I want to address this first, since it's central to your entire post:
But it's not budgeted power. It's not something you can assess with a metric, because flexibility involves every possible action you could perform (say, how many spells you could select) combined with every possible thing you might possibly need to do.
Flexibility is useful, but is there any meaningful way of measuring a given "amount" of flexibility against a level 1 spell slot? What even is an "amount" of flexibility?
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I will grant that one might trade power for flexibility, or vice versa, and thus the amount of flexibility is relevant to the overall class design. However without a means of defining what flexibility is, how to measure it, and how much it is worth, there is no value in focusing on it until you can at least provide a measure of the power side of the design.
Once you have a way of comparing power budgets, then you can go back and ask whether one class being less powerful than another (for example) is compensated by a certain degree of flexibility. You build and expand on the basics.
I don't disagree with you that it is incredibly difficult, maybe impossible to "accurately" measure flexibility, but ignoring it is a problem. If you were just proposing an initial way to begin addressing the issue, maybe that would be fine, but you aren't. You are using your method to come to conclusions, and those methods have an obvious, gaping hole in them.
I'd actually argue that a bad way of measuring the power of flexibility in this discussion is better than ignoring it, because by ignoring it, you are encouraging people to dismiss it, and it cannot be dismissed.
I based my analysis on spells considered solely in the abstract, that are assumed to be balanced against their spell level (we know that that is not true, but that's an issue for spell balance, not class budgets), and with a completely unknown selection criteria (ie: player choice), and thus must be considered entirely fungible.
I pulled this part out, because I want to say this again. You are wrong that spells are balanced against their spell level, and we know this because the Designers have explicitly stated that the spell list is part of the class power budget. They said, on camera, explicitly, that the power of the Wizard Class is based around having the best spell list. If it was fungible to state that class budget has no consideration for spell selection, then their statement would be nonsense.
We know, from the designers own words, that part of the Power Budget of the Wizard class is found within their ability to select the most powerful and useful spells for a given level. Any methods that do not take this into account, will lead to flawed conclusions.
WotC have decided that a 5th level spell/spell slot should be able to do an average of 44 damage (or healing) to a single target, or 28 damage to each of multiple targets. They have not said that the spell slot is determined by the total damage done across all targets. And it's not the same, because 44 damage will push a target closer to dead than 28 damage will. 56 damage across two targets is not a 6th level spell.
That depends on how you divide up the hitpoints on the battlefield.
You must consider that hit points can not only be considered on an individual monster level, but on a team level. This is why Mass Cure Wounds is a more powerful spell than a cure wounds cast at the same level, because affecting the team is more impactful than affecting the individual in most circumstances. So, while yes, dealing 28 damage to two or three or even four enemies is not brining the individual enemies closer to death, it is greatly affecting the health of the opposing side.
This affect is SO noticeable in the community, that you often get optimizers talking about how single target damage spells are not worth the spell slot. Because hitting a single enemy hard has a lesser affect on the entire battle than hitting mutliple enemies medium.
Additionally, not to get too in the weeds with the distinction between AOE and Single Target damage, control spells can end up doing effectively far more damage than what a single spell can do. Take Dominate Person, an example I already gave. In a situation where a powerful character like a barbarian fails that wisdom check (or is it charisma?) multiple things happen. 1) You have stopped incoming damage to your team by taking the enemy off the board 2) You have turned that enemy against their allies, dealing damage to the enemies 3) The enemies are know fighting their ally, taking even more damage off of your team and forcing them to spend resources hurting each other instead of hurting you. It is a DEVASTATING effect in the correct situation, and far more impactful than single target damage. In fact, it is so powerful that if you gave me an option between killing a target, or dominating it for two rounds of combat... I'd take the domination hands down every time. Because the stronger and more dangerous that target is, the more I want them pointed at my enemies.
And so, I think your method of using the damage dice and the spell points and converting things directly in terms of that is lacking. A single mid-level spell can devastate a situation far more than five or six low level spells. And your math doesn't show that.
