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Shining Wrath
2014-08-30, 01:22 PM
Greetings,

This is an attempt to quantify the spell casting abilities of the casting classes in the PHB based on two criteria:
Spell slots (power), and
Versatility (cantrips + spells known).

To compute the power of spell slots I present two methods of weighting a spell's power
2**(Level - 1), and Level**2, where the ** notation means "exponent".

Comparing these weighting methods looks like this


Level
1
2
3
4
5
6
7
8
9


2**(L-1)
1
2
4
8
16
32
64
128
256


L**2
1
4
9
16
25
36
49
64
81


As may be seen 2**(L-1) puts heavier weight comparatively at higher levels. Use what you prefer, just be consistent.

Here's the non-numerical stuff about the classes - the key ability score for casting, the source from which they prepare each days spells, and some comments.


Class
Ability
Source
Comments


Bard
Cha
Chosen at level up
College of Lore adds 2 L3 spells to known list


Cleric
Wis
Whole list
Domain spells and rituals


Druid
Wis
Whole List
Rituals; Circle of Lore adds 1 cantrip and circle spells


Eldritch Knight
Int
Chosen at level-up



Paladin
Cha
Whole list
Oath spells


Ranger
Wis
Chosen at level-up



Sorcerer
Cha
Chosen at level-up
Sorcery points


Warlock
Cha
Chosen at level-up
Invocations, Patron spell list


Wizard
Int
Spell book
Spell Mastery, Signature Spells



This table compares the power of spell slots as explained above, the versatility as measured by cantrips and by the number of spells of the class's highest level if the character always uses the "swap a spell" feature to gain more spells of higher levels. In some cases (hello, warlocks!) there is more ability to learn spells than there are slots to learn.




L4
L4
L4
L4
L10
L10
L10
L10
L16
L16
L16
L16
L20
L20
L20
L20


Class
2**n
n**2
C
N
2**n
n**2
C
N
2**n
n**2
C
N
2**n
n**2
C
N


Bard
10
13
3
4
78
138
4
5
302
287
4
3
655
478
4
7 (4)


Cleric
10
13
3
*
78
138
5
*
302
287
5
*
655
478
5
*


Druid
10
13
3
*
78
138
4
*
302
287
4
*
655
478
4
*


Eldritch Knight
3
3
0
4
10
13
0
5
22
43
0
7
30
59
0
4


Paladin
3
3
0
*
18
34
0
*
38
75
0
*
78
141
0
*


Ranger
3
3
0
3
18
34
0
3
38
75
0
6
78
141
0
6(4)


Sorcerer
10
13
5
4
78
138
6
4
302
287
6
3
655
478
6
5


Warlock
4
8
2
4
32
50
4
3
48
75
4
12 (6)
64
100
4
15 (6)


Wizard
10
13
4
?
78
138
5
?
302
287
5
?
655
478
5 (7)
?



As may be seen, all the full casting classes get exactly the same amount of spell slots. The exceptions are the Sorcerer, who can buy additional spell slots with Sorcery points; and the Wizard, who can recover (L/2) spell slots with Arcane Recovery, none being higher than 6th level. The combination of Arcane Recovery plus (DM willing) the most spells known plus the largest spell list makes the Wizard, as one would expect, the most powerful of the full casters. Throw in Spell Mastery which is essentially 2 more cantrips, but L1 spells, and the wizard is most flexible and has nearly the same spell points as the Sorcerer. At 20th level the Sorcerer's Sorcery points buy the equivalent of 40 (2**(N-1)) or 64 (N**2) spell slot points - about 10% more power.

In terms of versatility Sorcerers get fewer spells than Bards (!), but have the most cantrips, allowing them more flexibility in the spamming department, which is what you'd expect. Metamagic is very powerful and flexible.

Aside from the Eldritch Knight, the Ranger is the weakest spell caster. Less power than the Warlock, no cantrips, and the weaker "prepare from a small list you learn as you level-up" source add up to weak.

