How important is it for a spellcaster to increase primary ability scores quickly to 20 to remain at "party level"?

Question

One can increase ability scores at 4th and 8th level, or take a feat instead with the optional rule. Assuming player-characters are built with point-buy rules, one is probably going to start with a 16 or 17 in one's primary ability score — the spellcasting ability. In that case, it'll take both the 4th and 8th level ability score increases or feat choices to raise the spellcasting ability to the maximum of 20.

For this purposes of this question, the focus is on spellcaster utility in combat — damage or effective control.

Compared to a similar character who picks ability improvement each time, will a character who picked feats be significantly behind the curve in a fight?

1. At 4th level, will a Sorcerer with 18 Cha be noticeably more effective than one with 16?

2. At 8th level, will a Wizard with 20 Int be far ahead of one with 16 Int?

   Or does "bounded accuracy" make this less of an issue?

And, also for the purposes of comparison, let's assume that the feats taken are more focused on other parts of the game — Skilled and Dungeon Delver, say — rather than trying to compare which particular feats might compensate in which situations. In other words, ignoring how the cost might be paid, what is the cost of taking feats instead of ability score increases for a spellcaster character?

What's in a good answer?

I'm particularly interested in numbers-based analysis based on DM guidance for level-appropriate encounters and encounters from published adventures. I'd also love to hear experience from play where players at the same table took different approaches.

Answer 1

It depends on how you deal damage¹

The calculations are for level 8, ability is 20 with ASI, 16 without it. The target AC is 16, as usual for a CR8 monster.

Ability bonus to attack and damage

The list is short for cantrips; Warlocks with Agonizing Blast, Evokers and Dragon Sorcerers, Clerics with Potent Spellcasting. Weapon attacks also belong here:
20: +8 attack bonus, 65% hit chance. Damage for a Warlock is 2d10+10=21. DPR is 13.65.
16: +6 attack bonus, 55% hit chance. Damage is 2d10+6=17. DPR is 9.35, 46% lower.

For a Dragon Sorcerer the difference is smaller 35%, as he only adds the Charisma bonus to the damage once. Still, the difference is huge. Higher for Clerics, as Sacred Flame has smaller base damage.

As higher level spells are more powerful to begin with, your ability modifier makes less of a difference.

Ability bonus to attack, or save for no damage

Most damaging cantrips fall into this category, except for the combinations mentioned in the previous section. Disintegrate comes to mind from higher levels.
20: +8 attack bonus, 65% hit chance. Damage for a Diviner with Fire Bolt is 2d10=11. DPR is 7.15.
16: +6 attack bonus, 55% hit chance. Damage is the same, DPR is 6.05, 18% lower.

This is about the half of a Dragon Sorcerer's or Evoker's difference.

This category is closest in behavior to non-damaging, single save spells like Faerie Fire or Suggestion.

Ability bonus to DC, save for half damage

Most damaging spells above level 2 belong here.
20: DC16, 65% hit chance², 28 damage with Fireball, 14 with a successful save. DPR is 23.1.
16: DC14, 55% hit chance², DPR is 21.7, not even 7% difference.

Abilities do not matter

For completeness sake, Magic Missile is mentioned; your ability scores have no impact. Very rare, quite weak for offense³.
Except for Evokers, for whom it is probably the best damaging spell ever.

How this affects the game

If you are a weapon user or Warlock, not taking an ASI is close to crippling.
In the 20 level long career of a Fighter for example, there are only three class features that bring a bigger improvement to your combat effectiveness: Extra Attack 1, 2 and 3.

On the other end of the spectrum, an Evoker of level 6 deals half damage with cantrips even if the target saves successfully, meaning that your abilities matter even less. The difference between Int 16 and 18 is around 3%, invisible in practice.
This also means that if for some reason you have low abilities overall, a bit counter-intuitively a Blaster is your least bad option.

Most non-damaging spells are between these extremes. You can get by with a 16 in most encounters, unless it has a single target. Than increasing the chance of a failed save is your highest priority.

Of course it will always sting to know that the dragon would have failed that save against Disintegrate if your Cha were 2 points higher

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¹ There are other ways to be relevant in combat, but they are nearly impossible to quantify)
² For spells with saves I will assume the same hit chance, otherwise it would be very hard to calculate, as different monsters have different strong saves
³ Unless you are an Evoker with Magic Missile, which is brokenly powerful, and should have been errataed years ago

Answer 2

TL;DR: On a ballpoint analysis, you can expect something between 7% ~9% less damage per 2 stat points on the relevant ability for damaging spells that rely on ability for hit and save. Expect more if you add your ability to the damage too (evokers, EB-locks, etc).

