D&D 5E - Stat block for a CR3 villain sorcerer

Once you've DMed 5e a bit for your group you'll get a much better feel for what constitutes a "good fight." The guidelines in the DMG will only take you so far, maybe get you in the general ballpark, or maybe be useless. Don't get too hung up on the CR.

That said, when setting a CR for spellcasters I often will create an imaginary 3 rounds worth of that caster's actions. This is described in the DMG p.278 under "Overall Damage Output." Generally, I assume a bare minimum of defensive spells cast in advance (esp. mage armor), so those do not require actions in my imaginary 3 rounds. Then I follow the guidelines below for adjudicating targets caught in areas of effect, figure out the total damage each round, then arrive at my average for the DPR.

When calculating damage-per-round (particularly of spells), I reference DMG p.249 "Adjudicating Areas of Effect" which gives estimates on how many targets are caught in an area effect spell for theater of the mind (i.e. no map/minis) play. With this chart, I consider maximum party size to be 4 PCs, which is the default in the rules...so if you have a 90 foot cone, it's only going to count against 4 targets (not 9) for damage-per-round calculation purposes.

TARGETS IN AREAS OF EFFECT (round up)
Cone = size/10
Cube or square = size/5
Cylinder = radius/5
Line = length/30
Sphere or circle = radius/5

This is not the "iron word", but it's a good starting point. I apply a hearty degree of interpolation, however, in imagining how the monster would look in play and how PCs usually react. For example, few players are going to let themselves all get caught in an area of effect, especially not twice in a row once they're aware a monster possesses fireball capability (just an example).

This may seem imprecise. And, well, yep it is. The whole CR system is like licking your thumb, holding it into the wind and trying to calculate exact wind speed down to a decimal place from that. Sure, you'll be able to differentiate a breeze, from a blustery kite-flying day, from strong winds before a storm, but it takes experience to differentiate it much more precisely than that.

EDIT: I will add that giving a caster the fireball spell in particular will drastically increase their DPR and thus their CR. The designers acknowledged that certain spells are just better for their level, by design. If you gave your sorcerer fireball, I'd be surprised if you didn't end up with a CR of 4, 5 or 6.

EDIT EDIT: When I began playing 5e I got hung up on the CR because I was noticing my group of experienced player ploughing through encounters that were, according to the DMG maths, "hard" or "deadly." I think there's general consensus that a fresh, prepared party with feats and multiclassing and magic items played by experienced players are going to be hitting above their weight (as estimated by the DMG maths). Likewise, large parties (6+) seem to be notorious for hitting above their weight (even after factoring in their numbers using DMG maths). Also, myself and other "old hands" at D&D have reported that the DMG "hard" and "deadly" encounter guidelines feel anemic compared to what we were used to in AD&D where things were really deadly. Like everything with D&D, adapt and spice as desired.

EDIT EDIT EDIT: Last edit! I've found that the "Adventuring Day XP" guidelines on DMG p.84 are a better guidelines for how much to throw at the PCs. This will give you much harder challenges, and allow you get by with fewer encounters (which may suit your narrative style), but it will dramatically inflate the XP the party gets...so you may want to switch to milestone leveling if that pace feels too fast. And generally, I don't throw ALL of a day's XP worth of monsters at the PCs in one go...unless the situation is really dire, they've made a huge mistake, they've gone looking for trouble, or I've broken into waves (because numbers are a huge force multiplier in 5e).

For example, take a group of five 3rd-level PCs. A "deadly" encounter for them would be 2,000+ XP. However, suitable adventuring day XP for them would be 6,000 XP. So that's the range I play with, given that I run for experienced players with feats, multi-classing, magic items, and fewer encounters than default D&D.

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