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A few off the top of my head-
-maces, staves, and katanas use your magic power against the enemy's defense
-poles use your strength against the enemy's magic defense
-daggers bows and ninja swords take your speed into account somewhere
-guns and measures ignore defense entirely
-axes, hammers, and bombs have the highest max hit and lowest min hit
allegedly jobs change how damage is calculated now but I haven't seen it confirmed by a reliable source.
That's really odd to me... I wish it was more straightforward in explaining it if that's the case.
Most likely the enemies have higher mdef than pdef. Also, daggers use the speed stat as well as strength, which actually causes a basic Dagger to be better than a Broad Sword and likely is a factor in the Oaken Staff doing less.
It's all about the values involved. You don't need maximum MAG to do decent damage. STR alone still increases katana damage. It's a fairly complicated formula in terms of scaling, because the absolute value of the stats fluctuates based not just on how much you already have, but also with your level. You could well do great damage with very low MAG, but you could also very well be doing more if you balanced the two better. Do the math if you want to know!
As for OP's question:
Daggers scale with STR and SPD. Staves scale with STR and MAG. At low levels, it's not uncommon to see weird outcomes because the impact of the stats is larger, so even a small difference in SPD or MAG could have caused that very noticeable disparity. SPD-based weapons additionally have an edge at lower levels because they have a more generous damage formula (divided by 218, where STR-based is divided by 256) but in return their efficacy diminishes somewhat as you level up because SPD is the stat that grows the least with levels. For example, Penelo starts with 20 STR 24 SPD at lvl 1. At lvl 50, she's at 45 STR 30 SPD. At lvl 99, she's at 70 STR 36 SPD.
Weapons are quite complicated in this game.
Thanks. I do wish there was some sort of indicator in the game to give an idea of exactly what the outcome would be. I don't remember where it explained any of that.
I just remember it because when I got the original version of XII it came with a guidebook.
FFXII is also notorious for having a lot of obscure mechanics involved, not just in combat but also things like how certain enemies spawn etc. (not to mention the absolutely ludicrous mechanics of the original Zodiac Spear, which thankfully they removed in this version).
If you want to look up specific things, check the FF wiki. It's usually a good source of comprehensive information.
MAGIC!
No longer an issue since IZJS so doesn't apply to anything other than the original Playstation 2 release of the game. If you're playing that then you likely already know how to use the internet to look things up ;)
The dev explained the reasoning for all this garbage by saying they 'wanted to encourage discussion and discovery' among players. They seemed to be thinking very specifically of pre-internet Japanese schools or something (same as Pokemon basically) instead of our modern society in (current year argument) 2020.
I get the sentiment they were going for, but they definitely overshot that goal.
I still have nightmares about the Forbidden Treasures.
Might as well respond to the OP directly.
Here you go: https://gamefaqs.gamespot.com/ps2/459841-final-fantasy-xii/faqs/45900
I'd recommend scrolling to the end and choosing 'text only mode'
That is the 'Game Mechanics FAQ' and while it was made for the Playstation 2 vanilla version, it applies to everything in TZA as well.
Also a bit of curious trivia from the end of that FAQ: