The Mathematical Value of Advantage

[LudicSavant]

I wrote up this explanation (and graph) for another context, and thought that some folks over here might appreciate it too. Besides, this seems to be a topic that gets brought up often enough that it seemed worthwhile to have something convenient to link to.

https://cdn.discordapp.com/attachments/1145379188778471537/1145379200463798363/image.png
Effective +X bonus in white.

On passive checks, Advantage is worth a flat +5 to the roll. On active checks, it’s worth about +5 on the roll if you need to roll an 8-14 on the die, +4 if you need 15-16, +3 if you need 17-18, +2 if you need a 19, and +1 if you're trying to roll a 20.

Many will have heard that the mean average of Advantage is about +3.32 on the roll, and this is true, but it doesn't really convey the whole picture. Why not? Well, two reasons.

Reason one is that the average is weighed down by sharp falloff at the edge of the RNG. If we take the average of rolls where we need to roll a 5-16 on the d20 to succeed, the average benefit of Advantage is +4.4. If we took the average of needing a 7-14 to succeed, the average benefit is +4.7. See what I mean? Incidentally, this is probably why the designers of 5e made Advantage count as +5 for passive checks.

Reason 2 is that one of those edges of the RNG weighing down the average? It also affects +X bonuses! For example, if you would succeed on a roll of 2, then in that situation a +1 bonus is worth as much as a +10, and a +0.95 bonus is worth almost as much as a +1.

https://cdn.discordapp.com/attachments/1145379188778471537/1145479867748589568/image.png
The number in yellow is the benefit of a +5 bonus over Advantage. As we can see, unless we need to hit a 17+ on the d20, the difference is only +0 to +1.25.

It is also worth noting that not all +1s are creating equal. This is perhaps most clear when we look at effective durability. For example, if an enemy has a 95% chance to hit and you inflict Disadvantage on them (lowering that to 90.25% chance), you've barely changed anything at all (heck, there's a good chance they'll kill you in the same number of attacks). By contrast, if an enemy has a 5% chance to hit and you inflict Disadvantage on them (lowering that to a 0.25% chance to hit), it will on average take twenty times as many rolls to kill you.

Here are some simple, practical things you can take away from this:

Advantage on saving throws won't do as much to help a terrible save, but it will turn a decent save into a high save, and a high save into a near impervious save.
Likewise for inflicting Disadvantage on enemy attack rolls. Mook swarms in particular can quickly go from "deadly" to "virtually harmless." By contrast, if you have a low AC and you're fighting a giant, Disadvantage will barely help you at all.
Since needing to hit the middle of the RNG on skill checks tends to be more common than needing to hit the edges, Advantage is often better than Expertise until mid-Tier 3.

[Nagog]

Likewise for inflicting Disadvantage on enemy attack rolls. Mook swarms in particular can quickly go from "deadly" to "virtually harmless." By contrast, if you have a low AC and you're fighting a giant, Disadvantage will barely help you at all.

I can happily attest to this: In a one-shot the DM was planning on us struggling to fight a literal army of undead and probably die doing so (it's a one-shot so not too attached to the characters). Unfortunately for him, my character was a Valley Girl Death Knight who was determined to help these undead by finding out what raised them and destroying it so they could RIP, and so I cast Sanctuary on myself and sprinted into the middle of them. The ridiculously high AC Fighter followed, as did the 18 AC Sorcerer after casting Daylight.

Due to disadvantage on the attack rolls (and in my case, a Wisdom save precluding that, also at disadvantage), we made it through the entire army and only got hit once or twice amid DOZENS of attack rolls each round.

We had a lot of fun that game, and I still have my Valley Girl Death Knight in my back pocket for fun future adventures.

[strangebloke]

Great write up with a lot of good examples. A lot of this math was done ages of course, but its a pretty complete guide.

The good heuristic is that advantage/disadvantage removes a lot of the variance and pushes things in a general direction, but its isn't going to turn something unlikely into something very likely.

