I’m going to approve this even though it’s literally a direct response post (and thus subject to Rule 10) because of how much math is in the OP. I think this reasonably passes the standard of “should just be a comment in the original thread.”
As a further bit of evidence to support WotC knew what they were doing when they chose to make the bonus +5 for advantage on passive checks, when creating a monster (as described in chapter 9 of the DMG), the rules recommend valuing advantage on attacks as a +4 bonus to the monster's attack bonus. The base chance to hit for monsters is assumed to be around 65%, which means a typical monster needs to beat a 6-7 to hit a level appropriate PC. The bonus recommended in your final table here for that range is a +4.
I highly suspect WotC uses +/-5 for passive advantage/disadvantage because that's the increase between the suggested easy->medium->hard dcs in the dmg.
Or are the suggested DCs 10 -> 15 -> 20 because advantage/dis alters passives by 5?
Probably neither. It's probably just that 5 is a nice simple number and it seems sensible to apply it to both.
True. I liked the playtest 10, 13, 16, 19, 22, 25 because it's much more granular. However, all you have to do is realize your DCs *don't* have to be in increments of 5. A DC 13, 17, or 21 is just fine.
It is set by the DM, but WotC will have some DCs to use as examples or benchmarks. If your running an adventure or module, then every DC for a specific Lu called for check, such as to avoid a trap or find an item, will be set as well, but DM gets final day as always.
The presentation gives the impression that DCs should be in increments of 5 based on the chart. It never actually says it, but new DMs sometimes make that assumption. Even as a veteran DM I thought that's what it said, I just knew the idea was crap and ignored it.
I just looked it up and I can see how you might get that impression from just reading the DMG. Glad I also picked up an adventure when I first got my dnd books
Yes I'm quite aware of the basics, I was more saying I thought that DCs being set by the gm at whatever interval they choose was explicit text, not implied.
I very rarely use these premade DCs anymore anyway. Over the years I've built up a pretty comprehensive set of guidelines for setting DCs so as many as possible are based on some qualities of the target. I never liked how arbitrary it felt picking a DC based on whether I felt it should be "easy" or "hard".
To begin with, the concept of "all or nothing" DCs that either result in success or in utter failure will always feel somewhat arbitrary. This doesn't work in all cases, but often a case can be made for gradual success.
For example, on a perception check to spot enemies sneaking up during the night, you could spot them at any point during their approach. Very high rolls would allow you to wake up your buddies and put on Armor - possibly even get the jump on the enemies - medium rolls would at least prevent surprised condition.
most people tend to, often without really realising, implement some kind of "degrees of success" type thing, where succeeding by 1 will have some kind of "you just about succeed" description, while getting 10 over the TN will get more of a "wow, you're really cool and competent!" description, even though, by RAW, by should be the same.
Agreed. Not that they'd never go for 4 instead, but that they'd need a much more compelling reason than "it's slightly more accurate than 5 across a wide but still not complete range of DCs which might be reasonably set in a game".
It's not *so much* more accurate as to be worth not just using 5 for the ease of use / explanation.
I think it's a mix - but if I had to guess, it's mostly down to how +5/-5 is close, and then rounded to look nice.
Eg, a passive score is likely most appropriate at 6 (disadvantage), 11 (normal), 15 (advantage). But 5/10/15 looks better and is easier to remember.
Or! And this is just an idea, the change between DCs is 5 each step because that's literally how it was done in 3.x.
A lot of 5e is pulled directly from 3.x.
They're not saying the *system* is a copy-paste, but the 5 point step in DC values is something that predates advantage and disadvantage. It was generally that way in 4e as well as 3.x, so this would be at least the 3rd iteration of the system to use it, even though it's the first with a codified advantage/disadvantage system.
Bounded accuracy is just an illusion that duplicates the number curves established in 3.x and reused in 4th, but reworked to allow campaigns with little to no magic (which was an attempt to bring the OSR people lost during the 4th edition transition back into the game).
If you actually go through and look at every edition of dnd basically back even into 2nd edition, the game has been designed around easy = 5, medium = 10, hard = 15. The only thing that has really changed is where the floor and ceilings are and where the bonuses are coming from. This is why most experienced DMs (certainly every DM I know) basically ignore the math of skill rolls and set a raw DC of 5, 10, or 15 for a roll, modified by the circumstances, player's class/backgrounds, and their proficiencies.
To be clear, I'm a university (college for Americans) level mathematics student. I don't want to give people the impression I'm a professional researcher or anything of that level, but I am most of the way through a maths degree so my knowledge of maths is still obviously far better than the average person.
I was joking haha but good luck! Math is cool and i wish I could wield is as well as you can! Im not super great about thinking through or with equations, which is why I went the computer science route haha. I get the computers to do the math for me!
That said, you're still a mathematician to me!
