The Barbarian's Guide to Sorcery

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# <center class="title title-style">The Barbarian's Guide to Sorcery</center>

# <center class="subtitle subtitle-style">the sorcerer class is a class for beginners and other jokes you can tell yourself</center>

T his is an analysis of the Sorcerer's primary strategic repertoire. We will approach the Sorcerer class mathematically. This analysis focuses on the twin pillars of Font of Magic and Metamagic—the Sorcerer's two core class features. At the end of this process, you will see of the complexity of this class and its true power and flexibility when optimized.

- ### [1The Fundamentals](#The-Fundamentals)
- ##### [1Maximizing Font of Magic](#Maximizing-Font-Of-Magic)
 - [2Cardinality Target](#Cardinality-Target)
 - [3Quality, Quantity, and Cost](#Quality-Quantity-And-Cost)
- ##### [4Black Metamagic](#Black-Metamagic)
 - [4Twinned Spell](#Twinned-Spell)
 - [5Extended Spell](#Extended-Spell)
- ##### [7Red Metamagic](#Red-Metamagic)
 - [8Sorcerer's Ante and Metamagic Pot](#Sorcerers-Ante-And-Metamagic-Pot)
 - [8Quickened Spell](#Quickened-Spell)
 - [10Heightened Spell](#Heightened-Spell)
 - [12Distant Spell](#Distant-Spell)
 - [13Careful Spell](#Careful-Spell)
 - [14Subtle Spell](#Subtle-Spell)
 - [16Empowered Spell](#Empowered-Spell)
- ##### [18Closing Notes](#Closing-Notes)
- ##### [19Post Script](#Post-Script)
 - [19Change Log](#Change-Log)
 - [19Contact the Author](#Contact)
 - [19Thank You!](#Thank-You)

</div>

\columnbreak

## <div id="The-Fundamentals"></div>The Fundamentals

Sorcerers have two unique class features. In this section, we will gain an intricate understanding of both of them.

### <div id="Maximizing-Font-Of-Magic"></div>Maximizing Font of Magic

When you gain Font of Magic, you gain Flexible Casting. With this ability, you simultaneously gain the power to do the following things:

* the creation of more Sorcery Points by burning any of your spell slots
* the creation of high level spell slots by burning your low level spell slots
* the creation of low level spell slots by burning your high level spell slots

The first ability is widely used—more Sorcery Points also means more fuel in the tank for Metamagic. This is a very useful strategy, but it is not the only one.

The second ability can be very powerful as well. What this ultimately implies is, between levels three through ten, the Sorcerer can cast their highest level spell more often than any other full caster by sacrificing all of their lower level spell slots and Sorcery Points.

Between levels six through eight, Flexible Casting enables the Sorcerer to cast spells at a higher level than their peers. For instance, at Level 6, a caster can typically only cast as high as 3rd level. However, a Level 6 Sorcerer also gains six Sorcery Points, and Flexible Casting requires exactly that much to create a 4th level spell slot. Therefore, a Sorcerer could have access to 4th level spell slots at level 6.

Finally, the third ability can be situationally useful, but you will often not want to turn a 5th level spell slot into two 1st level spell slots unless the situation truly calls for it.

\pagebreak

With these abilities, we are essentially creating a long rest-based Warlock—but one with faster spell progression, more spell slots, and is optimal in a game where the party rarely takes any short rests.

#### <div id="Cardinality-Target"></div>Cardinality Target

With Flexible Magic, the Sorcerer can cast more spells at or above any given target level than any other full caster at the cost of casting fewer overall spells that day. For the sake of brevity, we will call the maximum number of times they can cast spells at a given target level the **cardinality target**.

It may be easier to understand this number when expressed as a formula:

<div class="MathJax_Display" style="text-align: center;"> <mi>c</mi><mi>a</mi><mi>r</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mtext>&#xA0;</mtext><mi>t</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>e</mi><mi>t</mi><mo>=</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="2.047em" minsize="2.047em">&#x230A;</mo></mrow></mstyle><mfrac><mrow><mi>L</mi><mo>+</mo><munderover><mo>&#x2211;</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>t</mi><mo>&#x2212;</mo><mn>1</mn></mrow></munderover><msub><mi>n</mi><mi>s</mi></msub></mrow><msub><mi>c</mi><mi>s</mi></msub></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="2.047em" minsize="2.047em">&#x230B;</mo></mrow></mstyle><mo>+</mo><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>&#x2265;</mo><mi>t</mi></mrow></msub></math>' role="presentation" >𝑐𝑎𝑟𝑑𝑖𝑛𝑎𝑙𝑖𝑡𝑦 𝑡𝑎𝑟𝑔𝑒𝑡=⌊𝐿+∑𝑡−1𝑠=1𝑛𝑠𝑐𝑡⌋+𝑛𝑠≥𝑡 </div>

Where: *L* is the Sorcerer's level; 𝑛𝑠 is the number of spell slots with a level equal to 𝑠 that the Sorcerer gains after a long rest; 𝑐𝑡 is the cost in Sorcery Points to create a new spell slot of a level equal to 𝑡; and 𝑡 is the target level.

##### Calculating The Cardinality Target

If you ask a Level 9 Sorcerer how many times they can cast *polymorph*, this is how they would answer: they convert all of their spell slots lower than 4th level into 19 Sorcery Points, in addition to the 9 Sorcery Points they already have, to get a total of 28 Sorcery Points. From this, they can create four 4th level spell slots with four Sorcery Points left over. They also have three 4th level spell slots and one 5th level spell slot for free. Therefore, this Level 9 Sorcerer can cast *polymorph* seven times at 4th level and once at 5th level: a total of eight times, and so eight is their cardinality target.

##### The Sorcerer's Cardinality Targets

<div style='position: absolute; top: 547px; left: 198px;'>
<h6>–Cardinality Target per Spell Level–</h6>
</div>

| Sorcerer Level | 2nd | 3rd | 4th | 5th |
|:-----------------:|:---:|:---:|:---:|:---:|
| 3rd | 4 | — | — | — |
| 4th | 5 | — | — | — |
| 5th | 8 | 5 | — | — |
| 6th | 9 | 6 | 4 | — |
| 7th | 10 | 7 | 5 | 4 |
| 8th | 12 | 8 | 6 | 5 |
| 9th | 14 | 10 | 8 | 6 |
| 10th | 15 | 12 | 9 | 7 |
| 11th | 17 | 13 | 11 | 9 |
| 12th | 17 | 13 | 11 | 9 |
| 13th | 18 | 14 | 12 | 10 |
| 14th | 19 | 14 | 12 | 10 |
| 15th | 20 | 16 | 13 | 11 |
| 16th | 20 | 16 | 13 | 11 |
| 17th | 22 | 17 | 15 | 12 |
| 18th | 23 | 18 | 16 | 14 |
| 19th | 24 | 19 | 17 | 15 |
| 20th | 26 | 21 | 18 | 16 |
</div>

\columnbreak

> ##### You Cannot Exceed the Maximum
>
> There is a rule under Font of Magic that states you can never have more Sorcery Points than the max number of these points you have as listed in the Sorcerer table of the *Player's Handbook*.
>
> So, how could a Sorcerer collect 28 Sorcery Points at Level 9 to create four 4th level spell slots? They collect them over time.
>
> Roughly: until all your lower level spell slots are gone, create a new spell slot with Sorcery Points, and then refill by choosing spell slots to convert such that you do not exceed your max limit.
>
> There always exists an algorithm such that you can convert all your lower level spell slots up to your target level without exceeding the max limit.
>
> As for exceeding your "max spell slots," there is no max number of spell slots. You can create as much as you like if you have the means for it.

The Sorcerer's Cardinality Targets table lists the cardinality targets of the Sorcerer for each of their Sorcerer levels and target levels. From this, we can observe a few things.

At Level 5, when other full casters gain two 3rd level spell slots for the first time, Sorcerers can cast five of them.

At Level 7, when other full casters gain a single 4th level spell slot for the first time, Sorcerers can cast five of them already. Indeed, they could have already been casting at 4th level one level sooner.

At Level 9, when other full casters gain a single 5th level spell slot for the first time, Sorcerers can cast six of them already. In addition, they could have already been casting at 5th level two levels sooner.

In order for even the Warlock to meet or exceed this many spell slots, they need two short rests—that is, a standard full adventuring day as planned by the designers. However, it is worth considering that, in many tables, the party may often have one or fewer short rests between long rests on average. In such cases, not even the Warlock can match this volume of high level spells.

\pagebreak

\columnbreak

#### <div id="Quality-Quantity-And-Cost"></div>Quality, Quantity, and Cost

In raw quantity of spells cast per day, the Warlock wins with no contest. With Eldritch Invocations that grant unlimited castings of *silent image*, *detect magic*, *false life*, and so on, they can cast 1st level spells all day without using up any resources.

Second are classes with Ritual Casting: once every ten minutes, they can cast a spell at its lowest level without expending spell slots. Though this is about two orders of magnitude slower than Eldritch Invocations, it is still far more sustainable than casting from spell slots. Also, 6th level ritual spells exist, whereas at-will invocation spells only go up to 4th level.

And so the question is, does the Sorcerer's large capacity to cast high level spells matter when stacked against these two class features?

The core principle to remember is this: the more unres-tricted a feature is, the less disruptive it must be to the game. For example, you can cast *identify* on as many objects as you wish, but since you are supposed to know the nature of the items in your possession, it will be rare for that to disrupt the game. Thus, in a sense, the *quality* of ritual spells is much weaker than non-ritual spells of the same level; and the same is true for at-will invocation spells.

Put in another way: you get what you pay for. The cheaper the cost of your ability, the lower its quality will be.

Obviously, this is not always the case—the Paladin's Divine Smite is both cheap *and* high quality, for example—but out-side these exceptions, and especially when relating Eldritch Invocations, Ritual Casting, and Flexible Casting with one another, this is a useful analogy.

This is *not* to say that ritual spells and at-will spells are not
     useful. They simply occupy a different niche than the limited but numerous high level spells that Flexible Casting provides. The Sorcerer cannot match the various situational utility spells of a ritual caster; but only the Sorcerer can cast five *haste* spells as a 5th level caster unaided.