[5eNeedsDarksun]

Some interesting interpretation of the math here. I take the point that advantage probably ought to be thought of as somewhat better than the 3.32 as most of the cases will fall into an area that's better than that; it could be undervalued as a result
The only point I'd disagree with is your take that the steep fall off at the edges is a good thing. The example of a foe requiring only a 2, with a 95% chance to hit, then being given disadvantage (let's say by being blinded) and having their chance to hit being reduced to roughly 90%, similar to a -1 penalty doesn't seem enough. While the advantage/ disadvantage system is efficient and easy, I can't say I like what happens at the edges. Characters and monsters end up with limited ways to impact rolls in these cases.

[MoiMagnus]

While the advantage/ disadvantage system is efficient and easy, I can't say I like what happens at the edges. Characters and monsters end up with limited ways to impact rolls in these cases.

This is why the Shield spell gives a +5 to AC and mirror image has a weird d20 roll, instead of simply a disadvantage (this and the fact that disadvantages don't stack with one another).

Disadvantage is a good "default tool", but not the only one. Well... some character classes have more access to those alternative tools than others, but that's another debate.

[Aquillion]

Remember that advantage on attack rolls also increases your chance of a crit, which certainly does matter.

[LudicSavant]

Remember that advantage on attack rolls also increases your chance of a crit, which certainly does matter.

Most certainly!

Advantage specifically on attack rolls increases the chance of a critical hit to 9.75%, while Disadvantage decreases it to 0.25% (1 in 400).


The only point I'd disagree with is your take that the steep fall off at the edges is a good thing. The example of a foe requiring only a 2, with a 95% chance to hit, then being given disadvantage (let's say by being blinded) and having their chance to hit being reduced to roughly 90%, similar to a -1 penalty doesn't seem enough.

It looks like you may have gotten what I said backwards. I said that decreasing a chance from 95% to 90.25% is worth very little (not at all a good thing).

By contrast, reducing a 5% to 0.25% is potentially worth quite a lot (indeed, if that's the enemy's new chance to hit you, you just made yourself twenty times as difficult to hit).

Basically, not all -1s are created equal. Same for +1s.


I can happily attest to this: In a one-shot the DM was planning on us struggling to fight a literal army of undead and probably die doing so (it's a one-shot so not too attached to the characters). Unfortunately for him, my character was a Valley Girl Death Knight who was determined to help these undead by finding out what raised them and destroying it so they could RIP, and so I cast Sanctuary on myself and sprinted into the middle of them. The ridiculously high AC Fighter followed, as did the 18 AC Sorcerer after casting Daylight.

Due to disadvantage on the attack rolls (and in my case, a Wisdom save precluding that, also at disadvantage), we made it through the entire army and only got hit once or twice amid DOZENS of attack rolls each round.

We had a lot of fun that game, and I still have my Valley Girl Death Knight in my back pocket for fun future adventures.

A most excellent demonstration of the mathematical principle! :smallbiggrin:

[Maan]

I'm saving the table for reference :smallbiggrin:

I can't thank you enough for your posts: you manage to put together solid knowledge and very clear exposition.

[LudicSavant]

Reason 2 is that one of those edges of the RNG weighing down the average isn't really a bad thing. For example, if you would succeed on a roll of 2, then in that situation a +1 bonus is worth as much as a +10, and a +0.95 bonus is worth almost as much as a +1.

For those who may find this particular point unintuitive, I have created an additional visual aid, comparing the benefit of an actual +5 bonus to Advantage:

https://cdn.discordapp.com/attachments/1145379188778471537/1145479867748589568/image.png

The number in yellow is the effective +X benefit of having an actual +5 bonus instead of Advantage.

So as you can see, while the effective benefit of Advantage when you only need a 2 on the roll is "only +0.95," the effective benefit of an actual +5 when you only need a 2 on the roll is "only +1."

Edit
And here's a +4 bonus:

https://cdn.discordapp.com/attachments/1100874982961188864/1145484873767854150/image.png

[Kane0]

I'm saving the table for reference :smallbiggrin:

I can't thank you enough for your posts: you manage to put together solid knowledge and very clear exposition.
Seconded, already saved and shared to my group (3 of 5 of us DM)

[Thane of Fife]

Advantage on saving throws won't do much to help a terrible save, but it will turn a decent save into a high save, and a high save into a near impervious save.
Likewise for inflicting Disadvantage on enemy attack rolls. Mook swarms in particular can quickly go from "deadly" to "virtually harmless." By contrast, if you have a low AC and you're fighting a giant, Disadvantage will barely help you at all.