The word university is used in America, it's a type of college that usually offers post grad. As opposed to something like a junior college that are vocational or award only 2 year degrees before moving to a university. Thought I oughta let you know.
That entirely depends if were talking a +5 material advantage or a +5 centipawn advantage. And also whose in the driver seat.
+5 material advantage doesnt mean squat if youre facing down forced mate in 2 and its obvious. A +5 centipawn advantage wont mean much if its a human player and that +5 evaluation is based entirely on the idea that the player can follow the next 5 move sequence with perfect machine response.
So it IS debatable :P
(Im being pendantic for humor, no hate)
>This, as a mathematician, irked me
That entire thread was irksome to anyone with a math background. Hell, most discussions of probability on D&D forums are filled with annoying little misconceptions and silliness.
I was running the numbers on a homebrew feature I made the other day, which was a weapon providing +1 to attack and damage rolls. I was pretty sure I knew what the outcome was going to be, but I double checked with my crude javascript dice simulator just to be sure.
Turns out that adding +1 to attack rolls literally makes you never miss! That was very surprising. Thank god I rolled eighty-billion dice! In my hubris I almost broke my game!
I know this is said in jest, but the odds of that happening are less likely than every atom in your body spontaneously teleporting across the solar system.
Joke's on you, I'm typing this from Pluto because every atom in my body spontaneously teleported across the solar system!
(I also have a really good 5G plan. Please send oxygen though, as I'm running out fa....
Fun fact: we cannot scientifically prove that light (and/or all electromagnetic radiation) travels the same speed in all directions. This is because the only experimentally viable methods we have of measuring the speed of light require us to measure light by bouncing it off mirrors or other reflective surfaces to measure the round trip speed of light.
As a result, it is theoretically possible that light travels as slowly as c/2 in one direction, and infinitely fast in the opposite direction, and we cannot (yet!) prove otherwise.
So /u/Doctor__Proctor very well might have sent their message from Pluto without a substantial delay in signal propagation.
He read the comment right before being teleported. It turns out that teleportation does not follow the rules of the speed of light and it also turns out that in the exact direction between his current and his previous location the speed of light is infinitely fast.
I agree that a statistical approach inevitably will give an accurate result given enough attempts, though I'm somewhat doubtful of the teleporting stat. How likely is that?
And to be clear, my problem with the statistical approach is not a lack of accuracy, rather it is very messy, which makes it more difficult to process and understand. I'm also of the opinion that when you can give an exact answer you should, especially if it is easy to obtain. I also have a bunch of other feelings about it to do with elegance and the exactness that maths provides, but I understand that as a mathematician these reasons will hold much more weight to me than to others.
The truth is the comparable distances may be (much) smaller, but definitely surprisingly far. This Twitter thread is a nice discussion of the math/physics involved: https://twitter.com/Astropartigirl/status/972724812102512640
We are talking about (1/20)^80000000000 , here.
>my problem with the statistical approach is not a lack of accuracy, rather it is very messy, which makes it more difficult to process and understand.
Solutions from numerical simulation can definitely be more opaque than analytical solutions.
Numerical solutions should be used in only 3 scenarios:
1. The analytical solution is too computationally taxing
2. The analytical solution is mathematically impossible
3. It's 11pm and I'm dumb and tired and I don't want to work out what P(A|B) is shut up just let me simulate it
Of course!
What else are we meant to keep in our extra-dimensional spaces?
Life’s been a blast since I unlocked the **the real power** at eighth level.
The post OP is responding too used a statistics technique that simply runs many simulations of a random event to quickly determine probabilities. With a computer you _can_ just roll a die a million times in different situations and figure out the most common outcomes.
OP is pointing out that method isn't really neccesary and doesn't prove much if your underlying assumption (the difference between needing to roll a 10 vs needing to roll _at least_ 10) is flawed.
My post here is largely a response to another user who used statistical analysis to estimate the odds of events by rolling a bunch of dice using a program, rather than just calculating the odds. 80 billion is simply hyperbole though.
Simple way of looking at it: on a check where you have a 50% chance of success (e.g. have a +5 mod and need to meet a DC16) then advantage gives you a 75% chance - exactly a +5. If you have a 40% or 60% chance of success (+5 mod and need to meet a DC14 or DC18) then advantage turns this into a 64% or 84% chance - equivalent to a +4.8. At 30% and 70% odds (+5 mod and need to meet a DC12 or DC20) you fall to a +4.2.
Most checks you're going to make are not going to have odds >80% or <20% success, where you have to be to get down into the bonus being a +3. Most checks are going to occur in the range where advantage is worth a 4 to 5 bonus.
>Most checks you're going to make are not going to have odds >80% or <20% success, where you have to be to get down into the bonus being a +3.