And so yes, we can conclude that the Sorcerer's capacity to cast a large number of high level spells does stack up against ritual spells and at-will powers.

> ##### Addressing Spell Points
>
> The Spell Point variant rule (DMG 288) allows casters to use a form of Flexible Casting: it enables the efficient and lossless conversion of lower level spell slots into higher level spell slots, up to a maximum level, no bonus action required.
>
> While this is a buff for all casters, it benefits the Sorcerer the least. Whereas before, only they could cast *fireball* five times as a 5th level caster, now all casters can do that, too. However, the Sorcerer does not gain more spells known, ritual casting, or at-will powers to remain competitive in that arena.
>
> While Sorcerers retain faster spell progression (only Flexible Casting allows the creation of high level spell slots early) and Metamagic, using Spell Points is still like giving away the powers of the class for little in exchange.

\pagebreak

### <div id="Black-Metamagic"></div>Black Metamagic

One of the most flexible abilities in the game is Metamagic: the ability to modify your spells on the fly to suit the needs of the moment. Your metamagic selection will inform your spell list and strategy as you play through the game, and therefore it is important to understand them.

We will evaluate metamagic by its synergy with Flexible Casting by asking: how does it affect your cardinality targets? For convenience, we will take inspiration from the accounting phrase *in the black* and call metamagics that increase your cardinality targets as **black metamagic**. We will examine them in this section.

#### <div id="Twinned-Spell"></div>Twinned Spell

When you apply Twinned Spell on an eligible spell, you are gaining the following benefits:

* you move with tempo in the action economy—you are casting two spells with one action
* you economize your concentration if you twin a concentration spell
* you convert Sorcery Points into a spell without loss and without spending a bonus action for the conversion

We will assume the first two points are well-known enough to not need explanation.

But, the third benefit may not be discussed as much. When you cast, say, *dispel magic*, you need to burn a 3rd level spell slot. To cast it again using Sorcery Points, you need to burn five for another 3rd level spell slot. The total expenditure is one 3rd level spell slot and five Sorcery Points.

But, if you twin *dispel magic*, you only need three Sorcery Points in addition to the spell slot. That is two points less than with Flexible Casting!

Here is the key insight: Twinned Spell is lossless. One spell slot level is equal to one Sorcery Point. On the other hand, Flexible Casting is lossy. Creating a spell slot of 1st or 2nd level wastes one Sorcery Point to entropy, while creating a spell slot of 3rd, 4th, or 5th level wastes two. Twinned Spell sidesteps entropy by directly converting Sorcery Points into a spell's second target.

Let's now introduce some constants and helper functions:

<div class="MathJax_Display" style="text-align: center;"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub></mtd><mtd><mi></mi><mo>=</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="2.047em" minsize="2.047em">&#x2308;</mo></mrow></mstyle><mfrac><mrow><mn>1</mn><mo>+</mo><mtext>sgn</mtext><mo stretchy="false">(</mo><mi>b</mi><mo>&#x2212;</mo><mi>a</mi><mo stretchy="false">)</mo></mrow><mn>2</mn></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="2.047em" minsize="2.047em">&#x2309;</mo></mrow></mstyle></mtd></mtr><mtr><mtd><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub></mtd><mtd><mi></mi><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>&#x03BC;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub></mtd><mtd><mi></mi><mo>=</mo><mtext>min</mtext><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.623em" minsize="1.623em">(</mo></mrow></mstyle><msub><mi>n</mi><mi>s</mi></msub><mo>,</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.623em" minsize="1.623em">&#x230A;</mo></mrow></mstyle><mfrac><mi>p</mi><mi>s</mi></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.623em" minsize="1.623em">&#x230B;</mo></mrow></mstyle><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.623em" minsize="1.623em">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><msub><mi>&#x03BD;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub></mtd><mtd><mi></mi><mo>=</mo><mi>p</mi><mo>&#x2212;</mo><mi>s</mi><msub><mi>&#x03BC;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>,</mo><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub></mrow></msub><mo>&#x2212;</mo><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>,</mo><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>&#x03BE;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub></mtd><mtd><mi></mi><mo>=</mo><mn>2</mn><msub><mi>n</mi><mi>s</mi></msub><mo>&#x2212;</mo><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>,</mo><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub></mrow></msub><mo stretchy="false">(</mo><msub><mi>n</mi><mi>s</mi></msub><mo>&#x2212;</mo><msub><mi>&#x03BC;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>h</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>+</mo><mn>1</mn><mo>,</mo><msub><mi>&#x03BD;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>&#x03C7;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub></mtd><mtd><mi></mi><mo>=</mo><msub><mi>n</mi><mi>s</mi></msub><mo>+</mo><msub><mi>h</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msub></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>=</mo><mi>L</mi><mo>+</mo><munderover><mo>&#x2211;</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>t</mi><mo>&#x2212;</mo><mn>1</mn></mrow></munderover><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi></mi><mo>=</mo><munderover><mo>&#x2211;</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>=</mo><mi>t</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi>t</mi><mo>+</mo><mi>a</mi></mrow></munderover><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub></mtd></mtr></mtable></math>' role="presentation" >𝑓𝑎,𝑏𝑔𝑎,𝑏𝜇𝑠,𝑝𝜈𝑠,𝑝𝜉𝑠,𝑝𝜒𝑠,𝑝𝑥𝑦=⌈1+sgn(𝑏−𝑎)2⌉=1−𝑓𝑎,𝑏=min(𝑛𝑠,⌊𝑝𝑠⌋)=𝑝−𝑠𝜇𝑠,𝑝𝑓𝑝,𝑠𝑛𝑠−𝑠𝑛𝑠𝑔𝑝,𝑠𝑛𝑠=2𝑛𝑠−𝑓𝑝,𝑠𝑛𝑠(𝑛𝑠−𝜇𝑠,𝑝)+ℎ𝑠+1,𝜈𝑠,𝑝=𝑛𝑠+ℎ𝑠+1,𝑝=𝐿+∑𝑠=1𝑡−1𝑠𝑛𝑠=∑𝑠=𝑡𝑡+𝑎𝑠𝑛𝑠 </div>

<div class="MathJax_Display" style="text-align: center;"> <msub><mi>h</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mn>0</mn></mtd><mtd><mtext>if&#xA0;</mtext><mi>s</mi><mo>&lt;</mo><mn>1</mn><mtext>&#xA0;or&#xA0;</mtext><mi>s</mi><mo>&gt;</mo><mn>10</mn></mtd></mtr><mtr><mtd><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.2em" minsize="1.2em">&#x230A;</mo></mrow></mstyle><mfrac><mi>p</mi><msub><mi>c</mi><mi>t</mi></msub></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.2em" minsize="1.2em">&#x230B;</mo></mrow></mstyle></mtd><mtd><mtext>if&#xA0;</mtext><mi>s</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msub><mi>&#x03B4;</mi><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>,</mo><mn>0</mn></mrow></msub><msub><mi>&#x03C7;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub><mo>+</mo><msub><mi>&#x03BE;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><msub><mi>&#x03B4;</mi><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>,</mo><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mtd><mtd><mtext>if&#xA0;</mtext><mn>1</mn><mo>&#x2264;</mo><mi>s</mi><mo>&#x2264;</mo><mn>9</mn></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math>' role="presentation" >ℎ𝑠,𝑝=⎧⎩⎨⎪⎪0⌊𝑝𝑐𝑡⌋𝛿𝑝,0𝜒𝑠,𝑝+𝜉𝑠,𝑝(1−𝛿𝑝,0)if 𝑠<1 or 𝑠>10if 𝑠=10if 1≤𝑠≤9 </div>

\columnbreak

We can finally define our updated cardinality target formula:

<mi>&#x03B3;</mi><mo>=</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><mi>y</mi><mo stretchy="false">)</mo><mo lspace="thickmathspace" rspace="thickmathspace">mod</mo><mo stretchy="false">(</mo><msub><mi>c</mi><mi>t</mi></msub><mo>+</mo><mi>t</mi><mo stretchy="false">)</mo><mspace linebreak="newline" /><mi>&#x03F5;</mi><mo>=</mo><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>&#x2265;</mo><mi>t</mi></mrow></msub><mo>+</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.623em" minsize="1.623em">&#x230A;</mo></mrow></mstyle><mfrac><mrow><mi>x</mi><mo>&#x2212;</mo><mi>y</mi></mrow><mrow><msub><mi>c</mi><mi>t</mi></msub><mo>+</mo><mi>t</mi></mrow></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.623em" minsize="1.623em">&#x230B;</mo></mrow></mstyle><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.623em" minsize="1.623em">&#x230A;</mo></mrow></mstyle><mfrac><mi>&#x03B3;</mi><msub><mi>c</mi><mi>t</mi></msub></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.623em" minsize="1.623em">&#x230B;</mo></mrow></mstyle><mspace linebreak="newline" /><mi>c</mi><mi>a</mi><mi>r</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mtext>&#xA0;</mtext><mi>t</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>e</mi><mi>t</mi><mo>=</mo><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>,</mo><mi>y</mi></mrow></msub><msub><mi>h</mi><mrow class="MJX-TeXAtom-ORD"><mi>t</mi><mo>,</mo><mi>x</mi></mrow></msub><mo>+</mo><mn>2</mn><mi>&#x03F5;</mi><msub><mi>g</mi><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>,</mo><mi>y</mi></mrow></msub></math>' role="presentation" >𝛾=(𝑥−𝑦)mod(𝑐𝑡+𝑡)𝜖=𝑛𝑠≥𝑡+⌊𝑥−𝑦𝑐𝑡+𝑡⌋+12⌊𝛾𝑐𝑡⌋𝑐𝑎𝑟𝑑𝑖𝑛𝑎𝑙𝑖𝑡𝑦 𝑡𝑎𝑟𝑔𝑒𝑡=𝑓𝑥,𝑦ℎ𝑡,𝑥+2𝜖𝑔𝑥,𝑦

Where: *t+a* equals your highest level spell slot when you com-plete a long rest; and 𝛿 is the Kronecker delta function.

