How can I convert D&D 5e Saving Throws into Defences?

Question

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)

Answer 1

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.

Answer 2

Wizards of the Coast's Unearthed Arcana: Variant Rules (PDF) details this under "Players Make All Rolls":

When a character forces an opponent to make a saving throw, that player instead makes a saving throw check. The bonus to the d20 roll for a saving throw check equals the effect’s save DC −8.

The DC for this check equals 11 + the target’s saving throw modifier. On a successful check, the character overcomes the target’s resistance and treats the target as if it failed its saving throw. On a failed check, the target is treated as if it succeeded on its save.

Answer 3

It should be d20 + attacker prof + magic stat bonus needing to hit 14 + monster def bonus to keep the same probabilities.

Example 1:

• Attacker has +2 prof bonus and +3 stat bonus.
• Monster has +1 stat bonus.
• Monster's saving throw would be 13 in existing rules, so they would need to roll 12 on d20. That's 45% chance of save, or 55% chance of a hit.
• That's the same as needing a d20 roll of 10 to hit. Which if you assume you add proficiency and stat bonus as the attacker, means the target number should be 15 ( 14 + 1 )

Example 2:

• Attacker has +1 prof bonus and +2 stat bonus
• Monster has +3 stat bonus
• Monster's saving throw would be 11, so they would need to roll 8 on d20. That's 65% chance of save, or 35% chance of a hit.
• That's the same as needing a d20 roll of 14 to hit. Which if you assume you add proficiency and stat bonus as the attacker, means the target number should be 17 ( 14 + 3 )

The reason the value is 14 and not 13 is because as well as reversing the rolls, we reverse the result when the target is hit exactly. Which adds another 1 offset. I got that wrong on the first posts.