Is there an accepted likelihood of hitting that is consistent across tiers, and how has it been determined?

Question

One can easily calculate DPR given a specific build (knowing proficiency bonus, ability scores, other relevant factors) and the AC of opponents, leading to spreadsheets with a matrix of customizable parameters. But what if one wants to calculate an average DPR considering typical build choices against typical CR encounters? As character attack bonuses go up, so do opponent ACs, so is there commonly used rule of thumb for an average chance to hit?

For example, the following sources use chances of hitting that are apparently intended to be applied across tiers:

• 50%: What is the expected DPR of an animate object spell cast on daggers? ("11+ on the d20 is required to hit")
• 60%: https://www.youtube.com/watch?v=zg0bAl1WPGQ&t=9m5s ("This warlock's going to have about 60% chance to hit. And, honestly, that ends up being pretty close to the average.")
• 65%: https://www.enworld.org/threads/guide-my-word-is-my-sword-the-paladin-guide.474035/ (used several places throughout the guide)
• 65%: Weapon attacks compared with damaging cantrips? based on:
  • ASI goes into attack ability
  • Attacks will be made against average AC of a CR = character level, as seen on DMG274

Is there a widely agreed upon likelihood of hitting in a generic, CR-appropriate encounter (e.g. 50%, 65%, etc.)? Is there one that is consistent across levels or tiers? How is this value arrived at? (E.g. likely character attack bonuses, AC of CR-appropriate opponents…)

Answer 1

Two minor disclaimers:

1. I've never seen an "accepted" or "general" number thrown around, so this answer represents both my own feelings, and my own inference given the available data.
2. All monsters are different, so we can only work in averages based on given guidelines.

Players should hit about 65% of the time

Using the DMG guidelines explained in this answer for Average AC at a given CR and a combat-optimized stat-array human, starting at 16 in their attack stat...

CR 0-3 : +5 to hit vs 13 AC requires an 8 or better; 65% to hit.
CR 4 : (ASI) +6 to hit vs 14 AC requires an 8 or better; 65% to hit.
CR 5-7 : (Proficiency +3) +7 to hit vs 15 AC requires an 8 or better; 65% to hit.
CR 8 : (ASI to 20) +8 to hit vs 16 AC requires an 8 or better; 65% to hit.
CR 9 : (Proficiency +4) +9 to hit vs 16 AC requires a 7 or better; 70% to hit.
CR 10-12 : +9 to hit vs 17 AC requires an 8 or better; 65% to hit.
CR 13-6 : (Proficiency +5) +10 to hit vs 18 AC requires an 8 or better; 65% to hit.
CR 17+ : (Proficiency +6) +11 to hit vs 19 AC requires an 8 or better; 65% to hit.

You can get ahead of the curve slightly by using either rolled stats or being a fighter, but you're still going to max out your attack ability and then you're back on track at level/CR 8.

And starting with a 14 (or 15) in your attack ability only sets you back to 60% until your ASIs catch up, at which point, you're back to 65%.

This jibes with what limited amount that I understand about game-building. The players should feel like they're effective more often than not, but not so much as to guarantee success.

Magic items can move you forward a bit

If you use the following table as a guideline from the DMG (p 135), you're going to move ahead five percentage points for every "+1" you gain to your attack.

\begin{array}{lll} \rlap{\textbf{MAGIC ITEM RARITY}} \\ \textbf{Rarity} & \textbf{Character Level} \\ \hline \text{Common} & \text{1st or higher} \\ \text{Uncommon} & \text{1st or higher} \\ \text{Rare} & \text{5th or higher} \\ \text{Very rare} & \text{11th or higher} \\ \text{Legendary} & \text{17th or higher} \\ \end{array}

Magic items are entirely optional and furthermore doling them out is DM dependent, so I'm not going to factor them into the chart above. Although, if you can get your hands on a +3 weapon at level 9, you're going to average a whopping 85% to hit!

Answer 2

Your question is inherently flawed and unanswerable

Let's start by stating that there is no real "typical build" for any of the classes, because there's no way to say what is and isn't 'typical':

I could make a level 4 fighter with 18 dex and archery fighting style to gain +8 to hit, or I could play a sword&shield tank fighter with only 14 strength and have half that chance to hit bonus, yet neither of these builds would be considered atypical.

The real problem is that there's also no generic AC to hit against. An Ogre is CR2 and only has an AC of 11, while an Azer is also a CR2 creature and that one has an AC of 17. Challenge ratings take both defensive and offensive features into their calculation, so there is no real way to truly say what AC a specific CR creature has, it depends on how their stats are distributed.

The DMG list on page 274 is not, in any way, useful for this purpose. Other answers in the past may have suggested using that list, but that is not how that list works. A creature's final CR depends on its AC, HP and expected damage output, plus an adjustment based on playtesting. If you flip through the monster manual, you'll find that the vast majority of monsters do not fit their suggested AC from the DMG list, because they have more or less HP, or deal more or less damage. It might have immunity to non-magical weapons, it might have resistances, there are a lot of things that go into CR that in no way tie to AC.

Do we go by the +8 archer hitting an Ogre? Do we go by the sword and shield fighter trying to hit an Azer? That's a massive difference in chance to hit, even though both are level 4 characters trying to hit a CR2 creature.

People who throw around a "has a 65% chance to hit a challenge appropriate level encounter" facts are mostly just pulling them out of thin air, because encounters are rarely just one static enemy of an appropriate CR. Ten goblins is often more likely as an encounter than one creature by itself.