It's generally taken as given that you can't assign a CR to PCs... but it turns out that D&D in effect actually does assign a CR to PCs, based on some fairly simple logic:
In theory, an NPC group with the same levels and numbers as the PCs should be a coin-flip fight.
High difficulty is still supposed to be a fight the PCs will probably win as long as they use good tactics and don't have unusually bad luck. This implies a ratio of PC to NPC of more than 1:1, but probably not more than 3:2. Thus, you can just find the High difficulty budget for a level X PC and find a CR that's between 1 and 1.5x that number.
You can also just assume the XP value of a level X PC build is 150% of the High difficulty budget for a level X PC.
If you do #2, it turns out that there's actually a pretty straightforward formula:
For most levels, the CR equivalent of level N is (N-1).
Level 1 is CR 1/2.
Levels 10 and 12-14 have a CR equivalent of (N-2).
Level 18 is CR 18, level 19 is CR 20, level 20 is CR 21.
I was a bit surprised by how simple the formula turned out to be. As for whether I believe it? Honestly... at the general resolution of CR and encounter building in 5e, it seems fine? When I put together some 20th level builds and evaluated them against the monster rules from 2014, using the gear rules from starting at higher levels, most of them came in pretty close to CR 20.
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It's generally taken as given that you can't assign a CR to PCs... but it turns out that D&D in effect actually does assign a CR to PCs, based on some fairly simple logic:
If you do #2, it turns out that there's actually a pretty straightforward formula:
I was a bit surprised by how simple the formula turned out to be. As for whether I believe it? Honestly... at the general resolution of CR and encounter building in 5e, it seems fine? When I put together some 20th level builds and evaluated them against the monster rules from 2014, using the gear rules from starting at higher levels, most of them came in pretty close to CR 20.