Hero Point Sword - Custom Magic Item

Homebrew and House Rules

So, one of my players is really into the Hero Point mechanics and built his character around those feats and other "Luck" based abilities. After a Particularly Challenging series of quests and adventures, the party has some downtime and a lot of cash to burn. He wants to pay a local wizard that they know that's also obsessed with Luck to research a weapon that does increased damage based on the wielder's luck (basically he wants it to add your Hero Point total to damage, but not to hit) and i was wondering how to price the actual enchanted sword.
I know the research rules and we've already worked out the wizard's fee for doing the research, I just have no idea what to ballpark the cost at.
To Clarify, I should state that i find the item relatively balanced and not overly powerful, but a scaling static damage modifier that fluctuates based on Hero Point totals is just hard to price if i'm being honest. Any input would be appreciated!

Yes, it would be tricky. The magic item creations rules don't cover what you're asking. I don't think there are any magic items either, that do what you are asking.

What you are asking for is for some magic item that gets proportionally more powerful as you gain more 'luck points'. Or get proportionally weaker as you spend those points. It could be like ki points for Monks have, or arcane reservoir for Arcanists. Or even be affected by things more abstract like ability score, attack bonus, or hit points.

I don't think such items exist, but I could be wrong. My knowledge base gets a bit fuzzy beyond the core rulebook. If there is any magic items, abilities, or spells that can do this, I would like to know.

There is an exception. I am aware that the mythic book does have magic items that use mythic points as fuel. Keywords, fuel, as in those magic items uses up the mythic points to power their many different abilities.

Unfortunately, the devs didn't include any rules for making new mythic items, especially ones that use mythic power points.

There is also the Holy Avenger, core rulebook p. 473, which becomes stronger in the hands of a Paladin. Strangely enough, the spell resistance it grants gets stronger the more Paladin levels the wielder has.

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