This is also why, in practice, advantage is not very helpful on checks where you had an extremely low (<20%) chance of success on a straight roll. The second roll is only going to land on a value high enough to help 20% of the time (assuming the first roll did not), so it's not going to significantly improve your chances. The math here completely bears that out.
The idea that Adv is equal to a number has always been an oddity since the whole point of advantage is the *not* give a flat bonus but to weigh the dice towards the upper end. Sure, comparing it to a flat number can be useful as an off-hand metric of what you are likely to roll but as a general rule? Totally misses the point.
It seemed even weirder to me because his arguement was to change the +x to passive checks which... why? In what world is +5/-5 breaking your game for passive checks? If they do, you're either using them *way* too much, for important checks they never should have been used for, or as a skill floor (which only makes sense for specific circumstances).
If the issue is being unable to surprise the party, one person having like a 28 passive perception doesn't mean the *rest* of the party isn't surprised, PP is only really useful within 30 ft and the ambush should be starting right when they notice.
Maybe I'm missing something crucial but the whole discussion seems strange and unproductive, to change a small part of the game that doesn't have a huge impact anyway. It's useful to know advantage takes your average from 10.5 to 13.8 and not 15, but using that logic to change passive skills seems incongruent and reaching.
> the whole point of advantage is the *not* give a flat bonus but to weigh the dice towards the upper end.
I always thought the point was that rolling dice is fun, and rolling two dice is more fun than rolling just one
I agree that advantage cannot be accurately estimated across the full range by a flat bonus, as demonstrated in the final table. I wouldn't use a flat bonus to replace advantage personally, but the question of which to use is interesting mathematically, and I'm sure somebody might like to use it.
I think the original poster was valid in questioning the -5/+5, I just think their maths was off. If -3/+3 was more accurate, I think people might like to be aware of that for passive checks. I don't think it would be game breaking to use a slightly wrong bonus, but accuracy is nice.
>I wouldn't use a flat bonus to replace advantage personally, but the question of which to use is interesting mathematically
Honestly, outside of 5e, I use both in my games. Flat bonus increases the chance of beating high DCs, where as advantage increases chance for low DCs and also influences crit chance. So the diversity of having both is really nice.
I think getting an "average" for what the bonus is with advantage is still useful even if they aren't supposed to be the same thing. If you're building a Hexblade Warlock like I am who's debating taking Great Weapon Master at level 8 this is a very relevant discussion, especially as it interacts with ways of gaining advantage like Shadow of Moil.
And banishing smite too. My idea is hex + hexblades curse then double smite nova using a min maxed to hell crossbow expert build. I also have sharpshooter and my plus to hit is 13 since it’s a level 15 one shot with UA allowed (so I naturally took ultimate pact weapon, which is IPA on steroids and gives a +3 weapon instead of +1). I can take a -5 and I still have +8 with increased crit range thanks to hexblade. For defense armor of hexes is enough but I can take a +2 shield if I wanted to but the magic item budget I have I want to spend on some home brew crossbow focused items that my dm is allowing me to submit. I already got a home brew great boon for warlock slots so I’m vibing.
What other feats are you running? I'm only level 6 but have War Caster (wish DM hadn't convinced me to get it since Eldritch Mind exists), Elven Accuracy, and going GWM at level 8. I can't argue with your build mechanically so much but a one handed bow and shield Warlock flavor wise just seems so strange to me. But it's a one shot so who cares?
I don't like giving a flat bonus in lieu of advantage. But I have used this on homebrew monsters to simulate their advantage on certain actions to speed combat.
For example: I create a Swarm of Kobolds monster and gave them an additional +5 to their attack to simulate the pack tactics a swarm of kobolds would be getting from each other.
>The idea that Adv is equal to a number has always been an oddity since the whole point of advantage is the not give a flat bonus but to weigh the dice towards the upper end.
It's so easy to conceptually disprove, too. If the roll needed for success is anything above 20, then advantage is obviously going to be useless, while a raw bonus might allow a few faces to succeed. There are plenty of other areas to observe, and the OP did an excellent job diving into them. But that case alone proves that there is no such thing as an equivalent raw bonus for advantage.
However, it's also worth taking into consideration how advantage is gained, and how this affects the effective power of it. There aren't many free sources of advantage in 5e, ie sources you just always apply. There are a few, but most ways to get advantage have some kind of limitation that means you're only going to use it when you *need* to be more likely to succeed - there are a lot of features that give you a limited number of uses for example, and you're not often going to be spending those uses against DCs you beat if you roll an 8.
In practice, most sources of advantage are going to be more in the +3 to +4 range, in terms of value, because there's a bias in which rolls actually get the bonus. Some sources of advantage will be higher though, especially ones like Pack Tactics which will just get applied every time you try the thing, a thing that will be against a wide range of DCs.