Warlocks are interesting because of the combination of invocations (all day buffs) and slightly better casting than a Paladin.

hymer
2014-08-30, 01:29 PM
As may be seen, all the full casting classes get exactly the same amount of spell slots. The exceptions are the Sorcerer, who can buy additional spell slots with Sorcery points; and the Wizard, who can recover (L/2) spell slots with Arcane Recovery, none being higher than 6th level.

A little note: Land Circle Druids get the equivalent mechanic to Arcane Recovery. They call it Natural Recovery.

Callin
2014-08-30, 01:31 PM
Land Circle Druids get Natural Recovery which works just like the Wizard Ability Arcane Recovery

edit- dang ninjas

hymer
2014-08-30, 01:47 PM
edit- dang ninjas

Hey, hey! I prefer the term 'shadow monk'!

Another on topic note:


Aside from the Eldritch Knight, the Ranger is the weakest spell caster.

Arcane Trickster is on par with EK, isn't it?

These nitpicks aside, it looks mighty impressive. I'm looking forward to seeing some people who have the math skills to understand it start talking to you about it, Shining Wrath.

Shining Wrath
2014-08-30, 02:41 PM
Hey, hey! I prefer the term 'shadow monk'!

Another on topic note:



Arcane Trickster is on par with EK, isn't it?

These nitpicks aside, it looks mighty impressive. I'm looking forward to seeing some people who have the math skills to understand it start talking to you about it, Shining Wrath.

I must have missed Arcane Trickster - I skipped Rogue.

In terms of raw casting power, a 20th level Paladin or Ranger is about a match for a L10 full caster. A L20 Eldritch knight is about a L6 or L7 full caster.

Prophes0r
2014-08-30, 06:01 PM
...** notation means "exponent"...

The standard notation for Exponent is ^ which is called a caret (or sometimes an up caret). Most English keyboards have it on shift-6.

(I'm not nitpicking to be a jerk. Just trying to help you be understood better. Someone who does not speak English would not be able to read your current notation using **)

In addition, there are many things you are discounting, or forgetting in your statistical analysis. You are also trying to shoehorn an entire class/level into one number, which just takes meaning away from that number in the end. It may be more useful in the end to make these changes:


Split apart sub classes that have large differences in casting potential. Example: [Moon Druid] vs [Land Druid]
provide a bit more granular results. Example:
Maximum spells per Encounter
Maximum spell levels per Encounter
Maximum spells per Day (assuming some number of short rests. 2 might be appropriate)
Maximum spell levels per Day
It may also be worthwhile to consider popular multiclass choices to show how they can drastically change a caster's "Spell Power"


I may just end up putting this stuff into MathLab and making a post myself.

EDIT: had to change carrot to caret since my spellchecker wants to keep auto-correcting it. Good catch.

Shining Wrath
2014-08-30, 07:50 PM
The standard notation for Exponent is ^ which is called a carrot, or up carrot. Most English keyboards have it on shift-6.

(I'm not nitpicking to be a jerk. Just trying to help you be understood better. Someone who does not speak English would not be able to read your current notation using **)

In addition, there are many things you are discounting, or forgetting in your statistical analysis. You are also trying to shoehorn an entire class/level into one number, which just takes meaning away from that number in the end. It may be more useful in the end to make these changes:


Split apart sub classes that have large differences in casting potential. Example: [Moon Druid] vs [Land Druid]
provide a bit more granular results. Example:
Maximum spells per Encounter
Maximum spell levels per Encounter
Maximum spells per Day (assuming some number of short rests. 2 might be appropriate)
Maximum spell levels per Day
It may also be worthwhile to consider popular multiclass choices to show how they can drastically change a caster's "Spell Power"


I may just end up putting this stuff into MathLab and making a post myself.

The notation ** is from FORTRAN, which is older than English.