Twinned Spell only makes spell slot creation lossless if you already have a spell splot to twin; if not, you need to make it via Flexible Casting first and incur inefficiency losses. The blending of lossy and lossless spell slot creation gives rise to these complicated equations.

The Twinned Spell Cardinality Targets table shows the resulting math already worked out for you.

##### Twinned Spell Cardinality Targets

<div style='position: absolute; top: 462px; right: 81px;'>
<h6>–Cardinality Target per Spell Level–</h6>
</div>

| Sorcerer Level | 2nd | 3rd | 4th | 5th |
|:-----------------:|:---:|:---:|:---:|:---:|
| 3rd | 5 | — | — | — |
| 4th | 6 | — | — | — |
| 5th | 9 | 6 | — | — |
| 6th | 10 | 7 | 4 | — |
| 7th | 11 | 8 | 6 | 4 |
| 8th | 11 | 10 | 7 | 5 |
| 9th | 15 | 12 | 10 | 7 |
| 10th | 16 | 13 | 11 | 9 |
| 11th | 18 | 15 | 12 | 10 |
| 12th | 18 | 15 | 12 | 10 |
| 13th | 19 | 16 | 13 | 11 |
| 14th | 20 | 16 | 13 | 11 |
| 15th | 21 | 17 | 15 | 12 |
| 16th | 21 | 18 | 15 | 12 |
| 17th | 22 | 18 | 15 | 12 |
| 18th | 24 | 20 | 17 | 14 |
| 19th | 25 | 21 | 18 | 16 |
| 20th | 26 | 22 | 20 | 17 |
</div>

We count twinned spells twice. Note, though, that twinning all your spells means you will be casting less often, but your overall spell output will be greater. Also, given a Sorcerer level and a target level, these cardinality targets are equal to or greater than what Flexible Casting alone can produce.

\pagebreak

##### The Economy of Expandable Spells

Some spells, such as *charm person* or *fly*, allow you to select more targets when cast at a higher level. We will call these **expandable spells**. So which is more efficient: twinning the spell at a lower level, or casting it at a higher level?

There are three cases to consider: (1) you have both the lower and higher level spell slots; (2) you only have the lower level spell slot and must create a higher level spell slot; and (3) you have neither spell slot and must choose at which level to create one.

We will look at inequalities for each of these cases. If the inequality is true, upcasting is better. If both sides are equal, upcasting or twinning costs the same. Otherwise, twinning is better. In all inequalities, 𝑠 represents the spell's base level. Note we count the cost of the spell slot used in addition to the Sorcery Point cost.

In the first case, casting is lossless. Thus, we upcast if the cost of the spell slot (equal to the level of the spell) one level higher is less than the cost of the twinned spell:

<div class="MathJax_Display" style="text-align: center;"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>s</mi><mo>+</mo><mn>1</mn></mtd><mtd><mi></mi><mo>&#x003C;</mo><mn>2</mn><mi>s</mi></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mi></mi><mo>&#x003C;</mo><mi>s</mi></mtd></mtr></mtable></math>' role="presentation" >𝑠+11<2𝑠<𝑠 </div>

From this inequality, we know that in the first case, for expandable spells of 2nd level or greater, we upcast.

In the second case, we introduce entropy since we need to create the higher level spell slot. We upcast if the cost of creating that spell slot via Flexible Casting is less than the cost of the twinned spell:

<div class="MathJax_Display" style="text-align: center;"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msub></mtd><mtd><mi></mi><mo>&#x003C;</mo><mn>2</mn><mi>s</mi></mtd></mtr></mtable></math>' role="presentation" >𝑐𝑠+1<2𝑠 </div>

In the third case, there is a lot of entropy since we need to create a spell slot to be able to cast at all. We upcast if the cost of creating the higher level spell slot is less than the cost of creating the lower level spell slot and twinning it:

<div class="MathJax_Display" style="text-align: center;"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><msub><mi>c</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msub></mtd><mtd><mi></mi><mo>&#x003C;</mo><msub><mi>c</mi><mi>s</mi></msub><mo>+</mo><mi>s</mi></mtd></mtr></mtable></math>' role="presentation" >𝑐𝑠+1<𝑐𝑠+𝑠 </div>

There is a special scenario for the second and third cases: since Flexible Casting can only create up to a 5th level spell slot, then if we do not have a 6th level spell slot available, we cannot upcast and are forced to twin.

The Upcasting vs Twinning Expandable Spells table shows the math already worked out for you.

##### Upcasting vs Twinning Expandable Spells

<div style='position: absolute; bottom: 194px; left: 229px;'>
<h6>–Scenarios–</h6>
</div>

| Spell Level | First | Second | Third |
|:---------------:|-------:|:------:|:-------|
| 5 | Upcast | Twin | Twin |
| 4 | Upcast | Upcast | Upcast |
| 3 | Upcast | Any | Upcast |
| 2 | Upcast | Twin | Any |
| 1 | Any | Twin | Any |
</div>

\columnbreak

#### <div id="Extended-Spell"></div>Extended Spell

This metamagic is, in theory, an amazing pick. When you use this on a spell you cast, you gain these benefits:

* you effectively create the effect of a second spell for one Sorcery Point
* you double the duration of the spell; so if you would have had to cast the spell again, your overhead cost is reduced to one Sorcery Point instead of another spell slot
* you delay the penalty of a spell's effect upon ending, if it has a negative effect when it ends
* you can make certain spells last the whole day, and some spells you cast before starting a long rest will still be in effect when the long rest ends

Despite its theoretical benefits, it's not favored in the meta for Sorcerers. We will dissect the reasons here while compa-ring them to its virtues.

##### Breaking Magical Thermodynamics

Extended Spell will produce the greatest cardinality target numbers among all the metamagics. This is because it pro-duces the effect of any eligible spell for one Sorcery Point—that is, you can get out of it more than you put in.

We calculate efficiency as follows:

<div class="MathJax_Display" style="text-align: center;"> <mtext>efficiency</mtext><mo>=</mo><mfrac><mtext>output</mtext><mtext>input</mtext></mfrac></math>' role="presentation" >efficiency=outputinput </div>

In this case, output is the level of the spell that was created, and input is the Sorcery Points spent to create the spell. The Efficiency of Spell Creation Methods table compares the effi-ciency values of different ways to create high level spells:

##### Efficiency of Spell Creation Methods

| Spell Level | Flexible Casting | Twinned Spell | Extended Spell |
|:---------------:|:--------------------:|:-----------------:|:------------------:|
| 1 | 1/2 = 50% | 1/1 = 100% | 1/1 = 100% |
| 2 | 2/3 = 66% | 2/2 = 100% | 2/1 = 200% |
| 3 | 3/5 = 60% | 3/3 = 100% | 3/1 = 300% |
| 4 | 4/6 = 66% | 4/4 = 100% | 4/1 = 400% |
| 5 | 5/7 = 71% | 5/5 = 100% | 5/1 = 500% |
| 6 | — | 6/6 = 100% | 6/1 = 600% |
| 7 | — | 7/7 = 100% | 7/1 = 700% |
| 8 | — | 8/8 = 100% | 8/1 = 800% |
| 9 | — | 9/9 = 100% | 9/1 = 900% |

Flexible Casting is the most inefficient spell creation me-thod. The three most efficient spell slots to create are at 5th, 4th, and 2nd levels, with a drop at 3rd level, and the least at 1st level. Meanwhile, Twinned Spell is always 100% efficient, and Extended Spell can reach 900% efficiency.

\pagebreak

Assuming you extend all your spells, you can calulate your new cardinality targets as follows:

<div class="MathJax_Display" style="text-align: center;"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd><mtd><mi></mi><mo>=</mo><mi>x</mi><mo>&#x2212;</mo><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>&#x2265;</mo><mi>t</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><mi></mi><mo>=</mo><msub><mi>c</mi><mi>t</mi></msub><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd><mtd><mi></mi><mo>=</mo><msub><mi>v</mi><mn>1</mn></msub><mo lspace="thickmathspace" rspace="thickmathspace">mod</mo><msub><mi>v</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>4</mn></msub></mtd><mtd><mi></mi><mo>=</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="2.047em" minsize="2.047em">&#x230A;</mo></mrow></mstyle><mfrac><msub><mi>v</mi><mn>1</mn></msub><msub><mi>v</mi><mn>2</mn></msub></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="2.047em" minsize="2.047em">&#x230B;</mo></mrow></mstyle><mo>+</mo><msub><mi>n</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>&#x2265;</mo><mi>t</mi></mrow></msub></mtd></mtr><mtr><mtd><mi>c</mi><mi>a</mi><mi>r</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mtext>&#xA0;</mtext><mi>t</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>e</mi><mi>t</mi></mtd><mtd><mi></mi><mo>=</mo><mn>2</mn><msub><mi>v</mi><mn>4</mn></msub><mo>+</mo><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><msub><mi>c</mi><mi>t</mi></msub><mo>,</mo><msub><mi>v</mi><mn>3</mn></msub></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><msub><mi>&#x03B4;</mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn><mo>,</mo><msub><mi>v</mi><mn>3</mn></msub></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math>' role="presentation" >𝑣1𝑣2𝑣3𝑣4𝑐𝑎𝑟𝑑𝑖𝑛𝑎𝑙𝑖𝑡𝑦 𝑡𝑎𝑟𝑔𝑒𝑡=𝑥−𝑛𝑠≥𝑡=𝑐𝑡+1=𝑣1mod𝑣2=⌊𝑣1𝑣2⌋+𝑛𝑠≥𝑡=2𝑣4+𝑓𝑐𝑡,𝑣3(1−𝛿0,𝑣3) </div>

The Extended Spell Cardinality Targets table shows the math already worked out for you:

##### Extended Spell Cardinality Targets

<div style='position: absolute; top: 242px; left: 197px;'>
<h6>–Cardinality Target per Spell Level–</h6>
</div>

| Sorcerer Level | 2nd | 3rd | 4th | 5th |
|:-----------------:|:---:|:---:|:---:|:---:|
| 3rd | 6 | — | — | — |
| 4th | 8 | — | — | — |
| 5th | 12 | 8 | — | — |
| 6th | 14 | 10 | 6 | — |
| 7th | 16 | 12 | 8 | 6 |
| 8th | 18 | 14 | 10 | 8 |
| 9th | 21 | 18 | 14 | 11 |
| 10th | 23 | 20 | 16 | 13 |
| 11th | 25 | 22 | 18 | 15 |
| 12th | 26 | 22 | 18 | 16 |
| 13th | 28 | 24 | 20 | 18 |
| 14th | 28 | 24 | 20 | 18 |
| 15th | 30 | 26 | 22 | 20 |
| 16th | 30 | 26 | 23 | 20 |
| 17th | 32 | 28 | 25 | 22 |
| 18th | 34 | 30 | 27 | 24 |
| 19th | 36 | 32 | 29 | 26 |
| 20th | 38 | 34 | 31 | 28 |

</div>

\columnbreak

We also count every extended spell twice. We can observe that for any Sorcerer level and target level, these cardinality targets are strictly greater than what even Twinned Spell can produce, further solidifying its status as the most efficient metamagic option available.

