I want to create a version of a Kobold that has the Ray of Frost cantrip, as well as resistance to cold damage. How would this affect the challenge rating of the monster? A normal kobold is CR 1/8. Would this bump their challenge rating up to 1/4?
We can determine the Challenge rating of the new "Koldbold" (like it? it's all yours!) by using the steps in DMG page 273.
Firstly, a few assumptions:
- The Kobold's ability scores do not change. With this, we can assume that the spell attack bonus is at +1 using either Int or Cha, because Wisdom is just... no...
- You're only giving it Ray of Frost as a cantrip, not the whole package of a Spellcasting ability.
Offensive Challenge Rating
Let's see if adding Ray of Frost will make the Koldbold hit harder. Since Ray of Frost does 1d8 Cold Damage, it deals an average of 4.5 DPR but with the caveat of a really low attack bonus (+1). While a regular Kobold has a Dagger attack that does 1d4+2 piercing, also a DPR of 4.5.
So, likely, giving it Ray of Frost is not going to affect OCR.
Defensive Challenge Rating
DMG page 277 tells us that:
Giving a monster resistance and immunities to three or more damage types (especially bludgeoning, piercing, and slashing damage) is like giving it extra hit points.
There is also a table on the same page telling us by how much we should multiply the HP to get the effective HP but because we only consult it when the creature has 3 or more resistances, we're not going to multiply it's HP by anything. So Defensive Challenge Rating doesn't change.
TL;DR Challenge Rating doesn't change
However, if you really want your Koldbold to be CR 1/4, you can give it the full spellcasting feature and tweak its stats a bit and recalculate OCR from there.
As ray of frost deals roughly the same damage on a hit as its normal attack (probably even less) and cold damage is far from common, its CR would not change.