Well, the difference between a 4th level spell slot and a 5th level spell slot is, at most, 2 SP. By Font of Magic, it would cost 6 SP to create a 4th level slot, and 7 SP to create a 5th level slot, meaning moving from 4th to 5th level is an extra 1 SP. If you use the DMG damage dice instead, it would move from 6 to 8, for a net cost of 2 SP.
Now, it would cost you more to get the SP you need by deconstructing the 4th level slot, but that inefficiency isn't what's being measured here.
But that clearly doesn't make sense. Like, sure, your math leads you to that conclusion, but if you could cast a 5th level spell, or a 4th and a 1st level spell then you would be kind of insane to take the 4th level slot. We all know, intuitively, that the increase of value is more than your math is trying to show. The nature of the things you are able to accomplish fundamentally changes between spell levels. Sure they all offer damage options, that never changes, but the most powerful and impactful effects always have a transformational value. For example, you go from being able to teleport yourself and one ally 500 ft to being able to construct a circle that can teleport upwards of twelve people where ever you want. That isn't an increase in power equivalent to 1d10 damage on a 1st level spell.
I don't think my argument is falling apart yet, but let's try another example. Careful Spell on Fireball. Careful Spell costs 1 SP. It's negating 8d6 damage on up to 5 targets, so could conceivably be viewed as a healing effect exactly countering the damage of the Fireball. 8d6 AOE is 5th level. Thus it could be mathematically described as a 7 SP effect.
This is a bit contrived, of course. Spells aren't constructed or budgeted that way.
But, importantly, Careful Spell isn't a spell. You can't dismiss the effect by claiming that spells aren't constructed or budgeted this way, because what you are describing is not a spell in the first place. And additionally, we absolutely know from testing these things out, that 1 Sorcery point is absolutely the correct value for Careful spell, while the effect it is producing is far and away more than what could be accomplished with half a 1st level spell.
And, let us not forget as well, Careful Spells value is VARIABLE. You say it is worth 7 SP because it prevents 8d6 damage on AOE targets? Well what if we cast Sunburst instead? Now it is preventing 10d6 damage on AOE targets and would be worth 10 SP. I've increased the value of the metamagic in your calculations by simply changing the spell. And so, does it make sense to measure Sorcery points as being equal to spell level cost, when a single sorcery point spent on Careful spell can have a "spell value" between 2 and 10 points, depending on the spell you cast?
How about Empowered Spell instead?
Suppose we had a non-overtuned Fireball that did the recommended 6d6 damage. Empowered Spell raises the average of each die from 3.5 to 4.25 if you reroll all values 1-3. That gives the overall spell a damage rating of about 7.2 d6s, or slightly better than a level 4 version of the spell.
So again, 1 SP was spent to raise the effective level of a spell by 1. And going from a 3rd level slot to a 4th level slot costs 1 more SP (6 vs 5), so we're still fine in that regard.
Sure, but we run into another problem here. That sorcerery point on Empowered spell is still a single sorcery point. Take Sunburst again, using that same Empower spell you can raise it from 12d6 to 14.6d6. That takes it from a 7th level spell value to a 9th level spell value according your math. That is 3 points of value.
And if we take this a step further, look at Meteor Swarm. It is doing 40d6 normally. And Empower could raise that to 48.6d6, which if we assume the chart continues upward, that starts getting into the 12 or 14 point values.
So, again I ask, with the value of a Sorcerery point being so highly variable in your math, can we really and honestly say that your system is working? You've assumed a very clear connection in value between a sorcery point and a spell point used to create a spell slot, but Sorcerery points often have effects far outside of that 1 to 1 conversion.
And what about sorcery points that are used in ways that seem to have no spell equivalent value? Elemental spell swaps damage types, but there is no spell level value here. A cold spell doing 6d6 damage is worth the exact same as a lightning spell doing 6d6 damage. Are you therefore losing value, creating an effect that is worth 0 points?