##### The Pitfalls of Extended Spell

Now that we've shown the good side of this metamagic, let's address why it doesn't translate in the game.

**Delayed Effect.** When you extend a spell, you do not get an immediate benefit from it. Due to the action economy, having two of the same effect active at the same time on demand ins-tantly is much more impactful than having only one effect ac-tive for twice as long when in combat.

**Insufficient Spell Synergy.** The core issue is that, gene-rally, most spells don't gain more value from doubling their duration. The best type of spell that can be extended is a non-concentration buff with an 8-hour duration. This means that, among the spells available to the Sorcerer, only *mage armor*, *darkvision*, *aid*, and *death ward* are compatible with it. Other spells, such as *foresight*, fit in this category, but they need a multiclassed build.

**Tedium of Time Tracking.** When you double a spell's du-ration, there is an implicit assumption that time is important, and therefore, time tracking is important. Not all tables agree and would rather abstract it away, focusing on role playing or combat instead of what they might consider to be bookkee-ping. Some Dungeon Masters are happy to assume a *mage armor* cast after a long rest will last until the end of the day.

**Somewhat Risky.** For spells that last between 10 minutes and an hour, doubling their duration can be a gamble: if no-thing happens on the second half of the extended duration, the Sorcery Point will have been wasted. Unless you cast the spell just before you actually need it, there is no guarantee that something interesting will happen over its extended duration, and even if something does, there is no assurance that it won't be resolved within the first half of the extended duration. If you can be efficient enough to finish your task before the spell's original duration runs out, then Extended Spell is redundant.

**Combat Isn't Long Enough.** Obviously, combats that last 10 rounds are rare. They do happen, but, depending on your level, perhaps not frequently enough to build a character for.

\pagebreak

##### The Verdict on Extended Spell

It's a decent 3rd level pick if you have the right spell list. Des-pite its pitfalls, the only other metamagic that can double your high-level spell output is Twinned Spell, and that is not nearly as efficient as this one. You can extend an 8 hour spell to 16 hours and then immediately take a long rest. You might find utility in 20-minute *fly* spells or two-hour *enhance ablity* spells. Because of how cheap this metamagic is, you can extend every spell you cast at your target level whether or not it's optimal to do so. The degree you will find these tricks useful depends on your build, campaign, and role in the party.

It's also a decent pick at 17th level. In particular, 10-round combats are a non-negligible possibility in high level play, and when your minute-long 8th level *holy aura* runs out, you will feel that impact because you won't have the high level spell slot to recast it with.

Moreover, you learn *wish* at 17th level. This means you can extend any spell of 8th level or lower outside of your spell list, such as *demiplane*, *glibness*, and *illusory dragon*.

\columnbreak

### Red Metamagic

When a company is *in the red*, it is losing money. In the same way, a **red metamagic** decreases your overall spell output by reducing your cardinality targets. When you take such a me-tamagic, you are giving up some amount of your higher level spell slots in exchange for its effect.

#### Sorcerer's Ante and Metamagic Pot

To offset the opportunity cost of the high level spell slot, a red metamagic must have an impact at least as great as, if not better than, the high level spell slot you will not be able to create due to using that metamagic.

To measure this in our analysis, we will create the idea of your **Sorcerer's ante**: the total Sorcery Points you spent on metamagics since your last long rest. For example, if you use Quickened Spell and Heightened Spell once each, that will raise your ante to five Sorcery Points.

The Sorcerer's ante represents another thing: the number of Sorcery Points that could have been used to create higher level spell slots via Flexible Casting instead. It is a measure of your opportunity cost in relation to your cardinality target.

We will call the value you *could* gain when you use a meta-magic a contribution to the **metamagic pot**. However, this quantity is subjective and difficult to measure. That won't stop us from fitting it in a measurement framework anyway so we can use it in our analysis, but we accept outright that any system of measurement that tries will have some degree of imprecision and subjectivity.

##### Tallying the Sorcerer's Ante

You cast a twinned *dispel magic* at 5th level. This raises your ante by five because you've spent five Sorcery Points to twin that spell. If you later use Flexible Casting to make a new 2nd level spell slot, you further raise your ante by three. Finally, if you cast a heightened *hold person*, you raise your ante again by three. So far, you have a ten point ante. When you take a long rest, your ante resets to zero.

##### Counting the Metamagic Pot

In the previous example, you twinned *dispel magic* at 5th level. This raised the pot by five because your use of the meta-magic produced a 5th level effect. When you created a 2nd level spell slot, the pot grew by two because a 2nd level spell slot can produce a 2nd level spell. Finally, when you heigh-tened *hold person* but the target succeded on their saving throw anyway, the pot doesn't grow. So far, you have a seven point pot. When you take a long rest, the pot resets to zero.

##### Black or Red?

If your target level is two, then we count how many spell slots we could have created at 2nd level from the ante. We need three Sorcery Points to make a spell slot, so a ten point ante can produce three. Three spell slots at 2nd level equals six spell levels, which is our **breakeven point**.

If the pot meets or exceeds the breakeven point, you are in the black; else, you are in the red. In this example, our pot is seven, so we are in the black. As we use more metamagic, it can change: if we heighten a spell and fail a second time, our breakeven point rises to eight while the pot doesn't change, so we would sink into red.

\pagebreak

##### Weighing the Pot

The effect of some metamagic options on the pot are easy to weigh: Twinned Spell and Extended Spell produce a second spell effect, so they raise the pot by the level of the spell they produce. But most metamagics do not have a well-defined value. To measure their weight, we must guesstimate with respect to your build, goal, and campaign—this is subjective. So, if you disagree with our measurements, just replace the specific values with what you feel is more accurate for your games. The goal is to present an agreeable enough set of weights that any disagreements will not be too far off from what is presented here.

This is our strategy: we will assume a context under which we cast a spell modified by some metamagic, and then turn all of that spell's benefits in that context into a new spell. We will guess the level of this new spell by benchmarking it with similar spells and, when we have decided on a value, increase the pot by the improvement in level of the original spell. We list them so it is extensible: if you have more ideas on how to use metamagic, you simply add them to your table.

Why are we considering the situation when evaluating spell level? Because metamagics are situational. Applying a meta-magic at the wrong time can add nothing, or even detract from, the spell's power. Using it at the right time, however, can add more value than what you pay for in Sorcery Points.

We also specify if you cast a spell and nothing happens, the pot does not increase since no effect has taken place.

#### Quickened Spell

When you use this metamagic option on a spell you cast, you gain the following benefits:

* you hijack the action economy by getting two actions on the same turn
* you enjoy the effect of a spell you cast on the same turn that you cast it
* you can bait an enemy caster's *counterspell* with a cantrip as your action or bonus action

Its power grows with your action's versatility. Plan around gaining powerful uses of your action so that you don't run out of things to do when you quicken a spell. Strongly consider multiclassing if you select this metamagic.

\columnbreak

##### Measuring Quickened Spell

Here are some strategies in using Quickened Spell and their corresponding spell level equivalents.

**Quadruple Set.** You are a Grave Cleric 2/Sorcerer 3 and your ally is a Fighter 5 with a greatsword and Great Weapon Fighting. You cast a quickened *hold person* and activate your Channel Divinity: Path to the Grave feature on the paralyzed target. Here is the equivalent spell:

<div class='descriptive'>
 
#### Grave Paralysis
*5th level enchantment*
___
- **Casting Time:** 1 action
- **Range:** 30 feet
- **Components:** V, S, M (a small, straight piece of iron)
- **Duration:** Concentration, up to 1 round

___
A humanoid within range must succeed a Wisdom saving throw or be paralyzed for the duration. The next melee attack that hits the target deals 41 (8d6+8ro<2) slashing damage instead of its normal damage.

You may not use a bonus action or cast a spell as a reaction on the turn you cast this spell.
 
</div>

Why is this spell 5th level? The fastest scaling single target damage spell below 6th level is *scorching ray*, and it takes one at 5th level to match this spell on damage alone. We will assume the other features cancel out (eg, *scorching ray* can target non-humanoids, doesn't need an ally, has better range; but *grave paralysis* has a 1-round paralysis effect).

*Hold person* provides two base spell levels. Quickening it in the given context boosts it to be effectively a 5th level spell. Quickened Spell thus provided us with a 3-level boost, and its pot value is three when used this way.

You may have questions. What if the target is resistant to the damage? Then the context changes and *grave paralysis* is demoted to 2nd level. What if you had a V. Human Paladin 2/ Rogue 3 pal with the Magic Initiate feat and *booming blade* cantrip? Then the context changes again and *grave paralysis* is promoted to 9th level.

The point is, it's context-dependent. You want to force the best contexts that can give metamagic its highest pot value.