I'm not sure that's the whole story? If someone needs anything but a 1 to hit, and you give them disadvantage, their odds of hitting don't change that much, but their odds of missing change substantially - they are almost twice as likely to miss.

For example, if you were being attacked by two monsters for one round, one hitting on 2+ and the other hitting on 20+ (acknowledging this is an unlikely scenario), and any hit would kill you, you would improve your odds of survival (i.e. not getting hit) more by disadvantaging the creature with the high odds of hitting than the creature with the low odds of hitting.

So, if Sir Missalot has a 5% chance to hit (hits on 20), or 0.25% with disadvantage, and Auntie Oakley has a 95% chance to hit (hits on 2+), or 90.25% with disadvantage, then:

Normally, you have a (1-0.05)*(1-0.95)=4.75% chance to survive. If you disadvantage Sir Missalot, then you would go to (1-0.0025)*(1-0.95)=4.99% chance to survive. If you disadvantaged Auntie Oakley, you would go to (1-0.05)*(1-0.9025)=9.26% chance to survive.

Without thinking it through entirely, I believe this is true is most circumstances where the dice are only rolled once and you only need one success. If you're trying a skill check that each character can try once, advantaging the character who is worst at it is probably more useful than the character who is best at it.

[LudicSavant]

I'm not sure that's the whole story? If someone needs anything but a 1 to hit, and you give them disadvantage, their odds of hitting don't change that much, but their odds of missing change substantially - they are almost twice as likely to miss.

Indeed!


For example, if you were being attacked by two monsters for one round, one hitting on 2+ and the other hitting on 20+ (acknowledging this is an unlikely scenario), and any hit would kill you, you would improve your odds of survival (i.e. not getting hit) more by disadvantaging the creature with the high odds of hitting than the creature with the low odds of hitting.

So, if Sir Missalot has a 5% chance to hit (hits on 20), or 0.25% with disadvantage, and Auntie Oakley has a 95% chance to hit (hits on 2+), or 90.25% with disadvantage, then:

Normally, you have a (1-0.05)*(1-0.95)=4.75% chance to survive. If you disadvantage Sir Missalot, then you would go to (1-0.0025)*(1-0.95)=4.99% chance to survive. If you disadvantaged Auntie Oakley, you would go to (1-0.05)*(1-0.9025)=9.26% chance to survive.

Without thinking it through entirely, I believe this is true is most circumstances where the dice are only rolled once and you only need one success. If you're trying a skill check that each character can try once, advantaging the character who is worst at it is probably more useful than the character who is best at it.

That looks correct at first glance.

So in this case, Sir Missalot is still being hindered more by Disadvantage than Auntie Oakley is, but Auntie Oakley is so much more of a threat that (if you only had the choice to Disadvantage one of them) you'd disadvantage her anyways.

Like, she is single-handedly bringing down your chance of survival to 5% before Missalot even does anything. Nothing you can do to Sir Missalot will raise that above 5%. But giving Disadvantage to Auntie Oakley can raise you to 9.26%

The difference is that if you get in a fight with Sir Missalot alone, putting Disadvantage on them solves the fight. If you get in a fight with the far higher CR enemy Auntie Oakley (whether alone or with their minion Sir Missalot), putting Disadvantage on anyone still puts your estimated time of death at round 1, and only extends it to round 2 if you're very lucky.

[sambojin]

One of the interesting things I've noted on DnD1. Only primal casters get Enhance Ability (ie, advantage on any skill for a particular stat) *and* Guidance on a reaction. So, +d4 on any skill check (+2.5'ish), plus advantage to it.

Rangers and druids truly are skill monkeys, but for anyone.