Curious what you mean by "Maximum spells per encounter", as you can cast them all.

The granularity question is countered by the copyright issue - I don't want to supply a complete description of "M L1, N L2, O L3".

Elderand
2014-08-30, 08:03 PM
The notation ** is from FORTRAN, which is older than English.

I think you clearly mispoke here, because last I checked, a programming language from the 50's cannot be older than modern english that dates back to the 17th century.

Shining Wrath
2014-08-30, 09:22 PM
I think you clearly mispoke here, because last I checked, a programming language from the 50's cannot be older than modern english that dates back to the 17th century.

Clearly you must not realize that God programmed the Universe using FORTRAN :smallbiggrin:

Prophes0r
2014-08-30, 09:35 PM
...The granularity question is countered by the copyright issue...

In what way? You can give plenty of information without duplicating the tables in the PHB. That also was not what I was suggesting. I was thinking more like this:




Possible Spells per Enc.
Possible Spell Levels per Enc.
Possible Spells per Day
Possible Spell Levels per Day


Cleric(War) lvl 1
2
2
2
2


Cleric(War) lvl 5
9
16
9
16


Warlock lvl 1
1
1
3
3


Warlock(Blade) lvl 5
2
6
6
18



This table ignores cantrips, and assumes 3 short rests per day.

We can clearly see that a traditional caster has the advantage in both number, and maximum total spell levels expendable during a given encounter. However, it should also be clear that given periods of rest, a warlock will be able to put out more total spell levels.

theMycon
2014-08-30, 10:02 PM
I think you clearly mispoke here, because last I checked, a programming language from the 50's cannot be older than modern english that dates back to the 17th century.

First, it's called a "caret", not a "carrot".
Second, I'm not sure whether ** notation is older or newer than ^ notation. It's certainly older than personal computers/graphing calculators; and (at risk of dating myself) superscript isn't hard to do on a typewriter.

It's still used in PERL & Python, I at least have seen it enough times that I forgot people might not recognize it (until I saw the note at the end).

Aquillion
2014-09-01, 04:56 AM
First, it's called a "caret", not a "carrot".
Second, I'm not sure whether ** notation is older or newer than ^ notation. It's certainly older than personal computers/graphing calculators; and (at risk of dating myself) superscript isn't hard to do on a typewriter.

It's still used in PERL & Python, I at least have seen it enough times that I forgot people might not recognize it (until I saw the note at the end).** is older, actually, at least according to Wikipedia.

Carets didn't even enter ASCII until 1967, whereas FORTRAN was created in 1957. (The caret (https://en.wikipedia.org/wiki/Caret) page does say that the up-arrow that was eventually replaced by the caret was used for exponentiation in ALGOL 60 (https://en.wikipedia.org/wiki/ALGOL_60), but that's still not as old as FORTRAN.)

But I would generally say that today, the caret is more clear for non-programmers.

Shining Wrath
2014-09-01, 05:28 PM
** is older, actually, at least according to Wikipedia.

Carets didn't even enter ASCII until 1967, whereas FORTRAN was created in 1957. (The caret (https://en.wikipedia.org/wiki/Caret) page does say that the up-arrow that was eventually replaced by the caret was used for exponentiation in ALGOL 60 (https://en.wikipedia.org/wiki/ALGOL_60), but that's still not as old as FORTRAN.)

But I would generally say that today, the caret is more clear for non-programmers.

And when I explain my notation on the same line where I use it, it's really a non issue. :smallsigh:

Prophes0r
2014-09-01, 07:16 PM
And when I explain my notation on the same line where I use it, it's really a non issue.

Assuming that the people you are explaining it to speak English well enough, or that Google translate works properly.

EDIT: I actually just notices that the forums editor already HAS a sub/super-script function built in.

2n

Aquillion
2014-09-04, 03:07 PM
That's cheating! How are we going to argue over obscure technicalities in the syntax of early computer science if people just use that?