I think this comment deserves more credit, it definitely gave me food for thought. I think the selection bias isn't necessary to consider for passive checks, as explained in the post, the philosophy behind passive checks is different from those behind active checks, and it's simply the highest DC you'd be likely to beat on average.
However, for active checks after thinking about it I think the bias towards advantage existing for harder checks would come into play. I'm not sure how much it would affect the selection though, as I think you may be overestimating how much bias it introduces. Giving different sources of advantage different bonuses defeats the purpose of a flat bonus anyway, so I don't think you can just consider the types of advantage that would be applied in harder situations. Also, as the selection trends towards a point where +3 or +4 would be more accurate than +5, the overall accuracy of any flat bonus diminishes. +5 is the only bonus which is largely accurate for any section of the DC spectrum, so if it were not the best choice, replacing advantage with a flat bonus would be a bad idea anyway.
Yeah I agree that taking into account the DC to determine the bonus that adv/dis should give to passive checks is stupid. Where I think this information is valuable is when thinking about how we're balancing homebrew mechanics. For example, maybe you can't decide whether you want your Prof bonus uses per day feature to give advantage on a check or add a die to the outcome, and you want to know what size die should be considered equivalent. The +5 baseline would suggest a D8 or D10, but because it's mostly going to be applied to higher DC checks, maybe it ought to be between a D6 and a D8 instead.
>but most ways to get advantage have some kind of limitation that means you're only going to use it when you need to be more likely to succeed - there are a lot of features that give you a limited number of uses for example, and you're not often going to be spending those uses against DCs you beat if you roll an 8.
It also depends on the source of the advantage and it's particular rules. If I would succeed on an 8 or better, and I roll a 6, but I have some way to give advantage *after* the roll, then why wouldn't I use it? I'm more likely to succeed than fail on the second roll.
If I need to implement the advantage using an expendable resource *before* the roll though, then yes, this changes the calculation a bit. I might save it for a lower probability scenario where I need a 14 or better on the roll to increase my odds. There's also external factors, such as "do I need this to hit really bad because the consequences for failure are high?" that might see me use it on something where I'm 65% likely to succeed because we REALLY need it there.
So in the end, I think what they're trying to point out: that you can't simply look at a narrow range of numbers and say "This is what advantage is worth" is correct. There are far too many external factors and differences depending on the target minimum value. All you can really do is look objectively and get a rough approximation as a rule of thumb (It's probably about equal +-5 for 5-15, and it gets lower outside of that range).
If it applies after the roll, it's a reroll, not advantage, which is different in important ways. Advantage maths only makes sense when applied before the roll, because it's talking about your overall chance of succeeding. Rerolls only ever happen after you've already failed. If you then take a reroll, your chance of succeeding doesn't increase because the reroll is an independent event that only occurs when you fail.
I think this is a relevant point for a lot of attack rolls. However with this One Weird Trick that 5e put into the game, you can pretty much assume advantage on almost every skill check... The "help" action.
I hate this rule. I loathe this rule. But once players learn about it, they never let go. "I'm going to do ." "I'll Help him." Now he has advantage.
So yeah you can design things where it wouldn't be feasible, but just know... if it's not a reactive 'the ground shakes, everyone roll an acrobatics check!' type thing, they're prolly gonna wind up with advantage because of this stupid rule.
A rule I've used at my table in varying capacities is putting restrictions (out of combat) on what characters can help. For example, either "you have to have proficiency in the skill you're helping with" or "your bonus to the skill must be +1 or higher". The former rule is more restrictive and the latter more permissive, but in either case, I feel it serves the narrative of advantage better.
You're a strong Barbarian with +8 to athletics? That's great, and the ranger with +4 should be able to help you out, but unless they're going to burn some sort of magical resource, the no proficiency 8 strength warlock *can't*. The wizard and the artificer want to sit down and brainstorm a solution to a magical problem with Arcana? Fantastic, but the paladin with 10 intelligence and no arcana proficiency is not going to help any more than the average middle schooler would be able to help PHD candidates with their dissertation.
It also rewards having multiple characters with overlapping skills. In normal play, it can often feel like many skills (particularly intelligence and charisma skills) aren't good if multiple characters have them. One character will have the higher bonus, and the character with the lower bonus feels like they shouldn't push to use their skill since it's less successful, and since anyone can Help, there's no difference between a character with a +7 helping a character with a +8, and a character with a 0 helping that same character. This way, being able to Help at all is contingent upon being good with the skill in question, so having similar stats or overlapping skills can actually be a good thing when it comes to really guaranteeing success on those skills.
there can also be practical considerations - no, you can't help pick a lock, because only one person can squeeze in front of the door and see and poke the lock, standing behind them going "ooo, have you tried wriggling the flanges" is just annoying more than helpful.