(There's also the oft stated case that the difference between 80% and 90% of success isn't so much a 10% difference in the roll succeeding, you are simply half as likely to fail. So, it's a fair higher "not fail" percent, twice as unlikely to on average)

[kazaryu]

Here are some simple, practical things you can take away from this:

Advantage on saving throws won't do much to help a terrible save, but it will turn a decent save into a high save, and a high save into a near impervious save.
Likewise for inflicting Disadvantage on enemy attack rolls. Mook swarms in particular can quickly go from "deadly" to "virtually harmless." By contrast, if you have a low AC and you're fighting a giant, Disadvantage will barely help you at all.
Since needing to hit the middle of the RNG on skill checks tends to be more common than needing to hit the edges, Advantage is often better than Expertise until mid-Tier 3.

one (IMO) important thing to remember about advantage/disadvantage is how it shifts the '50% line' as in, what you're likely to roll. when you roll with advantage you have ~ a 50% chance of rolling a 15 or better. as opposed to rolling better than a 10. and the reason i bring this up is because you say that advantage won't do much to help a terrible save, but you don't define what terrible is. in tiers 1 and 2 DC 15 or less saves are decently common, and having advantage on that saving throw effectively doubles your odds of succeeding just based on the die roll, before applying a bonus. (specifically it halves your odds of failing). and with just a tiny bonus (like a +2) you can even get into tier 3 with this effect. as you're much more likely to hit the DC 17 that comes up. IMO thats a pretty significant impact.

[PhoenixPhyre]

one (IMO) important thing to remember about advantage/disadvantage is how it shifts the '50% line' as in, what you're likely to roll. when you roll with advantage you have ~ a 50% chance of rolling a 15 or better. as opposed to rolling better than a 10. and the reason i bring this up is because you say that advantage won't do much to help a terrible save, but you don't define what terrible is. in tiers 1 and 2 DC 15 or less saves are decently common, and having advantage on that saving throw effectively doubles your odds of succeeding just based on the die roll, before applying a bonus. (specifically it halves your odds of failing). and with just a tiny bonus (like a +2) you can even get into tier 3 with this effect. as you're much more likely to hit the DC 17 that comes up. IMO thats a pretty significant impact.

Yeah. Looking at monster saves, they only hit DC 15+ (averaging across monsters of a given CR) at CR 10 and then jump to 18 at CR 14. And most of the really debilitating saves are actually a bit lower than that--monsters with mixed saves tend to have much higher Dex save DCs that just do damage than, say, Wis save DCs.

[LudicSavant]

One of the interesting things I've noted on DnD1. Only primal casters get Enhance Ability (ie, advantage on any skill for a particular stat) *and* Guidance on a reaction. So, +d4 on any skill check (+2.5'ish), plus advantage to it.

Rangers and druids truly are skill monkeys, but for anyone.

Yeah; getting the bonus on "whoever in the party has the highest bonus to the skill you need" instead of just yourself is great.


Yeah. Looking at monster saves, they only hit DC 15+ (averaging across monsters of a given CR) at CR 10 and then jump to 18 at CR 14. And most of the really debilitating saves are actually a bit lower than that--monsters with mixed saves tend to have much higher Dex save DCs that just do damage than, say, Wis save DCs.

Whatever the mean average of your dataset may be, DC 15+ saves are not uncommon before CR 10, and often are really debilitating, whether it's Hydroloths (which is a very long lasting effect that makes you lose all your proficiencies, forget how to cast spells, be unable to speak language, guts your attribute scores, etc), Mind Flayers (and stuff like Arcanist and Ulitharids), Flinds, Dusk Hags, War Priests, various Warlocks (like Warlock of the Fiend, Warlock of the Great Old One, or Githyanki Star Seer), various Wizards (like Abjurer or Diviner or Necromancer), various druids (like Githyanki Xenomancer and Druid of the Old Ways), an awful lot of the Young Dragons, and so forth.

In addition, I would expect to fight things of CR 10+ in tier 2, especially if I was in a campaign where optimization is a relevant topic.

[Corran]

Without thinking it through entirely, I believe this is true is most circumstances where the dice are only rolled once and you only need one success. If you're trying a skill check that each character can try once, advantaging the character who is worst at it is probably more useful than the character who is best at it.
More is hidden in the implied assumptions (independent probabilities of individual success or failure) than in your suggestion (eg buff the weakest character).

