How much is a spell worth?

[harpy]

I think a lot with the system as I tweak and houserule. One thing that has stumped me for awhile is how much a spell is worth in the system. Obviously, it varies due to a number of variables, but getting some general idea is something that I keep plugging away at.

Some of the things I've been taking into account:

The Action Economy

In 3.5 you had a dev formula given that basically a four combats ought to be expected in any given day, and further that each combat averages about five rounds. So four combats times five rounds gets you to 20 rounds per day. I don't buy that estimation, particularly for Pathfinder, but for simplicity I'll stick to 20 rounds a day for this discussion.

In terms of the action economy, you have 20 actions to perform each day. A fighter can pick up a sword and can reasonably be expected (between charges and standard attacks) of being able to perform 20 attacks in a given day.

Spells however, barring cantrips, can only be done once per day. Once a spell has been cast then it can't be replicated again, at least without other magical resources being used, but I want to ignore that because a fighter can perform attack actions the whole time, even unarmed strikes, without any additional help.

So spells at a base level are worth 1/20 of a standard attack. You could say that an attack is worth 20 points and a spell is worth 1 point.

Spell Levels

Spells are not equal to one another. You have a wide range of effects, so varied that you're reduced to eyeballing things most of the time. However they are grouped into spell levels, which at least gives a numerical scaling of their value that we can play with.

You could basically take the spell level as its point value, with cantrips being worth half a point. Thus a first level spell is worth 1 point. A ninth level spell is worth 9 points. Cantrips, because they are at-will, can be performed every round, and thus they are worth 10 points (20*0.5).

Caster Level

Spells quite often also scale with caster level in a variety of ways. This isn't always the case, which muddies the water, but in general you can expect some kind of scaling for effect and/or duration.

With 20 levels this means a 9th level spell is worth at least 153 points (9*17) and goes up to 180 points.

This all seems like it's going ok, but then you look at how you have to scale standard attacks. They scale also, directly with increasing BAB, but in general it will be assumed that additional damage will also accrue in the system in various ways.

If you scale up a standard attack it has a value of 400 points (20*20).

Iterative Attacks

Going back to the action economy. The fighter at 20th level is getting more actions in a round when performing a full-attack. That has to be factored in also.

The first attack is worth 400 (20*20), the second is worth 300 (15*20), the third is 200 (10*20), and the fourth is worth 100 (5*20), for a total of 1000 points for a full-attack at 20th level.

This is where the math starts to fall apart for me. The problem is that you have a full-attack worth 1000 points, and a 9th level spell worth 180 points. While it's true that the 9th level spell is fired off once per day, and the full-attack just keeps chugging along, but those values seem off since 9th level spells might, in one casting, solve the entire fight with save effects, or the duration of a spell is so long that the spell is in fact in effect through the whole combat or multiple combats.

Aside from tediously costing out every spell in the core book, I haven't been able to wrap my head around a baseline that “feels right” in regard to how spells, from 1st to 9th, have the potential of having a wider impact then they have on a per round basis.

Any thoughts are appreciated.

[Tyndmyr]

Well, it's awkward to cost this out. See, spells aren't even always the same cost. Invisibility 3/day is not 3x as valuable as Invisibility 1/day. You use the first one a lot more than the third one.

[Flickerdart]

A single attack (a 20-point value by your math) deals hit point damage to a monster. A single 9th level spell (a 9-point value by your math) creates a new plane of existence. How much hit point damage is equal to a new plane of existence? You can't really compare attacks and spells, because they do completely different things.

What exactly are you trying to measure with these points anyway?

[harpy]

Well, I've spent several years now fussing in various ways to break out the entire system into a point value system.

Basically, I want to "lego-ize" it so that I can construct things with more exacting precision and not rely on the endless eyeballing.

What I'm doing is building off of the Challenging Challenge Ratings document. However that document dealt with spells on a very broad benchmark level of measurement. I want something that is far more exacting.

I suspect the only way I'm going to be able to do that is to tedious cost out every spell, but I'm just seeing if someone with far better math/analytic skills can produce a magic algorithm that will make it more exacting without having to grind through it all.

[Larpus]

Also, don't forget to consider the area spells, which given the right circumstances can end up being as good as a hefty number of attacks, especially those like Glitterdust, which with some luck can shut off a bunch of enemies for quite some battle time.

[Parra]

I don't think you're gonna find 1 magic formula that you can fit every situation. The system is just too complex for a 1 shoe fits all solution.