\pagebreak

**Eldritch Cannon.** You are a Warlock 2/Sorcerer 3 with Agonizing Blast. You cast *eldritch blast* as your action and bonus action using Quickened Spell. Here's that as a spell:

<div class='descriptive'>
 
#### Magic Turret
*4th level evocation*
___
- **Casting Time:** 1 action
- **Range:** 120 feet
- **Components:** V, S
- **Duration:** Instantaneous

___
Make four ranged spell attacks against a target within range. Each attack deals 8.5 (1d10+3) force damage.

You may not use a bonus action or cast a spell as a reaction on the turn you cast this spell.
 
</div>

Once again, it takes *scorching ray* cast at 4th level to match this single-target damage, so the new spell is set at that level. The base spell is a cantrip, so that also happens to be the pot value of Quickened Spell in this context.

**Magic Item Hacker.** You are a Sorcerer 5 with a Pearl of Power. You quicken a *fireball* and then use your action to regain the spell slot you just consumed. This is that as a spell:

#### Gibbs Free Fireball
*evocation cantrip*
___
- **Casting Time:** 1 action
- **Range:** 150 feet
- **Components:** V, S, M (a tiny ball of bat guano and sulfur)
- **Duration:** Instantaneous

___
You cast a *fireball* spell. You may not use a bonus action or cast a spell as a reaction on the turn you cast this spell.
 
</div>

This unique case produces a spell effect at 3rd level at no cost. A *fireball* spell made cheaper by three spell levels implies Quickened Spell's pot value is three in this case.

**Extra Cantrip.** You are a Sorcerer 3 and are not aware about optimal spell synergy. You quicken a *shatter* spell and cast *fire bolt* as your action. In spell form:

#### Minor Explosion
*2nd level evocation*
___
- **Casting Time:** 1 action
- **Range:** 60 feet
- **Components:** V, S, M (a chip of mica)
- **Duration:** Instantaneous

___
Make a ranged spell attack against a target to deal 1d10 fire damage. The target and each creature within 10 feet of it must succeed on a Constitution saving throw or take 3d8 thunder damage. You may not use a bonus action or cast a spell as a reaction on the turn you cast this spell.
 
</div>

The effect is comparable to *ice knife* cast at 2nd level, offering no improvement to the base spell. The pot value here is zero.

##### Some Quickened Spell Pot Values

Here are some more uses of this metamagic, offered without further explanation.

**Triple Strike.** Quicken a *haste* spell on yourself. Use Extra Attack to make two strikes, and strike again with *haste*.

**Double Spells.** Quicken a *sunbeam* spell. Use your action to trigger it again. Continue to quicken spells and use your action to trigger *sunbeam* in subsequent rounds.

**Spellsword Nova.** Use your Thirsting Blade and +1 Pact Weapon to attack twice. Quicken a *lightning bolt*.

**Mage's Bane.** Cast *shocking grasp* on the lone enemy caster. As they no longer have a reaction for *counterspell*, quicken any spell.

\pagebreak

#### Heightened Spell

When you apply this metamagic option on a spell you cast, you gain the following benefits:

* you lower the mean value of one target's saving throw roll and reduce the variance that they fail their save
* you can apply it on the target as long as you can cast the spell on them with no other restrictions—whether they are flying, underground, invisible, etc; or whether you are blinded, restrained, deafened, etc
* you do not lose tempo in the action economy, be it a pre-vious setup round, bonus action, or reaction, from using it
* you produce no other visual effect other than the casting of the spell

This is the most expensive metamagic for good reason: ap-plied correctly, it can turn the tides of a campaign. This is the metamagic of power moves, but it also demands the most creativity and restraint from the player.

##### In Comparison to Alternatives

Though imposing disadvantage to saving throws against your spells is an overall rare ability, there are some class features that occupy a similar niche as this metamagic.

**Eldritch Strike.** This ability forces disadvantage on saves for no resource expenditure, and that's great. Unfortunately, it requires 10 levels of investment in a third-caster class, and you can only use it after you hit the target with a weapon attack. That means you can only use it in hostile situations even if you were to make the investment.

**Diviner's Portent.** The ability to sidestep saving throws altogether is incredibly potent. But, the Divination Wizard cannot guarantee they will roll low that day. If their portent dice are middling or high, they cannot force a failed saving throw. Heightened Spell can always be used for a force if you have the Sorcery Points. Despite the cost, even a 5th level Sorcerer already has a good stock of Sorcery Points in the form of spell slots.

**Hound of Ill Omen.** For the same cost in Sorcery Points, a Shadow Sorcerer can summon a hound that has the same impact on your target's saving throws. But, the presence of a hound can undercut the most stellar uses of this metamagic. The hound is visible, cannot swim or fly, and needs a bonus action to summon. A Shadow Sorcerer must also see their target to be able to call the hound. All in all, this leads to a combat focus in overt ways that Heightened Spell does not suffer from.

**Dust of Deliciousness.** Though not a class ability, this is an official magic item that imposes disadvantage on Wisdom saving throws if a creature eats food coated in one serving of it. Obviously, it is difficult to use in combat and is more limited in what spells it can enhance.

Overall, while we can consider these abilities as members of the same family, they do not obsolete one another.

\columnbreak

##### The Pitfalls of Heightened Spell

This metamagic is one of the hardest and clunkiest to use properly.

**Poor Scaling.** Heightened Spell is fantastic at lower levels, when monsters do not yet have Magic Resistance, Legendary Resistance, high saving throw modifiers, immunity to spells under a certain level, and *dispel magic*. At a high enough tier of play, spells that force saving throws fall obsolete outside of the Dungeon Master's mercy or the Rule of Cool.

**Easily Misused.** This metamagic does not pair well with blast spells and area spells. It does not work on boss mons-ters. Many fiends, fey, and celestials are resistant to it. It dep-letes your resources quickly. If you use it and the target fails their save but it does little to steer the situation in a different direction, it's wasted. There is a very slim error margin when using this metamagic, so unless it is applied surgically and creatively to achieve a specific goal, chances are higher that it will be wasted than be useful.

##### Measuring Heightened Spell

Here are some cases where Heightened Spell can be used, and their corresponding spell level equivalents.

**Reverse Uno.** You are a Bard 1/Sorcerer 4. Your party of four is about to face 16 bandits, two centaurs, and a human with five Rogue levels. You are the only caster. Initiative is rolled. On your turn, you cast heightened *phantasmal force* on the leader and in one turn, convince him that he should follow you, preventing a total party kill and reversing the power dynamics between your party and your enemy. Yes, I did this, and it worked. Here's the spell:

#### Gale's Strangled Heart
*8th level illusion*
___
- **Casting Time:** 1 action
- **Range:** 60 feet
- **Components:** V, S, M (a bit of fleece)
- **Duration:** Concentration, up to 1 minute

___
A creature you see within range must make an Intelligence saving throw at disadvantage or believe that you summoned a 10-foot tall angel of death that has reached into the target's chest and is squeezing their heart with cold fingers, but not enough to deal damage. At your Dungeon Master's discretion, make a Charisma (Deception) check contested by the target's Wisdom (Insight) check. On a success, the target believes the threat is real and will never attack you again. You recruit them to your side due to the fear you've instilled in them.

</div>

This spell punches 5th level to rival *modify memory* when used this way. The lowest level spell with no save that would have worked in this context is *illusory dragon*, thus the bump to 8th level. The pot value here is six.

\pagebreak

**Mind Trick.** You are a Trickery Cleric 9/Sorcerer 3. You are in a room alone with a hag, negotiating for lifting a curse she put on your friend. The hag wants your hands in return. You cast heightened *modify memory* to disagree.

#### Jester's Charm Monster
*9th level enchantment*
___
- **Casting Time:** 1 action
- **Range:** 30 feet
- **Components:** V, S
- **Duration:** Instantaneous

___
A target you can see within range must succeed on a Wisdom saving throw with disadvantage or think they spent the last 10 minutes having such a good time with you that they agreed to grant you a minor, simple wish with no payment in return. The target becomes your ally and friend.
 
</div>

This is Critical Role's legendary cupcake scene (minus the Sorcerer levels, plus a Dust of Deliciousness cupcake; but equating to disadvantage to saving throws in the end). Not even a *dominate monster* spell could have worked like this, so we place it at 9th level. Its pot value is four.

**Stronger Wards.** You are a Divine Soul Sorcerer 5. You cast *glyph of warding* and store a heightened *mind spike* into the spell glyph. Here it is as one spell:

#### Remote Alarm
*3rd level divination*
___
- **Casting Time:** 1 hour
- **Range:** Touch
- **Components:** V, S, M (incense worth 200 gp, consumed)
- **Duration:** Until dispelled or triggered

___
When a creature who does not speak the password enters the warded area, it must make an Intelligence saving throw with disadvantage or take 3d8 psychic damage, and you psychically know its location for the next hour. You designate a password and the area when you cast this spell.
 
</div>

This having no immediate effect, any spike in power can be expected to be diluted by time. The pot value of this is zero.

**Fireballer.** You are a Sorcerer 7. You cast a heightened *fireball* spell at 5th level. Here is the spell equivalent:

#### Mostly Fireball
*5th level evocation*
___
- **Casting Time:** 1 action
- **Range:** 150 feet
- **Components:** V, S, M (a tiny ball of bat guano and sulfur)
- **Duration:** Instantaneous

___
You cast a *fireball* spell at 5th level. One of the targets makes their saving throw with disadvantage.
 
</div>

There is no marked boost. For most creatures in the area, it is just an unmodified *fireball*. Its pot value is zero.

##### Some Heightened Spell Pot Values

Here are some more uses of this metamagic, offered without further explanation.

| Context       | Pot Value  |
|:-------------:|:----------:|
|  Paralyzer    | 0          |
|  Mind Control | 1          |
|  Dustmaker    | 0          |
|  Scry and Die | 5          |

**Paralyzer.** Heighten a *hold person* spell on a humanoid minion you're already fighting.

**Mind Control.** Heighten a *dominate monster* spell. You have one shot because you are still 15th level.

**Dustmaker.** Heighten a *disintegrate* spell against an ancient red dragon.

**Scry and Die.** You are about to cast *teleport* to bring your whole team to the enemy lair, complete with readied actions and pre-cast buffs. You cast a heightened *scrying* spell so you don't have to cast it multiple times, saving you the spell slot on a potential second casting.