Example:
A party of 5 stand before a slippery bridge that they have to cross one at a time. The DM announces the DC of the ability check that the pc's have to succeed if they are to cross the bridge without falling from it. Players look at their sheets and they see that the probabilities of their characters crossing that bridge are 40%, 45%, 50%, 55% and 60% respectively.

If the party defines success to be that everyone crosses the bridge, then it's best to grant advantage to the character with the lowest success chance (40%; bumping it up by 24%).

If the party defines success to be measured by how many many characters made the cross, then it is best to grant advantage to the character that profits the most from it (in this case the one with initial success chance of 50%, cause the bump will reach its max value of 25%).


Let's alter the examle somewhat, and have the bridge be creaky instead of slippery, so that failure means that the bridge collapses. So now you not only end up with a character falling off, but also with characters stuck to the wrong side of the bridge if they didn't already attempt to cross it.

By the first definition of success, it's still best to buff the character with the lowest success chance, and the order by which you have the characters cross the bridge is irrelevant.

Using the second definition of success, it's best to give advantage to the character with 60% and the optimal order of crossing is having the character with the higher success chance cross before others (from the "wrong" side to the correct one). Start adding more bridges with similar parties aiming to cross them next to each other, and the best solution will start moving to granting the bonus to a character with a lower success chance, eventally finilizing on the one with 50% chance (because they'll make the most out of the benefit). Aha! Found it. If you could go back in time a limited number of times n, to repeat crossing the bridge, then as n becomes larger you will want to grant advantage to someone with a lower success chance. The larger set of n's (assuming high enough upper bound for n) would correspond to granting advantage to the one who makes the most of it (in this case 50%), but as n gets higher and higher you'd start getting more from granting advantage to the even lower success chances (finalizing on the lowest one; ie even something very close to a 0% for a very big N).



It is also worth noting that not all +1s are creating equal. This is perhaps most clear when we look at effective durability. For example, if an enemy has a 95% chance to hit and you inflict Disadvantage on them (lowering that to 90.25% chance), you've barely changed anything at all (heck, there's a good chance they'll kill you in the same number of attacks). By contrast, if an enemy has a 5% chance to hit and you inflict Disadvantage on them (lowering that to a 0.25% chance to hit), it will on average take twenty times as many rolls to kill you.
It's hard to compare winning slightly more to losing slightly less. The equality of both ends can become clearer when you approximate the two opposing scenarios to look a little more like each other. For example, when the scenarios are of similar difficulty (and assuming I can inflict disadvantage for free), do I prefer to fight the monster with 95% hit chance which deals X damage on a hit, or the monster with 5% hit chance that deals 95X 19X damage on a hit?

[kazaryu]

Whatever the mean average of your dataset may be, DC 15+ saves are not uncommon before CR 10, and often are really debilitating, whether it's Hydroloths (which is a very long lasting effect that makes you lose all your proficiencies, forget how to cast spells, be unable to speak language, guts your attribute scores, etc), Mind Flayers (and stuff like Arcanist and Ulitharids), Flinds, Dusk Hags, War Priests, various Warlocks (like Warlock of the Fiend, Warlock of the Great Old One, or Githyanki Star Seer), various Wizards (like Abjurer or Diviner or Necromancer), various druids (like Githyanki Xenomancer and Druid of the Old Ways), an awful lot of the Young Dragons, and so forth.

In addition, I would expect to fight things of CR 10+ in tier 2, especially if I was in a campaign where optimization is a relevant topic.

so? the take away shouldn't be 'bad saves = don't bother with advantage. as pointed out, with as little as a +2 to a save even a DC 17 is passable 50% of the time with advantage as opposed to 25% of the time without. and most people would file a +2 as being really bad. borderline useless. if you're going to give generalized advice, you should be more specific, define your terms. the only time a 'bad' save isn't much improved (at least for tier1/tier2) is when its less than 2.

in other words, im not saying that your advice is wrong, per se im simply clarifying what modifier ranges are being referred to when you talk about 'terrible saves' as opposed to 'decent'

[LudicSavant]

so? the take away shouldn't be 'bad saves = don't bother with advantage.