That said, if your really looking to stick a number to things you need to broaden spells into multiple categories.
For example; direct damage, buff, debuff, save or lose, summoning etc

Direct damage would be easy to compare to a melée combatant.
A Buff would be a modifier to what ever it buffs (defences, saves, damage etc)
A Debuff would do similar though through a different method.
A Save or lose would potentially be comparable to a full encounters worth of output
A Summon would vary depending on what the summon did (beff, debuff etc)

And all of those variables will then change further depending on interparty synergy, levels involved and the encounter laid out before them

Honestly even attempting to derive some sort of numerical value from all of that gives me a headache

[Garwain]

But you didn't factor the relative 'power' aspect in.

Just a rough thought: power as an exponent: 1-5 with
1: ineffective usage of 6 sec
2: being the melee hit
3: being the autokill
4: I push this button, now the fight ends.
5: the world is altered/broken

Now full attack is: 1000^2 = 1 * 10^6
Brake the world is: 180^5 = 1.8 * 10^11

lvl9 spell = 10.000.000 times more expensive than a full attack. Was that the ratio you're looking for?

[Tyndmyr]

I tried such a thing at one time.

Synergy jacks it all up. See, a d6/cl single target spell...nice, steady number. Easy to calculate. CL booster? Oh, now you've changed everything. Metamagics?

Aright, toss it away. It's not going to be calculable as a single number in all contexts.

[Zombimode]

Cantrips, because they are at-will

Says who? Not the rule books for sure.

[Flickerdart]

Says who? Not the rule books for sure.

He's talking Pathfinder.

[NecroRick]

If we take your 20th level Fighter's attack as being worth 1000 points, I don't see a problem.

Okay, you solve 1 encounter with 1 ninth level spell, and now you are helpless in the next 3. :D

But of course a mage gets multiple spells/day.

Lets just consider the top 20 spells. For convenience I'm using Wizard from 3.5, not the Pathfinder one whatever that is. We have 4 spells at each level (ignoring bonus spells from high stats because meh, maths)

Let's calculate spell values according to your formula:
Level 9 = 9 x 17 = 153
Level 8 = 8 x 15 = 120
Level 7 = 7 x 13 = 91
Level 6 = 6 x 11 = 66
Level 5 = 5 x 9 = 45

(153 + 120 + 91 + 66 + 45) x 4 = 1900

So our intuition (that a level 20 wizard is worth more than a level 20 fighter) is preserved, even though you might have originally thought that the spell value is too low.

You could also make an argument for using level 20 in each of the spell values instead of the minimum level at which it becomes available, in which case the net result is 2800.

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From a game design point of view, pay careful attention to what the 4th ed guys did, they made almost everything a combat related activity. If you have a non-combat related spell, that typically represents an ability or capability that no one else can get access to.

And then it doesn't matter what values you assign to it - because the ratio of Wizard to Fighter in that situation is N:0 - so the Wizard is 'infinitely better' in that scenario (hence also the tier fallacy).

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It is well known that wizards increase in capability at a polynomial rate (e.g. level squared - a level 20 wizard is by that measure roughly 400 times more powerful than a level 1 wizard, without even taking into account the disparity between level 1 spells and level 9 spells), compared to other classes, such as fighter which may be increasing more linearly.

But I wouldn't put both their starting points at 1. Take the level 1 fighter, he is useful in every encounter that day. Odds are, the wizard is only useful in one, and he is baggage in the rest.

If combat is your only measure of usefulness then it actually takes the wizard quite a while to catch up to the fighter.

On this very board for instance there is an example of a 7th level wizard getting his butt handed to him by a much lower level fighter.

Very early on fighters have more staying power (hit points), hit harder, and can go all day. The wizard has to get to ~10th level before he can (for instance) cast 20 spells in a row (vis your original parameters).

Someone will always take exception when this is pointed out - they will say "but what about X?" when X is (for example) magic items, conveniently forgetting that fighters also get magic items. Some will take exception simply because they despise fighters so much, and all logic flies out the window whenever fighters and wizards are compared. Or they will take the section on extremely low-level fighters and wizards and triumphantly rebut it with a declaration that wizards can cast (for instance) Wish. Perhaps they will assume that every monster the wizard faces always fails every saving throw. Perhaps they will run through a massive list of defences the wizard has, conveniently neglecting that low level wizards do not in fact get 400 spell slots per day. You may laugh, but the trend is disturbing. It is better, for the sake a logical discussion, never to mention fighters and wizards in the same thread.

[Tyndmyr]

It is well known that wizards increase in capability at a polynomial rate (e.g. level squared - a level 20 wizard is by that measure roughly 400 times more powerful than a level 1 wizard, without even taking into account the disparity between level 1 spells and level 9 spells), compared to other classes, such as fighter which may be increasing more linearly.

Number of spells per day DO increase linearly.

They are only quadratic BECAUSE of the spell level increase.

You will also note that a level 20 wizard does not have 400 times as many spells as a level 1 wizard.

[NecroRick]

Number of spells per day DO increase linearly.

They are only quadratic BECAUSE of the spell level increase.

You will also note that a level 20 wizard does not have 400 times as many spells as a level 1 wizard.

You will fail to note that I did not say what you are saying I said.

Let us agree that if a level 1 wizard casts one spell that does 1d6 damage, and a level 20 wizard casts 20 spells that do 20d6 damage that this is not a linear increase, it is more similar to a polynomial increase.

[Tyndmyr]

Oh, if we're using purely damage based metrics without regard for actions, then the fighter clearly wins.

This'd be a clue that the metric is ridiculous.

[Telonius]

A couple things will throw off this scheme. First, as you've noted, duration-based spells. Not all spells have instantaneous effects. Passive, long-duration spells throw things out of whack tremendously. Basically, anything you cast before going into combat gives you additional actions during combat; since otherwise you'd have spent precious combat actions casting the spells. This is one of the (many) reasons why Divine Metamagic shenanigans are so powerful.

Second, spellcasters get ways to break the action economy that melee classes have a tough time duplicating (other than UMD'ing a scroll, which costs money). Time Stop and the Celerity line are the most extreme examples, but even lower-level spells can do this. A Druid casting Mass Snake's Swiftness, for example, could end up giving his group four or five extra attacks in a given round, if everybody's clumped together. Summon Monster/Nature's Ally spells do this too; so do the various Dominate and Hold spells.

Finally, casters can do things outside of combat altogether than can seriously help the team. Divinations of all varieties fall into this category. How do you assign a point value to the Bard using Glibness to get past the guards; or Legend Lore to figure out who the BBEG really is; or the Wizard learning from an extraplanar being that the left path leads to certain doom? A melee class using Bluff/Diplomacy or a Gather Information check just isn't going to do what a spell can do.

I suppose the gist of this is, assuming that each character takes one "action" in a round is good and correct, as far as it goes. But spellcasters can do things outside combat that help in (and out of) combat; and their actions will often affect foes (and allies) for more than just one round. Any system assigning point value to spells will have to take all of that into account.

[NNescio]

This is an FNP problem. FNP problems are NP-hard, which is geek-speak for "not frickin' worth your time".

[Karoht]

Hypothetically, we could produce a number that equates to a level 20 fighter with full round attack = X
Hypothetically, we could produce a number that equates to a level 20 wizard casting a 9th level spell = y.

If your basis of comparison is across the full day (as per your original post) and a fighter is expected to make 20 attacks per day, and each full attack is 1000 points, then that is 20000 points. Should a 9th level cast once per day = 20000 points as well by comparison? Or are we not going for equality and just raw numbers?

In other words, is X considered = to Y or is X =/= Y?


I would also argue that it takes significantly less spell casting to equal a fighter's full attack at level 20, depending on the context mind you.

[Tyndmyr]

X and Y vary wildly depending on a near infinite number of factors.

The equation needed to calculate this would need to include essentially every rule from the entire set of 3.5, as well as further factors which are not defined in the ruleset, but are rather, situational.

Trying to establish a relationship between X and Y in this manner is futile.

[Karoht]

Trying to establish a relationship between X and Y in this manner is futile.

I agree that you are most likely correct.

The equation needed to calculate this would need to include essentially every rule from the entire set of 3.5, as well as further factors which are not defined in the ruleset, but are rather, situational.

Or we could narrow down the parameters. A lot. In fact, if we assumed 20 levels of straight wizard and 20 levels of straight fighter, and all attacks were VS a level 1 Pig with infinity hitpoints...

On second thought...


PS-I'm pretty sure there are X jokes about how fighters suck, where X = any number between 1-100, but the number of jokes about how monks suck is X^2

[harpy]

If your basis of comparison is across the full day (as per your original post) and a fighter is expected to make 20 attacks per day, and each full attack is 1000 points, then that is 20000 points. Should a 9th level cast once per day = 20000 points as well by comparison? Or are we not going for equality and just raw numbers?

