up the damage formulas to see how true that was going to be. Just as a gut feeling Rikku seemed terrible for the longest time (except at killing robots and getting me the stealing achievement) even though she got to take the most actions. Even black mage Kimahri was significantly outdamaging her!
Anyway, it turns out that there's a bunch of complicated calculations in how much damage is done on a given physical attack but strength only factors in one spot so it's pretty easy to compare the damage done with X strength and the damage done with X+Y strength as a relative matter. The damage formula cubes your strength. CUBES! In the original Final Fantasy your strength was a linear factor in terms of damage done. Cubing is... Insane? It explains why Wakka seemed to be so much worse than Tidus and Auron despite only having a little bit less strength than they had. If Wakka has 20 strength and Tidus has 25 strength then Tidus will do twice as much damage. Not 25% more. Not less than that, which would be expected if weapons had any game effect.
So what happens if we give Rikku 72 bonus strength? Well, it depends on her current strength but it's always going to be _way_ more than 33% more damage. If she started at 10 strength then she'd do 552 times as much damage. If she started at 50 strength then she'd do 15 times as much damage. Even if she started at 183 (the highest she could have and still get benefit from 72 bonus strength) she'd just do 2.7 times as much damage.
This formula is completely ridiculous, and it goes to explain why my damage always seems to get out of control in a real hurry. You go through most of the game doing reasonable damage, but then around the time you unlock the ultimate weapons you find yourself starting to run into the 9999 barrier. Break that limit with a weapon and it isn't much longer before you're doing 99999 damage. It feels like a big difference and like there should be a more gradual growth between the two but there really isn't.
Magic damage works similarly, except your magic stat is only squared, not cubed. It's divided by a smaller number too so it works out pretty comparable at lower levels, but the insane scaling at higher stat values isn't quite as insane. Still pretty insane, but not as off the charts. Magic is also gated by having the magic sphere boss be significantly harder than the strength sphere boss. (Mostly because he's immune to physical damage entirely which shuts off being able to use the magic break skill while the strength guy can be hit with the armour break skill.)
I've reached the point where I've gone off the rails in terms of power. I farmed the strength sphere boss until I was able to hit 255 strength with Tidus and Rikku. I'm struggling with coming up with a way to max my magic without it taking forever and I think I've settled on just power leveling Yuna and letting her get all the magic on the real grid first. Kimahri does way more damage because he's already done most of that but he doesn't have 1MP cost on his ultimate weapon so he's actually a terrible caster. His spells cost 90 times as much mana so he runs in 4 or 5 rounds while Yuna can double cast ultimas all day long. So what I'm doing right now is farming a fast boss for money and dark matter. One-Eye dies in two attacks, so I can have Yuna wait and still kill the boss before he takes an action. This lets her score up a silly amount of experience since I built her a triple AP, triple overdrive, overdrive->AP weapon. (One-Eye drops 2 or 3 socket weapons with triple AP so it's easy to build an experience gaining weapon as long as you don't need it to break the damage limit.)