D&D 5E 14 is the Magic Number

[Guest 6801328]

In my Wednesday games for the last few weeks the poor Cleric has been having awful luck with his Sacred Flame: the monsters seem to always make their saving throws. It's become a running joke at the table.

But I started thinking about attack rolls vs. saves and whether it's more likely for an attack to land than for a monster to fail his saving his throw. I realized (apologies if this is so old that it's not even discussed anymore) that the magic number is 14. That is, the odds of hitting a monster are exactly the same as the odds of the monster failing a save when the monster's AC is 14 more than its saving throw bonus. (This assumes the character's attack bonus and casting bonus are equal). If AC is 15 or more higher than the saving throw modifier, your attack rolls are more likely to fail relative to the monster failing its saves, and if the difference is 13 or less your spells with saves are less likely to succeed than spells/attacks that require attack rolls.

I don't know how useful this really is, unless you're the sort of player who memorizes the Monster Manual, but I found it interesting. The bad luck with Sacred Flame really started with Ghouls and Ghasts, and looking at their stats they each have a differential of 10 (AC 12, Dex save +2, and AC 13, Dex save +3, respectively). So not surprising that Sacred Flame was the wrong choice.

Anybody know if there's a spreadsheet out there with the stats of all the monsters in structured form? I'd love to analyze the whole monster manual this way.

 

[Tony Vargas]

Nod. Saves are essentially inverted attack rolls, eyeballing the comparison is a little tricky because in d20 you match the DC, so on a save 'tie' goes to the defender, on an attack, to the attacker, and because of the save DC calculation. 'Balancing' is even trickier, because you don't have 6 different ACs (anymore - maybe 3e came close to that) with the attacker choosing which one to use.

But, yeah, say you have a 16 stat attacker, +5 w/prof, hits an AC 14 on a rolled 9, which is 60% of the time, similarly, 16 stat imposes a DC 13 save, beating that 40% of the time (so it 'hits' 60%) means rolling a natural 13, which requires only a +0 save.

Handy rule of thumb.

 

[FormerlyHemlock]

Yes. WotC even put out a set of optional rules in Unlimited Arcana for using this equivalence to let the player roll to beat the monster's saving throw instead of having the monster make the saving throw. Unfortunately WotC did the math wrong--I think they specified "12 + save modifier" instead of "14 + save modifier" as the target number to beat.

But yes, this equivalence is well-known. For high-level monsters, that often means that it would be better to attack them instead of forcing saving throws, except for one fact: you can target weak saves.

 

[flametitan]

Yes. WotC even put out a set of optional rules in Unlimited Arcana for using this equivalence to let the player roll to beat the monster's saving throw instead of having the monster make the saving throw. Unfortunately WotC did the math wrong--I think they specified "12 + save modifier" instead of "14 + save modifier" as the target number to beat.

They went to only 11+ bonus, which is even worse.

If you want to convert saves and attacks to a player does all the rolls system: 12 + attack bonus, 14 + save bonus.

But this conversation seems tangential to the odds of forcing a save vs the odds of attacking.

 

[Cognomen's Cassowary]

If AC is 15 or more higher than the saving throw modifier, your attack rolls are more likely to fail relative to the monster failing its saves, and if the difference is 13 or less your spells with saves are more likely to succeed than spells/attacks that require attack rolls.

I think you misstated your thought here. This is a "heads I win, tails you lose"-type statement. What you mean with the second independent clause, I think, is that if the difference between AC and modifier is 13 or less, attacks are more likely to succeed.

Two things to keep in mind: there's no such thing as proficiency in armor class, and you cannot crit with a save spell. In practice, these two facts mean that you are almost always going to do more damage with the attack than with the save spell, all else being equal. Unless, that is, you know specific vulnerabilities, like Str on a demilich or Dex on a tarrasque.

I have a spreadsheet somewhat similar to what you're asking for. It doesn't put names of creatures next to their stat blocks, but it collects the AC and ability scores of all creatures at each CR to find the median, and thereby it allows us to observe trends as CRs rise. I've slapped some comments on to try to make it intelligible to people who are not me. The forum won't let me upload it as an OpenOffice document, so you get instead OpenOffice's half-hearted attempt to convert it to outdated Excel.

View attachment D&Dmonstermath.xls

Edit: I found a website to convert it to modern Excel. I'm still not sure how good the conversion is; I'll try to remember to check when I'm at the library in a little bit.

View attachment D&Dmonstermath.xlsx

Edit 2: It looks like the numbers and comments survived, but the graphs are a little altered. You should be able to fix them fairly easily if it matters to you.

 

[Mishihari Lord]

This type of fact is most useful in game design. The designer tries to guess what percentage of attacks being successful will be the most fun at the table then build the rest of the mechanics around that. I seem to recall that there was some research that found that optimal fun for the average player was about 70% for melee attacks. I dunno if anyone ever looked into what it would be for more powerful magic effects.

 

[Ahglock]

On a pure accuracy level the saves seem more accurate at high levels. But by the time you get your save DC that high you are using cantrips less often so sacred flame never really shines.

In our campaign the same thing happened the cleric didn't pull off a successful sacred flame until 8th level. It was bizzare and yea became a running joke.

 

[Guest 6801328]

I think you misstated your thought here. This is a "heads I win, tails you lose"-type statement. What you mean with the second independent clause, I think, is that if the difference between AC and modifier is 13 or less, attacks are more likely to succeed.

Oops. Fixed.

Two things to keep in mind: there's no such thing as proficiency in armor class, and you cannot crit with a save spell. In practice, these two facts mean that you are almost always going to do more damage with the attack than with the save spell, all else being equal. Unless, that is, you know specific vulnerabilities, like Str on a demilich or Dex on a tarrasque.

I have a spreadsheet somewhat similar to what you're asking for. It doesn't put names of creatures next to their stat blocks, but it collects the AC and ability scores of all creatures at each CR to find the median, and thereby it allows us to observe trends as CRs rise. I've slapped some comments on to try to make it intelligible to people who are not me. The forum won't let me upload it as an OpenOffice document, so you get instead OpenOffice's half-hearted attempt to convert it to outdated Excel.

View attachment 76366

Edit: I found a website to convert it to modern Excel. I'm still not sure how good the conversion is; I'll try to remember to check when I'm at the library in a little bit.

View attachment 76367

Edit 2: It looks like the numbers and comments survived, but the graphs are a little altered. You should be able to fix them fairly easily if it matters to you.

Awesome! I'll check it out and see what I can do. Thanks.

 

[Ancalagon]

interestingly, 14 is also a "magic number" for stats - you really should have a 14 in your main stat, 14 in con will really help you survive and 14 dex is optimal for medium armor users.

Also, 14 AC seems to be a practical minimum to offer some kind of protection vs monsters

 

[ExploderWizard]

One thing that needs to be factored into the whole spell attack roll vs forced save debate is that when an enemy is in melee range that ranged attack roll will be made with disadvantage, while a forced save spell works just fine.