In other words, is X considered = to Y or is X =/= Y?

I wouldn't be aiming for equality, at least in the end result of the potency of a fighter and wizard. That would come from design.

Assuming that a wizard casts one spell per round, composed of all the slots from 5th level to 9th level spells, then he has outputted 2800 points, versus the 20,000 of the fighter.

If we assume the wizard is more powerful than the fighter from all of the play experience, then these number seem to be way off. If a wizard casts 20 spells in a day then, from play experience, you'd think the numbers would sail well past the fighter's full attacks. So scaling the formula as (20*9) isn't good enough. The value of a 9th level spell isn't 9, but some higher number. The suggestion for squaring it though seems too high. There definitely is a martial/caster disparity, but the gulf that squaring gives seems to overvalue wizards.

I can see the argument that this approach is futile, the system is so wildly complex that you'd need elaborate software and grinding analysis to get to some kind of "Newtonian Objectivity" in regard to the system.

Still, the game was designed. And while a huge amount of the design used the eyeballing technique, it seems after all this time you could get metrics that were a little more precise. I have no problem with the absolute values being fuzzy, but I think some kind of benchmark is possible, which can then assist the eyeballing.

Maybe the question to be asked isn't how much an individual spell is worth, but how much a spell slot is worth?

[Tyndmyr]

Still, the game was designed. And while a huge amount of the design used the eyeballing technique, it seems after all this time you could get metrics that were a little more precise. I have no problem with the absolute values being fuzzy, but I think some kind of benchmark is possible, which can then assist the eyeballing.

I fear you misunderstand. There is no objective benchmark to be had. This is not a matter of absolute values being fuzzy, it's like trying to assign oranges a value and freedom a value and determining which is superior.

It's literally no more objective than saying "Gee, I really like oranges". It cannot be. Research "travelling salesman problem", note that it is NP hard, and that this task is ridiculously more complicated than that one.

Step 1 is basically superseding the entire world's known mathematical ability.
Step 2 is realizing that D&D doesn't even define everything clearly enough to USE it in an equation. Plenty of rules remain ambiguous.
Step 3 is finding an easier task, like curing cancer.

Maybe the question to be asked isn't how much an individual spell is worth, but how much a spell slot is worth?

That is a different question, but it is one that is innately tied to how much spells are worth. It doesn't make it more possible at all.

[BlueInc]

Trollface.jpg

[harpy]

I guess what I'm confused by is how a game can be designed, but at the same time there is no way of creating benchmarks for the design.

Eyeballing is an assessment process. Deciding this or that effect is at a certain spell level is an assessment.

And there is a aim and direction to the game at it's core, which is to kill things and take their stuff. So it's true that there are oddball and ephemeral effects, but in a broad way they are only meaningful in relation to how useful they will support the main point of the game.

Like I said, I'm not trying to find some absolute value, but one that makes sense in relation to the system as a whole.

If you want to create a new monster and give it an at-will spell like ability, you're going to need to assess how that impacts its CR, so some value has to be applied. What I'm trying to figure out is one element in a more consistent and systematic approach to making that assessment.

So I can understand it's not easy, but since assessment and valuation has already been occurring for decades with D&D, it's hard to imagine that you can't have a more refined methodology than guestimating and maybe playtesting.

On the flip side you have systems that are complete point-buys, such as Hero or GURPS. Everything is broken down in those games, so I'm not sure why they can't be done in D&D. Mutants and Masterminds is d20 based and it's point buy also.

[Tyndmyr]

Look, things are broken down into points in gurps or hero, sure.

This does not mean that those point valuations are accurate.

[Emmerask]

If you want to create a new monster and give it an at-will spell like ability, you're going to need to assess how that impacts its CR, so some value has to be applied. What I'm trying to figure out is one element in a more consistent and systematic approach to making that assessment.

So I can understand it's not easy, but since assessment and valuation has already been occurring for decades with D&D, it's hard to imagine that you can't have a more refined methodology than guestimating and maybe playtesting.

On the flip side you have systems that are complete point-buys, such as Hero or GURPS. Everything is broken down in those games, so I'm not sure why they can't be done in D&D. Mutants and Masterminds is d20 based and it's point buy also.

Well first of all you can´t estimate the worth of a spell in general because spells itself vary greatly from useless to yeah the universe is yours now have fun with it.
An at will fireball ability will have very little impact while blackfire (army killer) will have far more and wish even more then that.