\pagebreak

#### Distant Spell

When you apply this metamagic to a spell you cast, you gain the following benefits:

* you turn expandable touch spells, such as *fly* or *invisibility*, into 30 foot area spells when upcast
* you turn any touch spell into a spell with a 30 foot range
* you quadruple the area of effect of some spells whose area depends on their range, such as *beacon of hope*, *seeming*, or *divine word*
* your spells double in range, including not just attack spells but also those whose reach depends on their range, such as *clairvoyance*, *dimension door*, and *telekinesis*

The uniqueness of this metamagic lies in that it has a dif-ferent effect depending on which spell you pair it with. In that sense, it is like four metamagic options rolled into one, but for the price of one.

##### The Pitfalls of Distant Spell

This is a specialist's metamagic, which means it can shine if a problem inside the area of your specialty is presented to you. However, it might encourage you to be *too* specialized, and the opportunities for you to shine might exclude the rest of the party.

**Situational Utility.** Outside combat, doubling the range of utility spells such as *enhance ability* doesn't add much value to the spell since there is no consequence to moving within range of your targets first. Sadly, most spells that work with Distant Spell this way are utility spells of this type.

**Too Much Range.** One of the common things people say when talking about this metamagic is that it synergizes with Eldritch Spear and Spell Sniper to create a sustainable 1200 foot range *eldritch blast*. Yes, this is a valid strategy, but the combat where it becomes relevant is also the combat that no one else in the party can participate in. Your Dungeon Master will probably not have a 240 x 240 grid map prepared.

**Dungeon Fights.** If most of your combats happen indoors and there are no flying targets, the increased attack range from this metamagic will be difficult to use.

**No Counterspells.** This metamagic does not work with *counterspell*, because while it could double its range, it is only triggered when a spell is cast within 60 feet of you, not when a spell is cast within range.

\columnbreak

##### Measuring Distant Spell

Here are some cases where you can find Distant Spell clutch, and their corresponding spell level equivalents.

**Kite Master.** This is both a strength and a pitfall. You are a Human Draconic Origin Sorcerer 7 ambushed outdoors, with Spell Sniper and Winged Boots. You *dimension door* the full 500-foot range, ending up in the sky with a clear view of the fight. From here onwards, you pop a distant *fire bolt* to a max range of 480 feet, bolstered by Elemental Affinity for damage and ignoring half and three-quarters cover from Spell Sniper. If anyone gets within 100 feet of you, you can *dimension door* away again. Here it is as a spell:

#### Death From Above
*5th level evocation*
___
- **Casting Time:** 1 action
- **Range:** 500 feet
- **Components:** V, S
- **Duration:** Instantaneous

___
You are beyond the reach of attacks other than the long range increment of a longbow or spells with a 500-foot range. As an action, you can spend 1 Sorcery Point to make a ranged attack roll, dealing 15 (2d10+4) fire damage to a target within range. This effect lasts until you decide to end the spell.
 
</div>

This effect is similar to—but not vastly superior than—*far step*, so we peg it at 5th level. You can also dip two levels in Warlock for more range using Eldritch Spear and distant *dimension door*, putting you out of reach of all weapons. But at that point, you are almost playing a solo campaign. With our base as *dimension door*, our pot value is one.

##### Some Distant Spell Pot Values

Here are some more uses of this metamagic, offered without further explanation.

| Context       | Pot Value  |
|:-------------:|:----------:|
| Jean Gray     | 1          |
| Mass Makeover | 0          |
| Beacon        | 1          |
| Mass Buffs    | 1          |

**Jean Gray.** Double the range of *telekinesis* so you can drop something 120 feet in the air.

**Mass Makeover.** Cast a distant *seeming*, affecting four to eight times more creatures than you normally could.

**Beacon.** Cast a distant *beacon of hope*, affecting four to eight times more creatures than you normally could.

**Mass Buffs.** Cast a distant *longstrider* at 4th level, hitting the Barbarian on the front lines and the Ranger in the back without moving from your spot.

##### Is Distant Spell Good?

Yes! Though the previous metamagics pull in high pot values, Distant Spell is much cheaper, so it pays for itself even if you only get 1-point uses from it. It's low risk and highly reliable. From a cost-benefit perspective, its game is slow and steady.

\pagebreak

#### Careful Spell

When you apply this metamagic to a spell you cast, you gain the following benefits:

* you can mostly disregard precisely positioning your area of effect spells—you know your allies will not get caught in the blast
* you get the first round of saves for free on spells that have a multi-round effect
* your allies can be immune to area of effect spells you cast that offer only one save on the first round
* you may cast area of effect spells in close quarters
* you do not need to see the creatures you exclude, nor are you bound by other similar restrictions

This metamagic option can be incredibly useful in close quarters—the opposite of Distant Spell. The strength of this option relies on your comfort level with melee- to mid-range combat. Strongly consider this metamagic if your build forces you into close range.

##### In Comparison to Alternatives

There is one alternative to this metamagic that you can get to faster, and it's worth evaluating.

**Sculpt Spell.** A Wizard can exclude creatures in the area of effect of their own spells with this feature, with two limita-tions: it must be an evocation spell, and they need to cast at a higher level to exclude more creatures. They share a large number of spells, and on areas overlap, Sculpt Spell is better on spells of 3rd level or greater. Otherwise, Careful Spell has the better effect.

##### The Pitfalls of Careful Spell

A Sorcerer who wades into melee: that is already a sticky concept. It can be very successfully done, if with much pain and difficulty. Here are the challenges you may run into.

**Hexblades.** A one-level dip will grant shield and medium armor proficiency, as well as access to *armor of agathys* and *hellish rebuke*. While this boosts your survivability by leaps and bounds, it functions as a multiclass tax for you.

**Poor Scaling.** Like Heightened Spell, this option relies on spells that force saving throws. At high tiers of play, monsters with Magic Resistance, Legendary Resistance, high saving throw modifiers, immunity to spells under a certain level, and *dispel magic* are common. Once your reliable spells become obsolete, this metamagic follows suit.

**Insufficient Spell Synergy.** Most area of effect spells are either high-level evocations (*fireball*, *cone of cold*, etc), or they force a delayed save (*web*, *sickening radiance*, etc). There are not a lot of non-evocation area of effect spells that also force a save the moment they are cast, so your choices are limited.

\columnbreak

##### Measuring Careful Spell

Here are some strategies to use with Careful Spell, and their corresponding spell level equivalents.

**Wild Mage.** You are a Tiefling Hexblade 1/ Wild Mage 3. You've used *armor of agathys* at 1st level. You enter melee and cast a careful *pyrotechnics* on your own torch. A Wild Magic Surge triggers, you cast *fireball* centered on yourself, and you pass the save with Tides of Chaos. Here that is as a spell:

#### Flashbang
*5th level transmutation*
___
- **Casting Time:** 1 action
- **Range:** 20 feet
- **Components:** V, S
- **Duration:** Instantaneous

___
Creatures 10 feet of you of your choice must succeed on a Constitution save or be blinded. Creatures 20 feet of you must pass a Dexterity save or take 28 (8d6) fire damage.
 
</div>

We consider this as an example of post-analysis, rather than a plan to be executed (you can't *precisely* plan around a wild surge), using the "TPK-inducing" self-*fireball* result advanta-geously. The spell's level is five because it deals the effect of *fireball* for free. The pot value is three.

**Humanoid's Bane.** You are a Divine Soul 3 trapped in a small dungeon against a horde of humanoids. Your ally casts *fog cloud*. You follow up with a careful *calm emotions*. Here's that as a spell:

#### Hypnotic Darkness
*6th level enchantment*
___
- **Casting Time:** 1 action
- **Range:** 120 feet
- **Components:** V, S, M (a pinch of powder)
- **Duration:** Concentration, up to 10 minutes

___
Each creature in a 20-foot radius of your choice must pass a Charisma save or become nonhostile to your party. This effect ends on a target if they are attacked or harmed by a spell.
 
</div>

The base spells are *calm emotions* and *fog cloud*, and it turns the fight into a series of 4v1s. This beats *wall of force*, so we place it one spell level above it. Its pot value is three.

##### Some Careful Spell Pot Values

Here are a few uses of this metamagic, offered without further explanation.

| Context        | Pot Value  |
|:--------------:|:----------:|
| Combat Ender   | 3          |
| Two Falls      | 1          |
| True Confusion | 3          |

**Combat Ender.** Cast a careful *hypnotic pattern* spell.

**Two Falls.** Cast a careful *reverse gravity* spell.

**True Confusion.** Cast a careful *synaptic static* spell.

\pagebreak

#### Subtle Spell

When you use this metamagic option on a spell you cast, you gain the following benefits:

* you avoid being perceived when casting a spell that has no material components, thus you cannot be the target of *counterspell* or be identified while casting that spell
* you can cast while gagged, underwater, in an area of silence, or otherwise prevented from speaking
* you can cast while your hands are occupied, given the spell has no material components

This metamagic is theoretically a very potent one, and it is also very cost-efficient for its impact. A favorite in the meta for Sorcerer builds, however, it is not all roses.

##### In Comparison to Alternatives

It's not often discussed, but this metamagic has alternatives. It isn't quite as bulletproof as one might think:

**Archdruid.** If a 20th level Druid is in a beast shape form, their Druid spells have no VS components.

**Magic Items.** Though it may seem strange, magic items do not require any spell components. By strict Rules-As-Written, you do not wave a Wand of Fireballs to cast a *fireball* spell—an explosion just happens. Also, though you have to read a spell scroll to cast the spell inscribed in it, that casting has no components. Since any spell can be scribed into a spell scroll, any spell can be stripped of its components. The one area where Subtle Spell is superior to magic items is when you are not given access to magic items in the first place—which is a huge advantage in some campaigns where magic items are rare, randomly generated, and not easily made or freely sold.

##### The Pitfalls of Subtle Spell

Though powerful by itself in a strictly Rules-As-Written game, this metamagic has its downsides.

