The best way to make a spellcaster feel powerful is to throw hordes of enemies that the caster can dispatch with a single blast. The problem is that actually running this math at the table can be an absolute chore. The time gap between rolling a ton of damage dice and actually narrating what happens leaves the experience a little flat.

In order to fix this, we need a faster way to adjudicate area effect damage against hordes of monsters. Taking a cue from Mob Attacks in the Dungeon Master’s Guide (p. 250), we can reverse-engineer the odds of an attack success to determine how many mobs it would take to hit. For mob saving throws, we just turn that formula inside out.

Spell Efficacy vs. Hordes

Here are the odds of a getting the full effect when casting a spell that triggers a saving throw. This represents a single…