So the only way to give it some meaning is not to give spells in general a value, but to give each and every single spell a cr and maybe even add an "x factor" to it like terrain or similar.

So lets say you do all that and create a system that lets you predict the CR of spells, even then it would give you very very littleand you still had to eyeball and playtest the challenge rating,
Because the party of optimized wizards is different then the party of unoptimized monks.

In short CR is extremely flawed anyway, why go through all the work to ascertain the CR-value of a spell if the CR system even then has next to no meaning?

[harpy]

True, they might not be accurate, but they might also be accurate. I haven't crunched their systems, but they've all gone through multiple versions. Presumably the devs have been evaluating how the system performs, using feedback from various sources and then tweaking the numbers and how those numbers interact to better dial-in to what they want out of the system.

What I'd linked to before, Challenging Challenge Ratings document, was created specifically so the designer could more reliably make epic level content for 3.5. He wanted benchmarks so that he could have more clarity with the CR system, and with that more clear view be able to design new content that has some rational basis behind it.

I'm just trying to extend that analysis out further. His goal was more broad than mine is and so I'm trying to get a more nuances evaluation of spells.

To look at it in another way. You have two GMs. One makes some house rules up and his methodology is, "I thought this would be cool" and then just made up some game statistics in five minutes that works off of one element of the system.

Then there is a second GM who likewise thinks, "this would be cool to do" but then spends a week looking at how his idea would impact the system, what cascading effects might occur if it was introduced, and then opens up a spread sheet to run some numbers to see how it compares to a similar effect that already exists in the system.

If the two GM's published their houserules on Drive Through RPG, and offered up their design notes as part of a preview, if I was going to spend money on the pdf I'd likely pay the second GM over the first.

[dextercorvia]

The main source of the problem seems to be that you assigned a fighter a base point value for one full attack based on how many times/day he could (or would be expected) to do that. That has no bearing on whether 1 full attack = one highest level spell (of equal level characters) or not.

By your system a Warlock can cast shatter 144000 times per day therefore casting shatter is worth 144000 points.

[harpy]

Well first of all you can´t estimate the worth of a spell in general because spells itself vary greatly from useless to yeah the universe is yours now have fun with it.
An at will fireball ability will have very little impact while blackfire (army killer) will have far more and wish even more then that.

So the only way to give it some meaning is not to give spells in general a value, but to give each and every single spell a cr and maybe even add an "x factor" to it like terrain or similar.

This has been a good conversation because it is being impressed upon me that to do this right you really need to break down the value of each spell, and then aggregate those values into spell levels to get benchmarks within the spell levels themselves. That way you could get a broad value based off of the averages of the collected spells in any given level and caster level.

That obviously takes a lot of time. So it's really just an issue of how much it's worth to me.

One thing that would be worthwhile to come out of it is that I'd likely find many spells that don't really belong in different spell levels, or that they ought to be adjusted to fit more within the average value of those spell levels.

[harpy]

The main source of the problem seems to be that you assigned a fighter a base point value for one full attack based on how many times/day he could (or would be expected) to do that. That has no bearing on whether 1 full attack = one highest level spell (of equal level characters) or not.

By your system a Warlock can cast shatter 144000 times per day therefore casting shatter is worth 144000 points.

I agree that there are issues with my methodology. That's why I'm on here to get ideas on how to refine that methodology.

I do think that the action economy is one of the factors that has to be calculated into an assessment. Wizard spells are a finite resource within a specific time frame, and a full attack is a consistent effect that can reasonably fill up that entire time frame. Further, the full-attack directly aims at the main intent of the game, which is to kill things and take their stuff. Thus some comparison needs to be made. It's the ratios that I'm trying to work out.

[Tyndmyr]

This has been a good conversation because it is being impressed upon me that to do this right you really need to break down the value of each spell, and then aggregate those values into spell levels to get benchmarks within the spell levels themselves. That way you could get a broad value based off of the averages of the collected spells in any given level and caster level.

That obviously takes a lot of time. So it's really just an issue of how much it's worth to me.

One thing that would be worthwhile to come out of it is that I'd likely find many spells that don't really belong in different spell levels, or that they ought to be adjusted to fit more within the average value of those spell levels.

You can rate spells within specific contexts(see class optimization guides), but it's harder to rate them universally.

Is haste as a level 1 spell better than haste as a level 3 spell? Does this depend on what class list it's a part of, and how fast the progression is? This is not a hypothetical scenario...