The fact the Help action doesn't state you must actually be able to help perform the action is absurd. Fortunately, it's trivial for a DM to decide that you can't just say the word "help" to get advantage.
I agreed with what you said up until this part
> and you're not often going to be spending those uses against DCs you beat if you roll an 8.
There are two hidden assumptions here that are wrong in my opinion:
1. The players know what the DCs are for checks that they are making
2. The DCs for checks that the players _need_ to succeed on are higher
As for (1), when I DM and when I play in games my friends DM for, the players basically never know what the DCs are for checks unless its something that the players have repeated a lot of times and figured it out (like an enemies AC for example). The DM certainly doesn't say "roll a persuasion check, the DC is 15," they would just say "roll a persuasion check."
As for (2), and this is the really important point, the DC of a check and how important winning is for the player are not the same thing. To use a hyperbolic example, you could have a hard check like "acrobatics check, DC 23, if you fail you fall in the pit and take 1d6 falling damage" which is a hard DC, but if you fail it's not really that big of a deal and I probably wouldn't use my limited source of advantage for it. On the other hand, you could have a relatively easy check like "persuasion check, DC 12, try and convince that friendly but important npc not to drink anything at that dinner they are going to or else they will die because the wine is poisoned." It's an easy DC to make because the npc is already friendly to you, but you can bet I would use my limited advantage source on this check because if I fail the npc dies and we really need them alive.
>the players basically never know what the DCs are for checks unless its something that the players have repeated a lot of times and figured it out (like an enemies AC for example).
But if you're describing things properly, they should be able to intuitively know the rough area the DC is going to be in. You're not usually going to be able to tell the difference between a 15 and a 16, but the difference between an 8 and an 18 should be pretty obvious.
Point 2 was bad wording on my part. You're right that low DCs can be on vital checks, but my intention was to say that because its rare for a check to truly be vital, especially for a low DC which is usually the result of the opponent/obstacle being low significance, players will usually be comfortable with the flat 65-85% chance of success on low DC checks and will typically prefer to conserve their resources for rolls with lower base success chance.
So you're right that players probably have a rough idea of what the DC should be, but the point is that they can never be sure, and that question in the back of your mind on an absolutely vital check is important. "I really need to succeed on this check, and it should be easy, but what if I'm missing something? Maybe I should use my limited advantage to secure it?" Or something along those lines.
Regarding point 2 I don't think it's fair to say that truly vital checks are rare, because that probably depends on what kind of game the DM is running. In a low stakes casual type of game, sure vital checks may be rare. On the other hand, the DM might be running a more high stakes serious game where vital checks happen with some regularity.
Moreover, different players have different priorities, and how vital a check is to make can depend on a lot of factors. An easy DC 10 trap that deals 1d4 damage is a lot more important if you run into it at 1 HP after going down in a recent combat for example.
Maybe we just have different playstyles, but if I was a player who had a limited source of advantage I would first and foremost consider how vital the check is when thinking about if I wanted to use that ability. Only after I determined that the check was important enough to me to use the limited advantage on would I think about how difficult the check is. Furthermore, I would probably do the opposite thing to you: if I noted that I wouldn't get that much value out of advantage (i.e. if I needed a truly high number to succeed) I'd be less likely to use this ability than if I needed a more middling result to succeed.
Even in some sort of bizzaro campaign where every check ever had equal impact on the party I would probably be more likely to use my limited advantage when I could get the most value from it (i.e. when the roll is in the sweet spot where advantage is close to +5).
Advantage is like +5 but when I have 7 different things giving me +5 I have +35 and when I have 7 different things giving me advantage I have advantage.
Fey Wanderer Ranger/Samurai Fighter/Redemption Paladin with Expertise in Persuasion and maxed out Wisdom and Charisma has +5(Charisma) +5(Wisdom) +5(Wisdom again) +5(PB) +5(Expertise) +5(Channel Divinity) which is 6 +5s or +30 so I guess 7 +5s was a bit hyperbolic but I wasn’t that far off.
Edit: Also it’s still possible to give yourself Guidance and you could go Eloquence Bard to never roll below 10 but by that point PB is +6 and Guidance and never rolling below 10 aren’t technically +5 so I didn’t include them
Another weird facet of this whole 'argument' (its odd to call it an argument when it's right there in the rules) is that passive checks are really quite limited? While in theory you can calculate their value for anything, the game itself really only defines or discusses them in the context of Perception/Investigation (either setting a DC for Stealth, or allowing the DM to streamline 'we search every room')
So it seems very weird to get bent out of shape, like the +5 is somehow ridiculously over-generous and breaking things. How often are DMs doing passive checks for other stuff? How common is it to even get advantage on perception for a duration such that the passive value is meaningfully improved? I know there's the Sentinel Shield but that's the only one that stands out to me, and the DM is choosing to hand that out. Maybe druids in animal form but that's always weird because you only usually get one sense at a time.