The intended takeaway is that Advantage helps more if you already have some kind of investment into the stat, rather than simply dumping it. As you say, even boosting up a little from a dumped save can meaningfully improve the payoff you get from Advantage.

Not being specific at the end is intentional, as that's the tl;dr section. For specific values, that's what the longer writeup and graphs before it are for. Doesn't hurt to clarify, though! :smallsmile:



in other words, im not saying that your advice is wrong, per se im simply clarifying what modifier ranges are being referred to when you talk about 'terrible saves' as opposed to 'decent'

https://forums.giantitp.com/images/sand/icons/icon_thumbsup.png

[MoiMagnus]

I'm not sure that's the whole story? If someone needs anything but a 1 to hit, and you give them disadvantage, their odds of hitting don't change that much, but their odds of missing change substantially - they are almost twice as likely to miss.

For example, if you were being attacked by two monsters for one round, one hitting on 2+ and the other hitting on 20+ (acknowledging this is an unlikely scenario), and any hit would kill you, you would improve your odds of survival (i.e. not getting hit) more by disadvantaging the creature with the high odds of hitting than the creature with the low odds of hitting.

So, if Sir Missalot has a 5% chance to hit (hits on 20), or 0.25% with disadvantage, and Auntie Oakley has a 95% chance to hit (hits on 2+), or 90.25% with disadvantage, then:

Normally, you have a (1-0.05)*(1-0.95)=4.75% chance to survive. If you disadvantage Sir Missalot, then you would go to (1-0.0025)*(1-0.95)=4.99% chance to survive. If you disadvantaged Auntie Oakley, you would go to (1-0.05)*(1-0.9025)=9.26% chance to survive.

Without thinking it through entirely, I believe this is true is most circumstances where the dice are only rolled once and you only need one success. If you're trying a skill check that each character can try once, advantaging the character who is worst at it is probably more useful than the character who is best at it.

While I agree mathematically, I'd say that in practice:

(1) If the choice is between 5% of surviving and 10% of surviving, the correct behaviour is to search for a third option. And if there is no third option of survival, the correct choice is to find a way to make this almost-certain-death as positive as possible for the peoples who will survive. Situation in which it is worth to do an action that will be useless 95% of the time (the 5% of "surviving anyway" plus the 90% of "dying anyway") are extremely rare.

(1bis) The same is true if you go from 90% chance of success to 95% chance of success, you probably have a much better use of your action/resources/etc than doing something that is irrelevant 95% of the time (the 90% of "succeeding anyway" plus the 5% of "failing anyway")

(2) Sequences of checks with a single point of success (or a single point of failure) are best to be avoided by the GM. And as soon as you leave this edge case, what matter is more the "average amount of successes" (or even "average amount of damage" if we're talking about combat) rather than maximising the chance of a single success/failure.

And while you're correct that to get the "full picture", it's important to have in mind how advantage/disadvantage interact with single points of success/failures, most of the time you want to give advantage/disadvantage to peoples who are in a ~50% situation.

[5eNeedsDarksun]

Most certainly!

Advantage specifically on attack rolls increases the chance of a critical hit to 9.75%, while Disadvantage decreases it to 0.25% (1 in 400).



It looks like you may have gotten what I said backwards. I said that decreasing a chance from 95% to 90.25% is worth very little (not at all a good thing).

By contrast, reducing a 5% to 0.25% is potentially worth quite a lot (indeed, if that's the enemy's new chance to hit you, you just made yourself twenty times as difficult to hit).

Basically, not all -1s are created equal. Same for +1s.



A most excellent demonstration of the mathematical principle! :smallbiggrin:

I'm wondering in an actual game if reducing a roll from 5% success to .25% really has an impact. If I'm only going to save 1 time out of 20 for (let's say a save or suck), then reducing that to 1 in 400 means I'm probably going to fail regardless. If I'm fighting a monster that only hits on a 2+ then I'm probably not going to bother spending a resource to make it worse, and if I'm an intelligent monster with options I'd probably do anything other than attack at that point anyway.
Of course a flat negative number just moves these rolls into unhittable/ unsaveable range anyway, so it's probably 6 of one/ half dozen of the other regardless.

