The math of Advantage and Disadvantage

[FrogReaver]

Unfortunately, your comments are incorrect which is why I posted the table in the first place.

Would you agree that an AC20 would be a high AC for a level 1-4 character? A level 1-4 character typically has +5 to hit (+2 proficiency and +3 stat) resulting a 15+ being required to hit. If you READ the table posted above. The effect of advantage when the target number is 15 is an increase of 21% in the chances to hit which is equivalent to just more than a static +4.

To get down to an effective +2.5 you would need to be fighting a creature with an AC of 23 at level 1-4 ... giving a required roll to hit of 18.

Over a wide range of AC (in fact almost anything not considered ridiculously high i.e. AC23 at tier 1 ... AC27 at tier 2-3, +5 stat and +4-5 proficiency), advantage is indeed equivalent to a static +4 to +5. THIS is exactly why I posted both the math and the tables since folks seem to have this mistaken impression that the effect of advantage is about the same as +2.5 to +3 which is generally incorrect.

Flat bonuses of +4 to +5, in most cases, are the equivalent of advantage. The exception being extremely high to hit numbers which come into play only for EXTREMELY high AC. If you have +10 to hit and the AC of the creature you are attacking is 25 (like a Tarrasque?) then advantage is STILL better than than a static +4.

Finally, if you can somehow arrange to get a static +4 on to hit through magical weapons (e.g. +2 bow +2 archery) then advantage ON TOP of this will be the equivalent of an additional +4 to +5.

It still boils down to the chances to hit you have at your table in play but realistic scenarios favor more than +3. The most common scenario is to look at using GEM and advantage. That makes lower chances to hit come into play more often. So I’d say +4 makes the best white room estimate. Or just do what I do when I really care and make a chart of likely AC’s and apply advantage to each independent chance.

 

[Keravath]

In my experience, what you are saying is true enough for the lowest levels of the ‘apprentice tier’ when the DM tends to coddle the players.

But at higher levels − for more ‘verisimilitudinous’ play styles − heroes are likely to come across creatures whose levels diverge significantly from their own. The AC can vary significantly. Often enough, the advantage proves unhelpful.





Yes, correct. The need for a natural 18 or higher happens often enough (especially for skill checks), and the advantage mechanic becomes less helpful when one truly needs a bonus.

I am not sure what you might mean by "for more ‘verisimilitudinous’ play styles"

However, if we are playing D&D 5e using monsters from the monster manual the highest monster AC is the Tarrasque at 25 (most ancient dragons are 20-22).

At tier 4 level of play (levels 17-20), the proficiency is +6, stat is +5 and a magical weapon of +2 is probably on the low side. In any case this gives a total modifier of +11 to +13 and a target number of 12 ... where advantage is equivalent to +5.

However, you seem to be playing in a 'verisimilitudinous’ game where a to hit die roll of 18 is common.

With a to hit modifier of 11 to 13 this means that you commonly fight home brewed creatures with an AC of 29 to 31. However, we are NOT discussing the effect of advantage in a homebrew setting with creatures with extremely high AC that have been created for a specific game. We are discussing advantage in the context of D&D and the monsters supplied with the monster manual ... and in that case, advantage, even at tier 4 is the equivalent of +4 to +5 over the vast majority of typical ACs.

Let's turn to skills. A character proficient in a skill at tier 4 will have a minimum of +5 even if they have a -1 in the stat. This goes to a maximum of +11 without expertise and to a maximum of +17 with expertise (assuming no magic items).

Have to roll an 18 on a skill check depends on the character and their skills. If you aren't proficient ... what do you expect .. the DC was probably about 20? And advantage is still the equivalent of +2.5 in this edge case.

For a proficient character an 18 required die roll is at least a 23DC task.
For a proficient character with the appropriate stat an 18 required is at least a DC29 task
For a proficient character with stat and expertise an 18 required die roll is at least a DC35

Keep in mind that "impossible" starts at 30.

The point? If you are commonly encountering DC18 skill checks from proficient characters then the DC of the task is already past very difficult.

On the other hand, a difficult DC20 task for a proficient character is again into the range where advantage is +4 to +5. An impossible DC30 task for a character with expertise and the stat required gives a target number of 13 and AGAIN, advantage is the equivalent of +4 to +5.

Finally, the reason you seem to devalue advantage is because it does not guarantee success. I have rolled with advantage MANY times and still rolled a 1 and a 2 (or other low numbers) ... and failed miserably. However, confirmation bias does NOT change the math that in the vast majority of situations even with high AC and DC at tier 4 ... advantage is equivalent to +4 to +5.

 

[Ovinomancer]

In my experience, what you are saying is true enough for the lowest levels of the ‘apprentice tier’ when the DM tends to coddle the players.

But at higher levels − for more ‘verisimilitudinous’ play styles − heroes are likely to come across creatures whose levels diverge significantly from their own. The AC can vary significantly. Often enough, the advantage proves unhelpful.





Yes, correct. The need for a natural 18 or higher happens often enough (especially for skill checks), and the advantage mechanic becomes less helpful when one truly needs a bonus.

A flat +3 is only improves success chances over advatange if the needed roll is 18+. You can trivially math this:

1) base chance for 18+ is 3/20 or 15%

2) advantage chance fir 18+ is 289/400 or 27.75%

3) +3 chance for 18+ is 6/20 or 30%

At 18+, a +3 improves your chances over advantage by 2.25%. If you need a 17+, advantage chance goes to 36% while +3 gies tp 35%.