**Stealth House Rules.** In many tables, stealthily casting a spell with VS components is allowed by the Dungeon Master through skill checks. Allowing this dilutes the benefit of this metamagic because skill checks are free while metamagic is not. Also, Subtle Spell loses its status as the only reliable and sustainable player option.

**Pushover NPCs.** When you cast *charm person* on some-one, if the Dungeon Master allows you to do so without con-sequence—be it their friends reacting to the blatant mind control in front of them, or the target of the spell recognizing their free will being subverted at the end of the spell's dura-tion—then the value of hiding your casting, and thus of Subtle Spell, is greatly diminished at that table.

\columnbreak

**Non-Social Games.** If you do not have social encounters, the most powerful aspect of this metamagic—the power to cast spells such as *enemies abound* or *charm monster* in front of others undetected—cannot be used to its fullest potential.

**Sparse Caster Enemies.** If the Dungeon Master does not throw casters your way, or if their casters don't have *counter-spell* in their spell list, you lose the chance to use its major in-combat benefit.

**Never Captured.** Subtle Spell can shine when you are chained up and all weapons, armor, and components are stripped away. But scenarios like this, where spellcasting is so restricted as to be nearly impossible, are very negatively slanted against the party. Players may not enjoy having their abilities stripped away so overtly. Dungeon Masters will opt not to do this often. So, while the party could be thrown in situations like this, you can assume it happens so rarely you shouldn't build a character around it.

**M Components.** If a spell has an M component, Subtle Spell can't make that casting imperceptible. While many spells work with it, not all spells can be subtly cast.

##### Measuring Subtle Spell

Here are ways to utilize Subtle Spell, and their corresponding spell level equivalents.

**Affirm Spell.** You are a Sorcerer 13. You cast a *reverse gra-vity* spell, and an enemy casts *counterspell* on you. A second enemy has their own *counterspell* prepared. You cast a subtle *counterspell* on the first enemy. Here that is as a spell:

#### Bold Gravity Reversal
*7th level transmutation*
___
- **Casting Time:** 1 action
- **Range:** 100 feet
- **Components:** V, S, M (a lodestone and iron filings)
- **Duration:** Concentration, up to 1 minute

___
You cast *reverse gravity*, which cannot be negated by the *counterspell* spell.
 
</div>

In this context, had you not had Subtle Spell, you would have spent a 7th level spell slot to do nothing. Subtle Spell turns nothing back to a 7th level spell, so its pot value is seven.

**Undetected Spell.** You are a Sorcerer 9. An enemy is ready to *counterspell* you. You cast a subtle *telekinesis* to deny them that. Here is that as its own spell:

#### True Telekinesis
*5th level transmutation*
___
- **Casting Time:** 1 action
- **Range:** 60 feet
- **Components:** None
- **Duration:** Concentration, up to 10 minutes

___
You cast *telekinesis*, which cannot detected or denied.

</div>

In this context, even if the enemy cast *counterspell* on you, your spell could still work by casting *counterspell* on them. But, Subtle Spell saves you that and the third level spell slot. Your pot value is three.

\pagebreak

**Anti-Mage.** You are a Sorcerer 5. Your Bard enemy casts *moonbeam*, and has *counterspell* as well. You cast a subtle *counterspell* on their first spell. This is that summarized:

#### Moonbeam Negation
*3rd level abjuration*
___
- **Casting Time:** 1 reaction
- **Range:** 60 feet
- **Components:** None
- **Duration:** Instantaneous

___
The *moonbeam* spell a target casts within range has no effect.

</div>

If you did not have Subtle Spell, you would both have used *counterspell* and the enemy gains the benefit of a 2nd level spell. With Subtle Spell, for the enemy, they lost two spell levels. Their loss is your gain. Thus, the pot value in this case is two.

**Purple Wedding.** You are a Sorcerer 9 and found a way into your target's wedding. When your target makes their toast and drink their wine, you cast a subtle *dominate person* and take precise control over their actions. They exhale all their air and stop breathing. They will drop to zero hit points in five rounds or less, and they cannot be healed or stabilized. If anyone tries to cast *dispel magic*, cast a subtle *counterspell* to deny them help.

#### Traceless Poison
*9th level enchantment*
___
- **Casting Time:** 1 action
- **Range:** 60 feet
- **Components:** None
- **Duration:** Concentration, up to 1 minute

___
A target must succed a Wisdom saving throw or fall uncon-scious for the duration, after which the target dies. This casting is undetectable and cannot be denied.

</div>

This effect is comparable to *power word kill* but it can affect humanoids beyond 100 hit points, though it takes longer to work. Nonetheless, its effective level is nine. Its pot value is four.

**True Illusionist.** You are a Warlock 2/Sorcerer 3 with the Misty Visions Eldritch Invocation. You can cast *silent image* without any components at any time.

#### Minor Image
*illusion cantrip*
___
- **Casting Time:** 1 action
- **Range:** 60 feet
- **Components:** None
- **Duration:** Concentration, up to 10 minutes

___
You cast *silent image*, which cannot be detected or denied.

</div>

In this vague context, there is no added value to removing the VS components of *silent image*. Its pot value is zero.

##### Best Scaling Metamagic

Due solely to *counterspell*, Subtle Spell is the best scaling metamagic among your options. *Counterspell* only becomes more relevant the higher the tier of play goes as spells get nastier the higher level they are. If your *counterspell* is more powerful than that of the enemy, you hold a firm advantage over them in combat.

##### Some Subtle Spell Pot Values

Here are some more uses of this metamagic, offered without further explanation.

**Psychic Reality.** Cast a subtle *wish* to replicate any spell of 8th level or lower.

**Soundless Entry.** Cast a subtle *dimension door*, leaving and arriving soundlessly at any point within range.

**Underwater.** Cast any spell with Subtle Spell underwater and you are unable to breathe.

**Silenced.** Cast any spell with Subtle Spell in a soundless area, such as in the area of a *silence* spell or the area of a *hallow* spell with the silence effect.

\pagebreak

\columnbreak

#### Empowered Spell

As the only metamagic option that can be combined with other metamagics, Empowered Spell is the most versatile choice among the Sorcerer's selection.

When you apply this on an eligible spell, you gain the following benefits:

* you reduce the variance and increase the mean of your damage dice with the right strategy
* you increase your effective spell level by at least one if used with the right spells

Let's figure out how Empowered Spell affects your average damage for any roll. Here is the general formula:

<mrow class="MJX-TeXAtom-ORD"><mover><mi>d</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mo>=</mo><mfrac><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mspace linebreak="newline" /><mi>D</mi><mo>=</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.2em" minsize="1.2em">&#x2308;</mo></mrow></mstyle><mrow class="MJX-TeXAtom-ORD"><mover><mi>d</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.2em" minsize="1.2em">&#x2309;</mo></mrow></mstyle><mspace linebreak="newline" /><msub><mi>&#x03B1;</mi><mi>k</mi></msub><mo stretchy="false">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">E</mi></mrow><mo stretchy="false">(</mo><mtext>highest n of m k-sided dice</mtext><mo stretchy="false">)</mo><mspace linebreak="newline" /><msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>q</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mn>1</mn></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>d</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mtext>&#xA0;</mtext><mtext>min</mtext><mo stretchy="false">(</mo><mi>&#x03F5;</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo><mspace linebreak="newline" /><msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>q</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mn>2</mn></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>&#x03F5;</mi><mo>,</mo><mi>r</mi></mrow></msub><msub><mi>&#x03B1;</mi><mrow class="MJX-TeXAtom-ORD"><mi>D</mi><mo>+</mo><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo>&#x2212;</mo><mi>&#x03F5;</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo><mspace linebreak="newline" /><msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>q</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mn>3</mn></msub><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>&#x2212;</mo><mtext>min</mtext><mo stretchy="false">(</mo><mi>&#x03F5;</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>&#x03F5;</mi><mo>,</mo><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo>&#x2212;</mo><mi>&#x03F5;</mi><mo stretchy="false">)</mo></mrow><mrow><mi>d</mi><mo>&#x2212;</mo><mi>D</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mspace linebreak="newline" /><munderover><mo>&#x2211;</mo><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><msub><mrow class="MJX-TeXAtom-ORD"></mrow><mi>n</mi></msub><msub><mi>C</mi><mi>r</mi></msub><msup><mi>p</mi><mi>r</mi></msup><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><mi>p</mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>&#x2212;</mo><mi>r</mi></mrow></msup><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.623em" minsize="1.623em">(</mo></mrow></mstyle><msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>q</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mn>1</mn></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>q</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mn>2</mn></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>q</mi><mo stretchy="false">&#x00AF;</mo></mover></mrow><mn>3</mn></msub><mo stretchy="false">(</mo><mi>n</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo><munderover><mo>&#x2211;</mo><mrow class="MJX-TeXAtom-ORD"><mi>j</mi><mo>=</mo><mi>D</mi></mrow><mi>d</mi></munderover><mi>j</mi><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.623em" minsize="1.623em">)</mo></mrow></mstyle></math>' role="presentation" style="position: relative;" >𝑑¯=𝑑+12𝐷=⌈𝑑¯⌉𝛼𝑘(𝑚,𝑛)=𝐄(highest n of m k-sided dice)𝑞¯1(𝑟)=𝑑¯ min(𝜖,𝑟)𝑞¯2(𝑟)=𝑓𝜖,𝑟𝛼𝐷+1(𝑟−𝜖,𝑟)𝑞¯3(𝑛,𝑟)=𝑛−min(𝜖,𝑟)−𝑓𝜖,𝑟(𝑟−𝜖)𝑑−𝐷+1∑𝑟=0𝑛𝑛𝐶𝑟𝑝𝑟(1−𝑝)𝑛−𝑟(𝑞¯1(𝑟)+𝑞¯2(𝑟)+𝑞¯3(𝑛,𝑟)∑𝑗=𝐷𝑑𝑗)

Where: 𝑛 is the number of dice; 𝑑 is the number of sides of the die; 𝑝 is the chance of rolling a number on the die that you would empower; and 𝜖 is your Charisma modifier.