This is correct. I didn't write that out because I didn't want to belabor the point when that wasn't really a major focus.
I am curious why you made an entire chart trying to show case the comparability between wizard and sorcerer values then, and calling out your results, if comparing the sorcerer and wizard wasn't a major focus of your point? It was your entire first act, setting the stage for your position. It seems rather important.
This I will agree with, mostly. You did leave out a few things for the new sorcerer abilities in the UA, while comparing against the full list of wizard abilities. Of the wizard abilities:
- Spellbook: Not a budget item
- Ritual Casting: Is a budget item because it bypasses an established resource, but ritual spells are heavily curated, so I don't think the actual power is that large. Has more value for flexibility.
- Scholar: Budget item, but low value. Vaguely equivalent to Guidance, but for a single skill.
- Memorize Spell: Not a budget item, but I feel is unbalanced on the flexibility side due to how frequently it can be used.
- Spell Mastery: Budget item, though it did get nerfed. Difficult to judge value.
Meanwhile, while I did give a ~3% boost from Sorcerous Recovery, I didn't give a percent increase from Innate Sorcery because it varies by level, being a relatively high boost at low levels (maybe doubling power at 1st level?), down to just a few percent at 20th level. I didn't want to try to figure out what percent it counted as, so just left it as 'somewhat of a boost'.
Wizard still has more power, in my opinion, but it's almost entirely wrapped up in Spell Mastery. (And of course Memorize Spell on the flexibility side.) Otherwise I don't feel they are out of line with each other on the budget scale.
As someone who has seen the power of rituals first hand? You are vastly underestimating how impactful it is.
And, again, your call that flexibility can be mostly ignored is blinding you. The Spellbook is absolutely a "budget item" because it directly ties into the sheer amount of power a wizard can bring to bear over a campaign. Again, optimizers and people who study the classes for their power often comment that it makes a large difference if your DM provides access to spells and gold for a wizard. To the point that in a video I watched some months ago, it was a notable strategy to have two wizards in the party, who would copy each others books, because that meant that instead of gaining 2 spells per level, they gained 4 spells per level.
And once more, it is a stated "budget item" that the wizard has the best spell list, with the best spells on it. Therefore, gaining more of those best spells is more power.
I don't think I have? I pulled in Arcane Recovery for the chart because its function is very similar to the spell slot-granting aspect of sorcery points, and wanted to have a comparison. I also focused on it more at the PHB level. I didn't start getting into playtest features until the UA7 section, and by that point the wizard was not being considered at all.
I mean, this is the sorcerer thread. That's what I'm focused on. The wizard comparison was merely tangential.
I didn't feel like it was. After all, you concluded "
We can thus conclude that the power budget for the wizard and the sorcerer at the class level is basically the same, though I won't try to compare the capstones."
In a discussion about whether or not the sorcerer needs more power in its class budget, stating it has the same, or basically the same, power budget of one of the most powerful classes in the game is a statement which shuts down the conversation. How could someone argue that the sorcerer isn't quite reaching their full potential if we "agree" that they are similiar in strength to the wizard? Any boosts at that point would be egregious and overtuning.
This is why I'm pushing back against your work here. It leads to conclusions, or assumes positions, that will end with the Sorcerer in a much poorer state than I think they deserve. For example, while innate Sorcerery may seem very powerful... it is actually probably a pretty minor effect. Increasing your spell DC by +1 sounds dramatic, but in practice, it is a 5% increase in accuracy. For 2 minutes a day. Compare to the Devotion Paladin using a Channel Divinity and a bonus action to increase their accuracy between 10% and 20%, for 3 to 5 minutes per day, with tertiary benefits. Spells are more valuable to land, but you can see the disconnect here. That is an awfully small boost for the sorcerer in comparison, and we can deduce from a full class comparison, that they are already falling behind.