So, an 8th kevel character with +4 stat and no magic is +7 to hit. To need an 18+ to hit, the target AC is 25. That's a Tarrasque. In Tier II. Pretty darned sure that it's not a matter of coddling, but one of math.

 

[Keravath]

It still boils down to the chances to hit you have at your table in play but realistic scenarios favor more than +3. The most common scenario is to look at using GEM and advantage. That makes lower chances to hit come into play more often. So I’d say +4 makes the best white room estimate. Or just do what I do when I really care and make a chart of likely AC’s and apply advantage to each independent chance.

I think you mean GWM? ... and I agree with you ... trying to figure out the target to hit number at which it is better to not use GWM/SS when you have advantage is a different and also interesting question.

However, in that case you have to factor in the lost damage when you miss against the extra damage from GWM if you hit. For a typical d10 weapon with a +5 to stat ... the weapon does an average 10.5 vs +10 from GWM. On the other hand, if you have not yet maxed the attack stat so that the average weapon damage drops (i.e. tier 1 with an average 8.5) then the extra damage from GWM is more than one weapon hit on average and this will shift the ideal to hit number where it is better to use GWM/SS.

The problem with this analysis is that you have to make some assumptions about weapon use (i.e. great sword may have a different change over point than a glaive).

I'll see if I can come up with a table for it

 

[FrogReaver]

I think you mean GWM? ... and I agree with you ... trying to figure out the target to hit number at which it is better to not use GWM/SS when you have advantage is a different and also interesting question.

However, in that case you have to factor in the lost damage when you miss against the extra damage from GWM if you hit. For a typical d10 weapon with a +5 to stat ... the weapon does an average 10.5 vs +10 from GWM. On the other hand, if you have not yet maxed the attack stat so that the average weapon damage drops (i.e. tier 1 with an average 8.5) then the extra damage from GWM is more than one weapon hit on average and this will shift the ideal to hit number where it is better to use GWM/SS.

The problem with this analysis is that you have to make some assumptions about weapon use (i.e. great sword may have a different change over point than a glaive).

I'll see if I can come up with a table for it

If you ignore the effect of crits then advantage can be viewed as a multiplier of your base dpr with different multipliers based on your starting chance to hit.

For example advantage on 50% to hit will turn into 50% more dpr (ignoring crits). This will be the same regardless of weapon.

 

[Yaarel]

We can all agree, the usefulness of advantage depends on how often a player needs to roll a natural 18 or higher.

In my games, this is often enough.

Magic bonuses from weapons and such, are rare.

Higher than expected level encounters are common. (Sometimes 1 out of 4 encounters. Lower than expected level is also common, but not relevant here.)

I am unsure why the arguments ignore the need for a character to succeed on a skill check that one is unproficient in. In my games, that is common and important. Similarly, succeed on a saving throw that is nonoptimal.

 

[FrogReaver]

We can all agree, the usefulness of advantage depends on how often a player needs to roll a natural 18 or higher.

In my games, this is often enough.

Magic bonuses from weapons and such, are rare.

Higher than expected level encounters are common. (Sometimes 1 out of 4 encounters. Lower than expected level is also common, but not relevant here.)

I am unsure why the arguments ignore the need for a character to succeed on a skill check that one is unproficient in. In my games, that is common and important. Similarly, succeed on a saving throw that is nonoptimal.

Most saves do t require an 18+ even for an 8 stat with no proficiency. Most skill checks end up being made by the character that has stat or proficiency or both in them. This they also don’t require and 18+.

It’s possible yes, but not likely. It’s better to just make a note to treat advantage as +4 or so except in extreme cases

 

[Krachek]

Simply remember.
Advantage or disadvantage have maximum impact when you are around 50% chance of success.
The closer you are from 0% or 100% the less it will impact you.

 

[dave2008]

In my experience, what you are saying is true enough for the lowest levels of the ‘apprentice tier’ when the DM tends to coddle the players.

But at higher levels − for more ‘verisimilitudinous’ play styles − heroes are likely to come across creatures whose levels diverge significantly from their own. The AC can vary significantly. Often enough, the advantage proves unhelpful.





Yes, correct. The need for a natural 18 or higher happens often enough (especially for skill checks), and the advantage mechanic becomes less helpful when one truly needs a bonus.

Please point to an official WotC product were needing an 18 is common. I don't use the APs, but in the MM the Highest aC is 25 (one creature) and then AC 22 for Ancient dragon is the next highest. When you are likely to face those creatures, PCs should be well above the 18 needed to hit threshold. Similarly the highest DC is 20 I believe, but I would have to verify that.

K's point is correct, yours is not (or so I would believe from the evidence I have seen)

 

[Azzy]

Please point to an official WotC product were needing an 18 is common. I don't use the APs, but in the MM the Highest aC is 25 (one creature) and then AC 22 for Ancient dragon is the next highest. When you are likely to face those creatures, PCs should be well above the 18 needed to hit threshold. Similarly the highest DC is 20 I believe, but I would have to verify that.

The only thing I can see is he's assuming the target numbers are the straight DCs rather than the number that you actually need to roll on the dice. Even then, with the highest listed DC being 30, I still don't see it. :/