The following tables show the damage for an empowered *fireball* and empowered *erupting earth* worked out for you.

##### Empowered Fireball Damage

<div style='position: absolute; bottom: 465px; right: 85px;'>
<h6>–Mean Damage per Charisma Score–</h6>
</div>

| SpellLevel | AverageDamage | 18 | 20 | 24 | 30 |
|:---------------:|:------------------:|:------:|:------:|:------:|:------:|
| 3 | 28 | 33.611 | 33.885 | 33.997 | 34.000 |
| 4 | 31.5 | 37.610 | 38.014 | 38.238 | 38.250 |
| 5 | 35 | 41.549 | 42.089 | 42.463 | 42.500 |
| 6 | 38.5 | 45.433 | 46.110 | 46.663 | 46.749 |
| 7 | 42 | 49.270 | 50.078 | 50.831 | 50.998 |

</div>

##### Empowered Erupting Earth Damage

<div style='position: absolute; bottom: 289px; right: 85px;'>
<h6>–Mean Damage per Charisma Score–</h6>
</div>

| SpellLevel | AverageDamage | 18 | 20 | 24 | 30 |
|:---------------:|:------------------:|:------:|:------:|:------:|:------:|
| 3 | 19.5 | 24.000 | 24.000 | 24.000 | 24.000 |
| 4 | 26 | 32.000 | 32.000 | 32.000 | 32.000 |
| 5 | 32.5 | 39.966 | 40.000 | 40.000 | 40.000 |
| 6 | 39 | 47.858 | 47.985 | 48.000 | 48.000 |
| 7 | 45.5 | 55.643 | 55.930 | 56.000 | 56.000 |

</div>

To determine the pot value, compare the mean damage of the empowered spell to the mean damage of the unmodified spell and find the new level. For example, an empowered *fireball* at 5th level deals about 42 points of damage. A raw *fireball* must be cast at 7th level to deal the same damage, so the pot value is two.

\pagebreak

##### In Comparison to Alternatives

Empowered Spell is tough to beat, but it faces competition.

**Overchannel.** An Invoker can deal the maximum damage on their spells. This damage goes beyond the spell's mean damage at 9th level. But, you get it at at Level 14, works only for 5th level spells or lower, and can only be safely used once per day. Overchannel is better on a nova basis, but the better long term choice is Empowered Spell.

##### The Pitfalls of Empowered Spell

Though this metamagic is very good, it has one weak point.

**Poor Scaling.** Empowered Spell only synergizes with blast spells. Unfortunately, blast spells do not scale at the highest tiers of play. Even *meteor swarm* can be taken from a mean of 140 to a mean of 17.5 by having high saving throw modifiers, damage resistance, and damage immunities.

##### Fastest Blaster Progression

On a 3rd level *fireball*, Empowered Spell elevates your dice to better than one at 4th level. Other blasters must burn a 4th level spell to deal the damage you do at 3rd level.

This exacerbates when paired with the rapid spell progres-sion from Flexible Casting: as a Level 7 caster, you can up-cast a spell to 5th level, and an empowered 5th level *fireball* deals the damage of one at 7th level. To rival this, others must wait six more levels. No other blaster progresses this quickly.

##### When to Empower?

To achieve maximum average damage, always roll when the result on the die is below average. The formula given here is only correct when 𝑝 = 0.5, though it can be generalized by removing 𝐷 and replacing it with a summation term.

That said, in some cases, mean spell damage can fall by less than half a point when 𝑝 < 0.5. Use your judgement to know if you are willing to reduce your output by that much in exchange for less variance.

Oh, what's that? You want me to prove that Empowered Spell reduces the variance on your damage dice? Well fuck, man, I'm a Barbarian. I don't know how to do conditional covariance. Ask a statistician or something.

##### No Cardinality Targets?

For resource management, it's easier to use the original cardinality targets formula and just track how many Sorcery Points you have left on hand after conversion. Assuming you used Empowered Spell alone, here's the formula for that:

<div class="MathJax_Display" style="text-align: center;"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="2.047em" minsize="2.047em">(</mo></mrow></mstyle><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mo>+</mo><munderover><mo>&#x2211;</mo><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi>t</mi><mo>&#x2212;</mo><mn>1</mn></mrow></munderover><msub><mi>n</mi><mi>s</mi></msub></mrow><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="2.047em" minsize="2.047em">)</mo></mrow></mstyle><mo lspace="thickmathspace" rspace="thickmathspace">mod</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi>c</mi><mi>t</mi></msub></mrow></mtd></mtr></mtable></math>' role="presentation" >(𝐿+∑𝑠=1𝑡−1𝑛𝑠)mod𝑐𝑡 </div>

Because you can combine another metamagic with this one, adjust your cardinality targets to match the second one. Adjust the leftover number of Sorcery Points formula as well.

##### Good Qualities of a Candidate Spell

One can observe from the tables on the previous page that Empowered Spell adds about the same damage for *fireball* and *erupting earth* until 6th level: an increase of 6±1. But cast at 7th level, *erupting earth* adds 10 points of damage. This metamagic boosts a spell when it has a lot of damage dice first, and then when those damage dice are large second.

\pagebreak

## Closing Notes

This is just a fraction of the complexity when planning a Sorcerer optimally. There's still Sorcerous Origins, feats, class dips, Unearthed Arcana, builds, combat strategies, metamagic valuation methods, races, Sorcery Point and spell slot management, and spell list curation.

We also haven't addressed some obvious issues, though perhaps you, the smart reader, may not need the answers to be explicitly spelled out at this point.

* Are Sorcerers really underpowered, or just hard to use?
* Should you cast more high level spells over low level spells?
* What should you do when you aren't casting your spells? Warlocks have *eldritch blast*, so what do you have?
* Why is a Barbarian teaching you how to use your innate, inborn magic?

If we meet again in future guides, we will tackle some of these questions. Later, and don't forget to rage!

\columnbreak

> ##### Art Credits
>
> The art used in this guide were created by the following stellar artists.
>
>  
>
> [Anna Lakisova](https://www.artstation.com/artwork/8oDKG)
>
> [Unknown Artist](https://w.wallhaven.cc/full/ey/wallhaven-eyvx8l.jpg)
>
> [Francisco Badilla](https://www.artstation.com/artwork/1nL98)
>
> [Diego Gisbert Llorens](https://www.artstation.com/artwork/OvoD6)
>
> [David Franco](https://www.deviantart.com/morkardfc/art/Arcane-Blast-643221019)
>
> [Olga Drebas](https://www.artstation.com/artwork/2ER2K)
>
> [Astri Lohne](https://www.artstation.com/artwork/rmoq5)
>
> [Tomasz Jedruszek](https://www.artstation.com/artwork/98GZL)
>
> [Nordeus Games](https://www.artstation.com/artwork/eXL2D)
>
> [Victor Brauner](https://www.metapsychosis.com/the-goddess-as-active-listener-part-4/)
>
> [Christian Benavides](https://www.artstation.com/artwork/lvPbO)
>
> [Randy Vargas](https://medium.com/fantastika/7-great-modern-fantasy-artists-1fe7a1fdf361)
>
> [Raymond Swanland](https://www.originalmagicart.store/products/firespout-print)
>
> [Antoine Ren](https://www.artstation.com/artwork/xzL4JR)
>
> [Remi Roundtree](https://www.artstation.com/artwork/1BNeq)
>
> [Randy Vargas](https://www.artstation.com/artwork/xzErwE)
>
> [Rob Joseph](https://www.deviantart.com/rob-joseph/art/Karacterz-Mage-Card-504786615)
>
> [Aaron Nakahara](https://www.artstation.com/artwork/PePmr)

\pagebreak

## Post Script

In this section, this guide will talk about change logs, ways to suggest edits to the author, links to other guides, and so on.

### Change Log

##### November 2020

* The subtitle is updated.

* The "Maximizing Font of Magic" section refers to charac-ter levels as "Level X" instead of "Xth level" when said in the same sentence as the level of a spell slot to remove ambiguity if the level refers to a character or a spell slot.

* The "Cardinality Target" section changes the variable used in the legend after the formula from 𝑐𝑠 to 𝑐𝑡

* The "Quality, Quantity, and Cost" section replaces *fireball* with *haste* in the final sentence of its penultimate paragraph.

* The "Twinned Spell" section corrects the typographical error in the helper function, such that the second term describing <msub><mi>&#x03BD;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub></math>' role="presentation" style="position: relative;" >𝜈𝑠,𝑝 is now <mi>s</mi><msub><mi>&#x03BC;</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msub><msub><mi>f</mi><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>,</mo><mi>s</mi><msub><mi>n</mi><mi>s</mi></msub></mrow></msub></math>' role="presentation" style="position: relative;" >𝑠𝜇𝑠,𝑝𝑓𝑝,𝑠𝑛𝑠 .

* The "Economy of Expandable Spells" section clarifies that the cost of the base spell level is counted, and defines that 𝑠 is equal to the base level of the expandable spell.
 
* The "Wild Mage" subline of the "Careful Spell" section clarifies the reason why we presuppose a wild magic surge result as being an example of post-analysis, rather than presenting a plan to be executed.

* The modified spell in the "Purple Wedding" subline of the "Subtle Spell" section has been renamed to "Traceless Poison."

* The "Empowered Spell" section fixes style issues with the formulae, changes "Xth level" to "Level X" when referring to character level in the same sentence as the level of a spell slot, and fixes some typos.

* A "Post Script" section is added.

\columnbreak

### Contact the Author

The author can be reached via his <a href="mailto:goliathbarbarian1@gmail.com">email address</a> or via his <a href="https://www.reddit.com/user/GoliathBarbarian">account on Reddit</a>.

### Thank You!

If you've read this far into the guide, then that is a huge time investment into this relatively esoteric document. When I wrote this, I thought I would be its only reader.

As it turns out, it's been very well-received. Writing, desig-ning, and styling this document took a while and was a work of love. It's gratifying to know other people have appreciated it too. So, thank you for giving my guide some of your time!