[LudicSavant]

I'm wondering in an actual game if reducing a roll from 5% success to .25% really has an impact.

The answer is yes, it really has an impact.

In the second post, Nagog gives an example of how such a thing had a major impact on their game. High AC + Disadvantage is an excellent way to handle mook swarms (a thing that can be very dangerous indeed if not properly countered). In addition, iterative probability is a thing. You can face many, many rolls over the course of a campaign.

[5eNeedsDarksun]

The answer is yes, it really has an impact.

In the second post, Nagog gives an example of how such a thing had a major impact on their game. High AC + Disadvantage is an excellent way to handle mook swarms (a thing that can be very dangerous indeed if not properly countered). In addition, iterative probability is a thing. You can face many, many rolls over the course of a campaign.

I mean, maybe if there are huge numbers of attacks or the attacks carry some kind of rider that is a real problem, but it seems kind of situational. Most of the time, even with a fairly large swarm are you going to face more than 20 attacks? So if one hits, so what; reducing that to zero probably isn't going to make a lot of difference over the adventuring day.
As I alluded to in my previous post, anything with intelligence or other options is probably going to go another way if possible when it becomes clear that making a regular attack is almost impossible anyway. If I'm DMing and I've got that many mooks under control of a caster or 2, I'd probably have them try and grapple or just dodge and act as cannon fodder/ shields anyway. Obviously situations vary, but there's also likely an opportunity/ resource cost on the player to impose the disadvantage as well.

[LudicSavant]

Obviously situations vary

Yes, it depends on the situation.

If you're in a situation where the cost to use (some defensive ability) exceeds the cost of (whatever the defensive ability is preventing the enemies from doing) or has less payoff than (some alternate option you could take), then said ability is not worth it / is overkill / etc.

[Chaos Jackal]

Easy and quick referral for when I'm trying to get through someone's head that not all +1s are created equal for the umpteenth time, thanks.

And yes, on the matter of turning low odds to no odds, it will obviously not be every time, but there will be situations where DMs will try to deter you by saying "oh, there's 50 of them, it would be suicidal to charge through" or fights that will balance high damage with low odds, and while anecdotal, in my experience both of those happen quite often. I've faced situations with a whole wall vanguard raining down arrows and spears with their +4 or whatever while someone with 22 AC just walked forward dodging and at least one of my DMs is quite fond of throwing things at us that have really terrible hit chances but a boatload of attacks with a mountain of dice attached to them.

Mind you, for the latter case, it's even bigger because of crits. Going to a basically nil chance of crit thanks to disadvantage can be a pretty big deal when the thing you're fighting can crit for 150% of your HP.

Also, very applicable post on the matter of things like Indomitable. That 10 or 8 in Wisdom won't do you many favors even with a second die.

[KorvinStarmast]

Nice Picture.

This was asked about in 2012 here and got a variety of good answers (https://rpg.stackexchange.com/q/14690/22566).

As a short hand...

Advantage => 50% chance of rolling 15 or greater.
Disadvantage => 50% chance of rolling 7 or less.

I will use this to pitch my players on the difference :) –

An interesting explanation of how it works is from RSConley:

With an advantage you are looking for best of two results.
To figure out your odds you need to multiply the chance of FAILURE together to find out the new chance of failure.
For example if you need 11+ to hit rolling two dice and taking the best means instead of a 50% of failing you have only a 25% chance of failing (.5 times .5), and 75% chance of success (.5 times 1.5).

For a disadvantage where you take the worst of two dice roll you need to multiply the chances of SUCCESS to find out the new odds. For example if you need a 11+ to hit your chance success drops from 50% to 25% (.5 times .5).

[Aquillion]

Since needing to hit the middle of the RNG on skill checks tends to be more common than needing to hit the edges, Advantage is often better than Expertise until mid-Tier 3.
There's an extremely important caveat here, though. Multiple sources of advantage don't stack. So for things that you can already get advantage on easily, getting guaranteed advantage isn't worth much.

If your group frequently uses the help action, say, and therefore almost always has advantage on skill checks made out of combat, then a feat or ability that grants advantage on a skill check that help can be reliably applied to is nearly worthless, whereas expertise remains incredibly valuable.

