Solving magic weapon cost with MATH

[Zhorn]

So we've had many price guides on giving magic items a lists cost, Both the Sane Magic Items and Discerning Merchant price guides are the ones I see the most often.
An issue though that has been pointed out in both of those (and a few others) is all +X weapons having the same cost, and the same for +X armors.
a +2 dagger is the same cost as a +2 greataxe
A +1 padded costing the same as +2 plate
Madness, right? A +bonus to hit is more valuable on a weapon that deals more damage, so the item's price should reflect that in some way.

So what I've been playing about with is trying to develop formulas to derive values that roughly fit the pricing of the DMG, but have the values reasonably separated based on how numerically effective the items are.

So as an example of what I've got so far using variables of:
Base Cost of the item
Base AC of the armor type
Bonus that the +x is adding
Dis being a value of 1 for applying disadvantage to stealth checks (0 if not), &
Mod being a value for if the wearer applies their Dexterity to their AC (1 for light, 0.5 for medium, 0 for heavy)

[ Base Cost + { ( Base AC - 10 ) * 50 * ( Bonus + 1 ) ^ 4 } ] * [ 0.9 + { 0.2 * ( 1 - Dis ) } ] * [ 1.1 - { 0.2 * ( 1 - Mod ) } ]

Still tweaking that formula, but what this yields is a highly varied price list that is close to the ranges in the DMG price guide (p135), but has the values spread out.
+1 leather is ~980 gp, while +1 plate is ~6,400 gp
+3 leather is ~15,500 gp, while +3 plate is ~84,000gp

As for weapons, I'm a bit stumped and could use some help with a starting point.
Key things I'm trying to do with this:
Avoid arbitrary prices from rarity. Trying meet those values, not start with them.
All variables of the equations are drawn from the item's mechanical values.
At a later point will try and work in a value modifier for extra dice damage, so weapons like flametongues and holy avengers could be priced with it.
though I'm betting someone will still pipe up with "if Rare use this value, if Very Rare with this value"
So how about it? Any suggestions or examples of similar attempts you have to share?

[MarkVIIIMarc]

I like where you are heading but I think there is a bit more at play which make exact figuring too difficult.

In a dwarven region where people love making armor perhaps the metal armors are cheaper. In the middle of an enchanted elven metropolis maybe plate mail is rare but enchanted armor is easier to come by.

[heavyfuel]

Madness, right? A +bonus to hit is more valuable on a weapon that deals more damage, so the item's price should reflect that in some way.

Ehh, no?

A bonus to hit is only more valuable on a weapon that deals more damage if you disregard the rest of the game. A dagger might deal 1d4, but a dagger wielded by a 7th level Arcane Trickster deals 1d4+4d6+1d8+4 (avg 25). That's not considerably less than a Greataxe wielded by a 7th level Bearbarian dealing 1d12+4+3 times 2 (avg 27), especially when you consider more stuff, like the Barbarian not Raging every combat, the AT dealing more damage on OAs, and Booming Blade sometimes proc-ing for extra damage.

The same goes for armor. A Scale Mail doesn't actually give more AC than Studded Leather for most characters, even if its base AC is higher. Plate armor does, but it's already super expensive.

Plus, there's the in-game problem of "is an axe considerably more difficult to enhance compared to a dagger? If so, why? If not, why would the axe be more expensive?"

Anyway. I'm calling this a bad rule

[PhantomSoul]

An issue though that has been pointed out in both of those (and a few others) is all +X weapons having the same cost, and the same for +X armors.
a +2 dagger is the same cost as a +2 greataxe
A +1 padded costing the same as +2 plate
Madness, right? A +bonus to hit is more valuable on a weapon that deals more damage, so the item's price should reflect that in some way.


I'm slightly torn on this one, but I think it's fine if there's the right adaptability elsewhere in the formula. The lower-AC armour benefits more from the +, so it seems sensible to have a proportionally larger increase in price... BUT the proportional value of +1 AC is also not consistent across the range of possible ACs anyway. I think the bigger thing is that weapons and armour are presumably gated by proficiency even for NPCs in-fiction, which means the die size isn't the only factor that might go into a calculation; rarity and/or market share might play an important role. (I'm quite happy with the possibility that things aren't equally easy to enchant, or that some items are more likely to have been preserved than others from the good ol' days when enchantment was actually being done, or that enchantments came from gods and so the item range is based on divine whims or historical utility rather than contemporary usefulness.)



