Modelling D&D Spells with Maths

In terms of the game, the author focuses on computing save-adjusted damage to compare two spells, Fireball and Cloud Kill. These aren't very comparable as Fireball is an instantaneous damage spell while Cloud Kill can stick around for up to 10 minutes, making it more of an area denial-type spell. Fireball and Lightning Bolt, which are both 3rd level direct damage spells, are more comparable using this analysis, although they still have distinct ranges, area of effects, and types of damage.

More generally, this is an example of a complex decision process. The game designers want to avoid spells that are "mark II" versions of another, because diversity of effects is more interesting for the system and for players. Thus, many factors are situation-dependent. Although Fireball is an iconic third-level spell and more effective than others at the same level, it is balanced by the fact that many creatures are resistant or immune to Fire. Any sort of decision tree would need questions about the nature of the opponents, who might be also be in the area of effect (allies, other opponents, burnable items), and if the casting makes sense given the resources available and anticipated need. (D&D is largely a resource-management game and spells are a finite resource.)