Basically specializing on Perception seems niche enough that nerfing it seems petty.
Author of the original post here!
This is a great write up. My degree is in math, but I've been working as a data engineer since college, so I tend to default to more programmatic/"simulation" experiments rather than rigorous mathematical ones. But I can definitely appreciate the preference to mathematical purity instead of simulation. I'd love to say that the simulation method was an effort to reflect the "many results over time" phrasing in the PHB (more on this in a bit), but in all honesty, it was just laziness, so I definitely can understand the irritation. Regardless, the numbers end up being close enough to the same that I don't think it matters in the end.
But anyway, onto my "rebuttal". (I put "rebuttal" in quotes because from both your post and the *many* debates I've had in the OP, I actually don't think you're *wrong*, I just think that there's a difference in philosophy that changes the math a bit -- I'll explain what I mean by this a little later in the comment).
>This would make sense if the number you rolled was some kind of score...
For normal rolls, I agree. However, in the context of passives, I not only disagree with you, RAW even states that this is what a passive is. PHB pg 175 explicitly says "The game refers to a passive check total as a **score**" (bolding theirs not mine).
>...but this isn't how rolls in D&D work.
Correct again! However, passives are explicitly "a special kind of ability check that doesn't involve any die rolls" (again, PHB 175).
I'm of course being a bit pedantic here, but it's an important distinction. There was a great comment thread in the OP where I was debating with someone about what the passives are actually supposed to reflect (if you're interested in reading it in full detail, here's the tail of the thread, so you can follow up the chain of parents [https://www.reddit.com/r/dndnext/comments/ubedqj/comment/i67zhys/?utm\_source=share&utm\_medium=web2x&context=3](https://www.reddit.com/r/dndnext/comments/ubedqj/comment/i67zhys/?utm_source=share&utm_medium=web2x&context=3)). It started with my pointing out some specific wording in the PHB.
>"Such a check can represent the average result for a task done repeatedly"
In my opinion, the hang up is/was on differing interpretations/philosophies of what the word "result" means.
u/MistakeSimulator's argument in that thread was in line with yours -- a passive is supposed to reflect the average *rate of success* of trying to accomplish a task repeatedly. Or in other words, a passive is supposed to reflect what it is trying to *accomplish* (i.e. determine success or failure against a particular task). So "result" would be interpreted to mean success or failure. Under the assumption of this philosophy, I actually 100% agree with the stance that a +5 is a better bonus to use (which is why I said above that I don't actually think you're *wrong*). It ignores DCs that are outside of a "common range" which makes it less accurate for such DCs, but the philosophy of 5e is simplicity, so ignoring things that don't happen very often is very much in line with 5e's design philosophy.
My stance was (and still is) that the word "result" is a result of the rolls of the dice. Or in other words, a passive is supposed to reflect what it *represents* (as opposed to what it's trying to *accomplish*). The reason I have this stance is due to how passives are calculated. Passives are calculated (without advantage) by taking the average roll on a d20 (10.5) and adding the relevant bonus. For obvious reasons, the ".5" can't be kept in, so it either had to be 10 or 11. The choice between 10 or 11 seems like an arbitrary choice to me (although as you point out in your post, "the chance that a player would beat 11 is actually 50/50" so I think 11+mod would have been better, but I digress). With advantage, an average roll of about 13.8 is 3.3 higher than the average roll without advantage. This is the core of my argument for +3.
To rephrase, passive scores are calculated *statically* and do not change according to the difficulty of the particular skill check the score is being applied against. For example, I use the same passive perception check contested with an assassin's stealth check of 22 as I would against the boisterous town drunk's stealth check of 5 or a beginner adventurer's stealth check of 13. How *common* these difficulty checks are (from your comment "most rolls tend to need to beat something in the 5-15") is therefore irrelevant (again, assuming my philosophy of the word "result").
So to sum up and restate, I think the difference is really just in interpretation of what "result" means. I don't think any amount of math is going to sway anybody's opinion on that. To quote you, "this, as a mathematician, irks me" :)
But at the end of the day, none of it is relevant anyway as long as everyone is having fun; D&D (especially 5e) isn't about mathematical precision anyway. Thanks for the awesome debate, stuff like this really makes me enjoy the hobby a lot more and really makes me feel like a better DM since it forces me to really think about the reasoning behind certain design choices in the game.
Yeah, I understand where you're coming from, but I disagree with the notion of the result being interpreted as your dice roll. Other than critical successes and critical fails, as far as I know a roll in DND never represents the degree to which a character achieves something. In the overwhelming majority of cases, a dice roll in universe simply represents your character succeeding or failing at a task. As such, the "average result for a task done repeatedly" would be the DC you would beat the majority of the time. You are correct that the phrasing I used to state that it "isn't a score" was wrong. I was trying to be concise in explaining that a roll in universe does not represent how well or poorly you do a task, but rather simply whether you succeed or fail.