Avoid arbitrary prices from rarity. Trying meet those values, not start with them.

I think meeting the rarity ranges probably doesn't make sense as a goal -- if you're just recreating the existing prices or ranges, it's going to contribute less (you're just doing more work to get to the start point). Instead, I think it would be better to consider the rarity a mechanical property: it's in the item info and it's used for other things in the game (mainly or only artificers and downtime crafting, if either are in the game). The rarity could act like a price multiplier, which intuitively makes sense to me; a more rare non-powerful item is still likely going to cost more than a less rare item with about the same (im)potency. That also makes it more useful for other DMs; they can change the estimated rarity to fit their world and end up with a useful adaptation to the price. (I'd be tempted to have rarity have a range of multipliers, to adjust for smaller or regional differences, e.g. Rare can map onto 1.6 to 1.9, to provide entirely made up numbers.)



I like where you are heading but I think there is a bit more at play which make exact figuring too difficult.

In a dwarven region where people love making armor perhaps the metal armors are cheaper. In the middle of an enchanted elven metropolis maybe plate mail is rare but enchanted armor is easier to come by.

I think this could delightfully be captured by local adjustments to rarity! (Which would be a change relative to the OP, for sure.)


Ehh, no?

A bonus to hit is only more valuable on a weapon that deals more damage if you disregard the rest of the game. A dagger might deal 1d4, but a dagger wielded by a 7th level Arcane Trickster deals 1d4+4d6+1d8+4 (avg 25). That's not considerably less than a Greataxe wielded by a 7th level Bearbarian dealing 1d12+4+3 times 2 (avg 27), especially when you consider more stuff, like the Barbarian not Raging every combat, the AT dealing more damage on OAs, and Booming Blade sometimes proc-ing for extra damage.

Hm... but if characters getting that different benefit are roughly the exception (specific classes, especially if the setting doesn't formally assign classes to the majority of NPCs), then that doesn't actually seem like a problem to have the proportional benefit vary by wielder. (It was inevitable anyway, really!) And the baseline would remain, e.g., a bland fighter or generic NPC, for whom it holds. I would suspect that accuracy boosts should probably be "penalised" more than raw damage boosts, though, since that's where the big discrepancies arise and a seller is likely to price based on the higher end of what they can think they'll actually get.



The same goes for armor. A Scale Mail doesn't actually give more AC than Studded Leather for most characters, even if its base AC is higher. Plate armor does, but it's already super expensive.

Yeah, I think having some flexible rarity or supply/demand variance seems useful.


Plus, there's the in-game problem of "is an axe considerably more difficult to enhance compared to a dagger? If so, why? If not, why would the axe be more expensive?"

It might not matter how hard it is (historically) if now people just don't enchant, or if people do enchant now maybe that gets folded quite easily into another variable (e.g. rarity or marketability).


Anyway. I'm calling this a bad rule

I'd go with it being a start -- good concept, but more levers are needed. At the very least it could be giving a more interesting baseline, and seeing what it yields could suggest refinement. (Though I wouldn't really count the rarity as a goal, but rather a factor!)

[Pildion]

So we've had many price guides on giving magic items a lists cost, Both the Sane Magic Items and Discerning Merchant price guides are the ones I see the most often.
An issue though that has been pointed out in both of those (and a few others) is all +X weapons having the same cost, and the same for +X armors.
a +2 dagger is the same cost as a +2 greataxe
A +1 padded costing the same as +2 plate
Madness, right? A +bonus to hit is more valuable on a weapon that deals more damage, so the item's price should reflect that in some way.

So what I've been playing about with is trying to develop formulas to derive values that roughly fit the pricing of the DMG, but have the values reasonably separated based on how numerically effective the items are.

