I agree the assignment of a Challenge Rating is a "hot mess", but the system itself is functional IF you just build the monsters using consistent (unified) rules.
Sure. But since there is a lack of official unified rules, and what does exist needs fixing anyway, it is for many reasons to refer to "level" that are a meaningful unit of measurement, rather than the opaque hot mess of "challenge".
1. Link Hit Dice with Challenge Rating as follows:
CR 2 = 3 HD
CR 4 = 6 HD
CR 6 = 9 HD
CR 8 = 12 HD
CR 10 = 15 HD
CR 12 = 20 HD
CR 16 = 30 HD
CR 20 = 40 HD
CR 24 = 60 HD
CR 28 = 80 HD
2. Derive base damage from Hit Dice
Main Attacks: # of dice = 1/4 HD
Reactions: # of dice = 1/8 HD
"Super Attack" (like a Breath Weapon): # of dice = 1/2 Hit Dice
E.g. CR 12 Dragon: 20 Hit Dice, Claw 5d6/Claw 5d6/Bite 5d12, Breath Weapon: 10d8 (cone); Tail (Reaction) 2d12, etc.
From that baseline you can modify for creature role or whatever. But it gives you a core consistency.
I will check out these numbers, but again it is better to refer to "level" when creating a standard.
The inflation of hit points requires attention. For a player character to have this amount of hit points at this "level" would mean something like usage of Second Wind, bonus
Cure Wounds spells, regeneration, etcetera.
I know, but you can see from the random assignment of Hit Dice (throughout that book, not just the spell casters) WotC are completely inconsistent.
Apparently the "hit points", along with AC, are the most consistent aspect of "challenge" relatively speaking, and anything else even less consistent!
4e had official standard rules for monsters, that were so clear it was possible to critique precisely the math. Inevitably, the 4e fans were merciless in their criticism of small discrepancies. 5e succeeded in avoiding criticism by making its "in house" rules for monsters an opaque hot mess.
It surprises me that noone's mentioned Forge of Foes, that has a CR to level comparion chart.
But Giffyglyph of Reddit has made 4e-fication of 5e monsters years ago. You could do worse than checking it out:
I will look into these numbers too.
In terms of "a CR X monster is a reasonable fight for a level Y PC", it is closer to:
CR 1/4: L1
CR 1/2: L2
CR 1: L3
CR 2: L4.5
CR 3: L6
CR 4: L8
CR 5: L11
CR 6: L13
CR 7: L15
CR 8: L17
CR 9: L19
4 CR1/4 monsters have a 400 XP budget. A party of 1 L 1 PCs has a deady budget of 400.
4 CR3 monsters have a 5600 XP budget. A party of 4 L7 PCs has a deady budget of 5600.
4 CR9 monsters have a 20000*2 = 40000 XP budget. A party of 4 L 19 PCs has a deadly budget of 43600.
However, 5e D&D monsters are written as "solo" medium difficulty encounters for a group of 3-4 PCs instead of individual deadly threats for a single PC.
And I will look at these numbers.
I also want to call attention for the important reverse engineering here, by
Blog of Holding. It is referring to the 2014 math, and we probably need new numbers for 2024 math.
In any case, in any new monster math system, it is better to refer player character "level" as the standard unit of measurement.