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Also you can use things like this:
https://www.tarnished.dev/weapon-calculator
to compare different weapons/infusions fast.
Why id fire the worst? Simple, there is a bunch of staff that raises fire def, like rain, or standing in water. + Leveling Vigor raises fire def, and everybody has at least 55 on meta
Sorry I should have elaborated that this is for PvE not PvP
Typically, split damage infusions like fire have higher base AR and the AR you get from scaling depends on base damage, so even if a heavy infused sword has better strength scaling, the AR from scaling is usually higher with heavy than with fire. Note that with fire infusion, the strength scaling applies to both physical and fire damage.
However, AR is not damage and Fextralife only looks at AR, not the actual damage.
Basically, with a split damage weapon, your attack has to go through two flat defenses, which both reduce your damage by a flat value (which is not equal to the defense value, I didn't find a formula). A non-split damage weapon only has to go through one flat defense value, so you might get better damage with a non-split weapon even though AR is lower.
I remember watching a video where someone said that he tested both heavy and fire in PVP and did more damage with fire on his mid-level build (maybe lvl 80?) and more damage with heavy on his meta-level build. That was several patches ago, however, and I don't know if this applies to PVE.
Also note that due to how split damage works, a buff like the one you get from Flaming Strike on the heavy attack follow-up is almost worthless on a pure physical weapon because the added fire damage is neutered by the flat reduction from fire defense, but the buff is pretty good on a fire-infused weapon because the fire damage has to go through the flat reduction anyway.
Stat scaling is important, but not as important as upgrading weapons as far as damage goes.
There are a couple of factors. Infusions/affinities basically do 2 things: they change what stats contribute to damage, and they change the type of damage.
That's why there are 2 different fire affinities, Fire and Flame Art - Fire gets damage from STR and DEX, while Flame Art gets damage just from FAI. Both do "fire" type of damage, but your build will determine how big or small that number is.
Additionally, as Honk1 mentions, weapons with 2 damage types go through 2 different defenses, so in general, a weapon with 2 damage types such as Fire (physical + fire damage) will do less damage per hit than the AR number. On the flip side, sometimes it's better to split damage (getting some damage to apply to a weaker defense value), and there are non-damage reasons to use damage types, like how fire damage will set some enemies on fire.
Explanation is above but the reason fire and flame arts affinity are so good is because they have the most enemies in the game that have weaknesses or less resistance to them and fire has a stagger effect. You can also stack damage buffs in a way that no other element can(including phys) since flame grant me strength doesn't have a counterpart for other elements.