[RPG] How to convert D&D 5e Saving Throws into Defences

dnd-5ehouse-rules

In D&D 5, the saving throws for spells has the following formula:

The DC is set to 8 + prof bonus + magical stat bonus.

The target then makes a saving throw, adding their stat bonus and hoping to get above that DC.

Instead of having the defender roll the saving throw, we would like the attacker to roll the attack against the "defense" of the monster. (Mainly to make play by post run smoother)

Would this mean that the attacker just rolls d20+prof + magic stat bonus, and they try to get a number which is higher than 8+ monster def stat bonus, or is there a different formula which better maintains the math? (This math sounds wrong to me, so I assume there is a better formula)

Best Answer

To preserve the probabilities exactly, the new DC should be "14 + monster defense."

How I got that number

So, you want to convert this:

d20 + monster_save vs. 8 + caster_modifiers

Into this:

d20 + caster_modifiers vs. ?? + monster_save

Here's how to figure out the "??" using a bit of intuition about probability:

  1. Ignore the modifiers for a second, since you'll be keeping those the same anyway. What's the probability of making a DC 8 check on a straight d20 roll? There are 7 values on a d20 (1 through 7) that fail, and 13 values (8 through 20) that succeed. So 13/20, or 65%. (Try output d20 >= 8 in AnyDice.)
  2. Now, flip the percentages. You know you want the monster to succeed 65% of the time and fail 35% of the time (before mods). So that means the caster should succeed 35% of the time (7/20) and fail 65% of the time (13/20).
  3. In other words, you want the lowest 13 numbers on the d20 (conveniently, those are 1 through 13) to be failures. What DC is that? It's actually 14 (because a roll equal to the DC means you've beaten it).
  4. Thus, to preserve the probabilities exactly, the new formula is:

    d20 + caster_modifiers vs. 14 + monster_save

  5. Try a few examples to check your work.

System caveats

(This is a bit speculative because the game is unreleased, so we haven't necessarily seen all the rules, and some of them are likely in flux.)

Note that just being the one who gets to make a roll is sometimes a big benefit. For example, D&D Next playtest stuff had the concept of advantage, which lets you roll two dice and keep the highest. If defenders were previously able to claim advantage on saves, then shifting rolls to the attacker's side can make spells and monster abilities more powerful even though the raw math is the same.

Likewise, if the system features any kind of "bennies" or "action points" that you can use to enhance a roll, then shifting rolls from defenders to attackers generally makes combat faster and attacks harder to resist. Whether this favors PCs or enemies really depends on who's forcing more saving throws.

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