So as an example of what I've got so far using variables of:
Base Cost of the item
Base AC of the armor type
Bonus that the +x is adding
Dis being a value of 1 for applying disadvantage to stealth checks (0 if not), &
Mod being a value for if the wearer applies their Dexterity to their AC (1 for light, 0.5 for medium, 0 for heavy)

[ Base Cost + { ( Base AC - 10 ) * 50 * ( Bonus + 1 ) ^ 4 } ] * [ 0.9 + { 0.2 * ( 1 - Dis ) } ] * [ 1.1 - { 0.2 * ( 1 - Mod ) } ]

Still tweaking that formula, but what this yields is a highly varied price list that is close to the ranges in the DMG price guide (p135), but has the values spread out.
+1 leather is ~980 gp, while +1 plate is ~6,400 gp
+3 leather is ~15,500 gp, while +3 plate is ~84,000gp

As for weapons, I'm a bit stumped and could use some help with a starting point.
Key things I'm trying to do with this:
Avoid arbitrary prices from rarity. Trying meet those values, not start with them.
All variables of the equations are drawn from the item's mechanical values.
At a later point will try and work in a value modifier for extra dice damage, so weapons like flametongues and holy avengers could be priced with it.
though I'm betting someone will still pipe up with "if Rare use this value, if Very Rare with this value"
So how about it? Any suggestions or examples of similar attempts you have to share?

Well, this is a pretty big buff to Dex martials... the last ones who need it haha. Weapons I would go with a damage dice approach? Or size maybe. So have light weapons be one price, 1 handed weapons another, bows\xbows another, heavy two hand weapons another?

[JackPhoenix]

Pluses are nice to have, but the main power of a magic weapon has exactly the same value for the dagger and for the greataxe: ability to get though non-magical resistances and immunities.

[Zhorn]

I like where you are heading but I think there is a bit more at play which make exact figuring too difficult.

In a dwarven region where people love making armor perhaps the metal armors are cheaper. In the middle of an enchanted elven metropolis maybe plate mail is rare but enchanted armor is easier to come by.
I get that, but as stated in the dot points I'm trying to limit the scope to drawing information from just the item's mechanics.
Damage dice? yes that matters.
Properties? most probably yes.

Where it was made, or who made it? nope, not relevant. A +1 dagger made by a dwarf is indistinguishable from a +1 dagger made by an elf. And if their where mechanically discernible differences mechanically, those mechanical differences would be what I'd look at, not the lore or flavour text.


--snip--
Different classes will personally value different things. Acknowledged the difference of opinion, but respectfully disregarding. The class that wields the weapons, or the stats of the character that wields it it not a property of the weapon itself. Not getting caught up in that as to avoid scope creep.


I'm slightly torn on this one, but I think it's fine if there's the right adaptability elsewhere in the formula. The lower-AC armour benefits more from the +, so it seems sensible to have a proportionally larger increase in price... BUT the proportional value of +1 AC is also not consistent across the range of possible ACs anyway. I think the bigger thing is that weapons and armour are presumably gated by proficiency even for NPCs in-fiction, which means the die size isn't the only factor that might go into a calculation; rarity and/or market share might play an important role. (I'm quite happy with the possibility that things aren't equally easy to enchant, or that some items are more likely to have been preserved than others from the good ol' days when enchantment was actually being done, or that enchantments came from gods and so the item range is based on divine whims or historical utility rather than contemporary usefulness.)
Proficiency of the wield not being a property of the weapon/armor so skipping past that.
Same for market shares, enchanting difficulties, or any other layers of 'lore'. Too easy to overcomplicate things with delving into the multitudes of possible story elements.
Taking a spherical cow approach on this, not a simulation of an anatomically accurate depiction of a cow.

But the value of those +1's +2's and +3's being of different worth depending on where a characters total AC ends up is something I considered in that armor formula. Still tweaking the rate of increase for each in it, but the trend I have is;
- the higher the final AC (of just the item) the more expensive it will be, but also
- the more unrestricted an armor is in adding a modifier the greater a price multiplier it has

Studded leather's multiplier increases the total cost, while Plate's multiplier decreases it since one lets the full dex bonus apply while the other doesn't use it at all.
But the raw AC potential of plate is just so far ahead of studded leather that is it still ahead. You can get close with max stats, but plate is not depending on such an investment to be that high.
Again, the multipliers are still being played with, but those values are being paid attention to.


