For monsters, we have the guidance of how much damage they are expected to deal in a round based on their CR from the DMG on page 274. In contrast, there is no such explicit guidance for expected PC damage output per round and level.
That damage output clearly can vary wildly, both by character build, and by class — some excel at nova-damage, pouring limited resources into big effects, others are strong on sustained damage over time. But the designers must have had some rational expectation of what it would be, when they designed the system.
I understand that this cannot be answered exactly, as there are way too many moving parts. I'm not looking for exact. I'm looking for rough, average damage at each level, across all classes. Essentially anything that it better than the nothing I'm currently aware of.
Is anyone aware if there is a resource with statistics for this, either empirically collected from something like Adventure League play, from someone who recorded it for their play group, or from someone who collected stats for a popular streaming show like Critical Role; or from the designers talking about it in interviews; or theoretically, from deriving this from fundamentals of the combat and CR system; or from simulating/estimating this for a range of character builds?
Best Answer
You can calculate this by reversing the CR tables. For example CR1 is a medium encounter for a party of 4 level 1 characters. CR1 has 71–85hp, if you assume it takes 3-5 rounds to kill an encounter that means you can assume 3.5-7 DPR per character.
If you continue through the table in the DMG you will arrive at an answer that is a rough average across all classes, builds, and party composition. It's certainly better than nothing, and is in line with the designers' intent.
This methodology will give you an answer that seems to agree with longstanding optimization artefacts like The Optimists' Guide to D&D 5E Damage by Class.