[KorvinStarmast]

While I agree mathematically, I'd say that in practice:

(1) If the choice is between 5% of surviving and 10% of surviving, the correct behaviour is to search for a third option. Bingo.

In the bridge scenario, we are reminded of why adventurers carry 50 feet of rope, typically. (I always upgrade to silk rope when I can afford it, since it weighs less ...)

The party of five puts together enough rope to reach across the ravine.
The PC with highest chance is buffed for advantage, and the other four hold / tie down the other end of the rope so that the first bridge crosser has a good chance that any slip which creates a fall can arrest that fall.
If he makes it across, then he ties off the rope to give the next crosses a bit more security. Whether or not the DM then offers adv or decreased the DC of the next attempt is up to the DM.

:smallbiggrin:

Alternatively, with a monk of level 4 or higher, send the monk across and if she falls, slow fall will mitigate some of the damage ... :smallwink: So we then ask "how deep is this ravine, anyway?"

[LudicSavant]

There's an extremely important caveat here, though. Multiple sources of advantage don't stack. So for things that you can already get advantage on easily, getting guaranteed advantage isn't worth much.

If your group frequently uses the help action, say, and therefore almost always has advantage on skill checks made out of combat, then a feat or ability that grants advantage on a skill check that help can be reliably applied to is nearly worthless, whereas expertise remains incredibly valuable.

Indeed! That is a valuable thing to mention: Features that grant Advantage to ability checks are not very useful to skill checks that can be Helped.

[Chronos]

Quoth MoiMagnus:

And while you're correct that to get the "full picture", it's important to have in mind how advantage/disadvantage interact with single points of success/failures, most of the time you want to give advantage/disadvantage to peoples who are in a ~50% situation.
I'd still say that it depends. Suppose, for instance, that you're fighting enemies that have decent intel on the party, and that you're defining "failure" (the thing you're trying to avoid) as "at least one party member is killed". The enemies are going to attempt to focus fire on whichever party member is least tough, which means that durability buffs on anyone other than that one party member have almost no effect. In a situation like that, you don't give the buff to the person who will benefit most from it; you give it to the person who most needs it.

[MoiMagnus]

I'd still say that it depends. Suppose, for instance, that you're fighting enemies that have decent intel on the party, and that you're defining "failure" (the thing you're trying to avoid) as "at least one party member is killed". The enemies are going to attempt to focus fire on whichever party member is least tough, which means that durability buffs on anyone other than that one party member have almost no effect. In a situation like that, you don't give the buff to the person who will benefit most from it; you give it to the person who most needs it.

I agree that those situations are not impossible, especially if you leave the extreme example of 95%->90% to some more reasonable 80%->65% or 70%->50%.

But if you're in a situation where what look like the optimal choice is "giving a minor buff to someone who is still very likely to die even with the buff", then you should likely accept that the party member is a dead man walking and revise the definition of failing to be "at least TWO party members are killed and/or we fail to get away with the body of our soon-to-be-dead friend for a future resurrection".

When I was saying "finding a third choice", it included the "giving up the current objective and trying to advance some new objective instead".

[Aquillion]

Also, especially if you're a caster, you have buffs and options that completely recontexualize the problem. Advantage is usually the weakest option in your toolkit, so if it's not enough you reach for a better option.

[Corran]

But if you're in a situation where what look like the optimal choice is "giving a minor buff to someone who is still very likely to die even with the buff", then you should likely accept that the party member is a dead man walking and revise the definition of failing to be "at least TWO party members are killed and/or we fail to get away with the body of our soon-to-be-dead friend for a future resurrection".
Agreed, of course. But you are seeing high risk low reward options where there can be more than them. The point is, that shifting the "buff" away from 50% does not inherently come with either higher risk or lower reward, as math continue from where the probabilities stop.

[Chronos]

But the Dead Man Walking situation is also fairly rare. In a typical fight, the players will win (meaning everyone surviving). If one member of the party is particularly vulnerable, that might mean something like "10% chance of dying, in the hardest fight of the day". That's bad enough that the players really don't want to just accept it, but it's nowhere near so bad that they'll just give up on saving that character.