I think meeting the rarity ranges probably doesn't make sense as a goal -- if you're just recreating the existing prices or ranges, it's going to contribute less (you're just doing more work to get to the start point). Instead, I think it would be better to consider the rarity a mechanical property: it's in the item info and it's used for other things in the game (mainly or only artificers and downtime crafting, if either are in the game). The rarity could act like a price multiplier, which intuitively makes sense to me; a more rare non-powerful item is still likely going to cost more than a less rare item with about the same (im)potency. That also makes it more useful for other DMs; they can change the estimated rarity to fit their world and end up with a useful adaptation to the price. (I'd be tempted to have rarity have a range of multipliers, to adjust for smaller or regional differences, e.g. Rare can map onto 1.6 to 1.9, to provide entirely made up numbers.)
Probably my bad for not explaining as well as I should have. The rarity ranges as a target goal, but not being present in the equation is for pricing things that either have a power not reflected by their rarity, or don't have a rarity to begin with (homebrew items). The later goal will be for plugging in the values of such things to get a price for them that is independent of exactly how rare they are.
An item's rarity not being a factor of the equation is so I can use this in cases where a rarity isn't listed to begin with.

[PhantomSoul]

Probably my bad for not explaining as well as I should have. The rarity ranges as a target goal, but not being present in the equation is for pricing things that either have a power not reflected by their rarity, or don't have a rarity to begin with (homebrew items). The later goal will be for plugging in the values of such things to get a price for them that is independent of exactly how rare they are.
An item's rarity not being a factor of the equation is so I can use this in cases where a rarity isn't listed to begin with.

That's how I understood the goal -- I just don't fully understand why that's the goal, to be honest! I think that if rarity is meant to be put aside, it could still be a multiplier in the formula, and it just happens to be a variable sent to 1 as a baseline; rarity is ignored when the goal is purely finding the "objective" value of the item.

However, I don't see why the rarity price range should be a goal at all. I'd ignore what the book says for the price by rarity altogether, but then have a later stage adjusting what the multiplier recommendations should be for different rarity ranges. Effectively, the rarity price ranges are already "tainted" by the rarity (definitionally, even!), so targeting those prices without including the rarity in the formula seems like muddying the contribution of the formulae you're working on. Recreating the existing ranges just doesn't seem as appealing as a raw measure of power that then has an easy knob or two to turn to adjust to the world -- it seems that the whole starting premise is that the price ranges just don't relate well enough to the power to begin with!

Anytime the price would matter for the DM, they could decide the rarity multiplier that applies to their world (and/or this time and region of it). Just like they could choose to keep or modify the rarity of existing items, and thereby easily know what type of price shift to apply to the item.

[Zhorn]

However, I don't see why the rarity price range should be a goal at all.
Part of my base principle of houserules is to try to adhere to existing structures to a reasonable degree.
It means if I plug'n'play with some changes but not others, the overall system doesn't run into hiccups with things no longer matching.

The price ranges of the existing rarity levels is being targeted as a loose goalpost since the existing hoard/loot tables exist with those assumptions. If the formula is spitting out reasonably close value for the items I'm configuring it to, the overall value of the roll tables should also be loosely maintained.
The extreme ends may vary wildly (see padded armor vs plate in my example formula), but the overall average for each tier is still close to the target, meaning the average wealth gain of rolling on each table is also kept reasonable consistent.

Agree or disagree; in any case I'll not be using a rarity modifier in the formula.

[PhoenixPhyre]

Side note: the DMG random magic items table do not contain entries for +X padded armor, hide armor, or ring mail. Or even any of the specific variants (ie Armor of Resistance (Hide)).

Personally, I'd just prefer to make (permanent) magic items not generically buyable or sellable. You can buy them, but the price is favors or trade, not a fixed sum of cash. You can sell them, but each one's a negotiation. But that's just me and my style.

[heavyfuel]

Different classes will personally value different things. Acknowledged the difference of opinion, but respectfully disregarding. The class that wields the weapons, or the stats of the character that wields it it not a property of the weapon itself. Not getting caught up in that as to avoid scope creep.

I get what you're trying to do, especially with disregarding of rarity, but analyzing things in a vacuum is not the greatest way to go about such analyses. The game isn't played in a vacuum, and pricing things as if it was is guaranteed to not have the best result.

Your game, your call. But having players pay a premium for wanting to play a guy in heavy armor just seems like a recipe for resentment, though.