For damaging spells, it would mean one of the 3 below:

• reducing the save DC by 2.
• reducing your chance to-hit by 2.
• nothing.

I'll assume no class feature adds the stat to the damage (evoker?)

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• Attack Rolls (scorching rays):

  Assuming you would be hitting 65% of the time with a 20 stat, a 16 would give you a 55%. This means a 18% reduction [(65/55) -1] in Damage over a long number of castings.

• Save DC for 1/2 damage (fireball):

  An opponent that would save 50% of the time with a 20 spellcasting stat, now saves 60% of the time. Saving 50% of the time means a 25% DPS reduction, but at 60% is a -35%. This is the equivalent of doing 15.4% less Damage per Casting.

• No hit, no save (Magic Missile):

  Doh. No changes.

• The inner MinMaxing-CharOp Demon tugging at your heartstrings because you made sub-optimal character-depth-adding choices:

  Priceless.

Answer 3

The difference is really easy to state:
18 over 16 represents +1 to attack rolls and spell save DC
20 over 16 represents +2 to attack rolls and spell save DC
This translates directly into a 5% or 10% change in your chance of success, assuming reasonable target numbers (i.e. not >20 or <1).

At 1st level, you would expect +5 to hit and a spell save DC of 13.
At 5th level, using a stat boost gives you +7/DC15 (versus +6/DC14 without)
At 9th +9/DC17 with versus +7/DC15 without.

Straight away we can see that your 9th level character is no better than someone else's 5th level character - I have chosen these levels since you also have to consider the impact of the change in proficiency bonus - between 4th and 9th level you will spend way more time at 5th to 8th then at 4th.

As a general observation, D&D 5e’s “bounded accuracy” suggests that each +1 is more valuable than in previous editions, not less because they are harder to come by. However, its not immediately clear what difference that would make so let's break down spells into general types:

1. Stats don't matter - Magic Missile, most utility spells.

   Well, stats don't matter.

2. Spells that make attacks - most cantrips.

   Cantrips are a spellcaster's "go to" - the thing you do a lot because either you're out of options or you don't think the threat warrants burning a spell slot. You use these a lot.

   From p. 274 of DMG we expect CR1/5/9 to have AC13/15/16. If you boost your stats you will hit 65%/65%/70% at each level; if you don't boost, this drops to 65%/60%/60%. A typical cantrip does 2d10 damage between 5th and 10th levels so you are giving up an average of 0.5-1hp per round.

3. Spells with saves for half damage - most AoE damaging spells.

   The go-to for a 5th level wizard/sorcerer is Fireball with 8d6 (28) damage. A save therefore reduces damage by an average of 14 points. The actual target number varies significantly depending on the creature's Dexterity and if they are or are not proficient in the save. However, a 5%/10% reduction always means a difference of 0.7-1.4 hp per creature affected.

4. Spells with saves where the spell does nothing on a save - some damaging cantrips, most "save or suck" effects.

   These are more problematic - partly because creature saves are highly variable because stats vary greatly and low CR monsters tend to have few or no save proficiencies, while higher CR can have a lot, and partly becuase, unlike the damaging AoE, if the target makes their save you blow a spell slot and get nothing for your effort.

   On the flip side, you can usually apply some strategy to you choice of spell - an enemy tank should be targeted by Wisdom, Charisma and the vanishingly rare Intelligence save spells, while an enemy spellcaster should be targeted with Constitution, Strength and Dexterity - you did choose your spells with diversity of saves in mind, didn't you?

While this is more of a feeling than an empirical analysis, I think your chance of the enemy failing a save is less then your chance of hitting them with an attack - say 55%/55%/60% which drops to 55%/45%/50%.

In addition, these spells are often concentration spells and the target can usually save every turn until they succeed. For this type of spell, the expected number of rounds they will be affected is:

\begin{array}{r|lll} \text{Target No} & \text{Rounds} \\ \hline 9 & 0.67 \\ 10 & 0.82 \\ 11 & 1.00 \\ 12 & 1.22 \\ 13 & 1.50 \end{array}