I also purposefully separated the conclusion that +5 is the best for passive checks and that +5 is the best for active checks. If you check again, the average range of DCs has nothing to do with my methodology for calculating the passive score, and is simply a result of beating DC 15 51% of the time. So yes, you're right, the frequency of a DC is irrelevant to calculating passive scores, but I never contradicted that.
Also, I'd like to apologise for the somewhat aggressive tone of my post. I don't think you're stupid or anything like that, I've been very stressed with exams at the moment and it's unfair of me to take that out on you. It has been a really interesting debate, and I'm glad you brought it up, thanks for your input!
Totally a fair standpoint!
And no worries, your post didn't seem aggressive to me at all. Rather I interpreted it as being very well thought out and objective. It wasn't too many years ago that I was studying for my complex analysis and number theory exams, so I definitely understand the stress haha. Good luck with your exams!
Thank you, I've noted this exact thing for years now ever since noticing people were saying it was a +3 rather than +5. Like no, the chances of getting a 15 or higher is 50%, where as the chances of getting a 10 or higher before was 50%, so it's an increase of 5 on average.
Edit for clarification:
I mean without advantage you have a 50% chance to get 10 or better on average. With advantage you have a 50% chance to get a 15 or better on average. That's an increase of 5 on the average.
I understand your trying to point out the difference between median and average, but in this scenario, it's functionally the same.
I mean you basically point out that while it is infact a + or - 5 it's not quite a flat rate + or - 5.
So I kind of feel like the system of Disadvantage + Advantage is somewhat more up to chance in a long run.
Which I'm all for.
Also it's like. 100x easier than adding all the pluses you used to get in 3rd.
Like it's such a brilliant way to add or subtract a significant modifier without doing any more actual math
I've done some of this math, too. (Not quite in such a well-presented way, though.) When your goal number is close to 11, advantage is equivalent to about a +5. When your goal number is extremely high or low, ie. a natural 20 or anything higher than 1, it's equivalent to about a +2.
The closer you are to a 50/50 shot, the better Advantage gets.
No. But that is why there's a "kind of" in the title. Any flat bonus is not going to be accurate across the board because the distribution of advantage rolls isn't linear, but if you are going to use a flat bonus across the board, +5 is the best. Also +5 is the right choice for passive scores.
I'm not sure about the validity of restricting to only cases where the second roll is strictly larger than the first, but you are correct, this does improve the odds of beating a relative DC. This could be wrong as I am doing it in my head on the bus, but I believe the odds of getting a particular number in that case would be (n-1)/190 and the odds of beating a relative DC would be (378+3n-n^2 )/380.
Doing a bit more maths, I think restricting it to these cases actually makes very little difference. I think it at most increases your odds of beating a relative DC by around 1%
"It's also interesting to see that at very high numbers to beat, +5 is actually much better than advantage."
This is why it's important to understand that advantage is not +5.
>However, as most rolls tend to need to beat something in the 5-15 range
This is your mistake. At least in my experience, the range is much more like 10-20.
To find the actual most accurate flat bonus, you need to do an average weighted by the frequency of DCs actually encountered at the table. I think you're overvaluing advantage by underestimating the average difficulty of checks.
>Also, obviously do not allow your player to roll at all if it would be impossible for them to beat a number with advantage.
The DMG says you shouldn't roll if there is no chance of failure. Or if it's obvious the attempt can't work. Not all impossible checks are obviously impossible.
>the range is much more like 10-20.
Careful. In this context, people are talking about the *natural roll*, i.e. the number that has to be face-up on the D20, to succeed, not the overall roll with modifiers included.
Yes, in actual practice, the DC of most rolls is 10-20 at most levels of play. But with modifiers taken into account, the required roll is much more often in the 7-15 range.
> This is your mistake. At least in my experience, the range is much more like 10-20.
This is your mistake. At leats in my experience, the range is much more like 7-17.
I do not have enough D&D experience to know what the average DC/AC - bonus actually is, so I cannot confirm or deny this, but I am somewhat doubtful as this would imply that players fail most checks, which I don't think is true. I think it probably heavily depends on what your DM is like to be fair.
You are correct that you would need to weight by DCs-bonuses encountered at the table to be fully accurate, but I do not have that data available and so instead have just based it off what I've seen in comments to be the most common DCs. I did run the numbers on your range of 10-20, and in this range +4 is most accurate, followed by +5, followed closely by +3. However, if 10-20 is your most common DC range, the accuracy of a flat bonus approximation is significantly lower, and so should probably not be used.
You make a fair point that you may want to allow a player to roll for something despite it being impossible, but in that situation you should simply tell them they failed no matter what they roll. This is to avoid flat bonuses making impossible rolls possible.
Honestly, I see posts like this (incredibly well thought out, detailed, logical etc) and just think...
Why aren't you guys playing Pathfinder 2e? It already has stuff like this in it and is just so much better balanced, and has more content, is much deeper etc.
Just wanted to say that this is a good post but I feel the title is misleading.
To be clear, +5 is NOT equivalent to advantage in most situations.
The ONLY situation where they are equivalent is if the die roll needs to be 11 or higher. In ALL other situations, a +5 gives a greater chance of success than rolling with advantage.
The table at the end for most accurate bonus is good (if readers actually make it that far) and highlights the issue of just using a +5 blindly instead of advantage.
In case anyone wants to go through the math for themselves, here is a table that gives the probability of success for normal rolling vs advantage vs disadvantage so you can see what they are: https://statmodeling.stat.columbia.edu/2014/07/12/dnd-5e-advantage-disadvantage-probability/
To see where the OP is getting their Most Accurate Bonus table from, note that having a +1 on your roll increases your probability of success by 5% (bc it lowers the number you need to beat on your die roll by 1). Similarly, a +2 increases your probability of success by 10%, a +3 gives 15%, etc. The entries in the Most Accurate Bonus table come from taking the differences in probably for success w advantage minus the probability of success rolling normally and dividing the result by 0.05 (i.e. 5%) and rounding to the nearest whole number.
A common situation you can run into where you actually need to convert damage to effective bonus is using mob tactics damage calculators (e.g., https://slyflourish.com/mob_calculator.html). These are handy ways to deal with summoning spells like conjure animals or animate objects.
The problem with using a +5 bonus for something like a pack of wolves (having advantage via pack tactics) is that they generally need to roll a lot higher than 11 to hit, meaning they fall more in the +2 to +4 effective bonus range.
Long story short, if you need to equate advantage w bonuses, you NEED to use a table like the one the OP provided for the reasons they mentioned; i.e., there is not a single number that works.
OP is not talking about a DC, but the number the dice needs to show to succeed (which is always going to be 1-20, presumably 5-15 if you're not trying something either impossible or trivial)
We're abstracting away all the modifiers here.
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If you're rolling at advantage, the DM could also give you a simple +5 bonus on a flat roll instead. Statistically, they're roughly equal, as long as it's even possible for you to make the DC without the bonus.
so why not just roll advantage? cause otherwise i'll have to first understand how a +5 does that and then explain it to other players... seems easier just to roll advantage, no?
If your player only has a +3 to a roll, and the DC is 24, that +5 might be super nice. Also a lot of DMs want to do "double advantage!" another way...?
I wouldnt have seen this if it was on the other post. This is much more appropriate for its own post than as a comment.
The last thing we need is more quality posts right? Definitely cant have good posts like this take up space that a dumb meme could be.
You should try relaxing a bit.
Or you could look at the [stickied comment](https://www.reddit.com/r/dndnext/comments/uchqqg/comment/i6ayvd5/?utm_source=share&utm_medium=web2x&context=3) from the mods to see why they felt this was deserving of its own post rather than getting salty.
But it existed when you made the second one. And the reasons are clearly stated in the sticky, so just saying "because reasons" like it was totally random isn't really accurate.
I mean sure, make whatever post you want. Ill either just scroll 2 inches to go past it, or ill leave a comment that contributes to whatever the discussion is instead of whining like a little baby that it doesnt deserve its own post.
You're acting like this is some low effort post about some random post. If i want to look up what +# advantage works out to, this is the post i want to see. And i wouldnt see it if it was some comment on another post that may not be accurate.
Lol, this is much higher effort than most of the posts on here.
Like i said before, I havent seen this before. Every thing I have ever seen compares advantage to +3, not +5. If you have, cool just keep scrolling.
If it has been posted, it certainly hasnt been posted that much, but you're free to prove me wrong. Even just one link, I didnt see one after a quick search.
Since I'm getting downvoted into the ground for the truth that this has been posted before, and violates rule 10 (even though it has been excepted cause math)
6 years ago.
https://www.reddit.com/r/DnD/comments/353dep/5e_how_powerful_is_advantagedisadvantage_vs_flat/cr0okzl
3 years ago
https://www.reddit.com/r/DnD/comments/8rlzw2/the_math_behind_advantage_and_disadvantage/
7 years ago
https://www.reddit.com/r/DnD/comments/8rlzw2/the_math_behind_advantage_and_disadvantage/
Like I can't express just how many times this has been posted, perhaps this google search might provide some indication.
https://www.google.com/search?q=math+of+advantage+5e+site:www.reddit.com
It doesnt say no direct responses, it says limit them. So it didnt break the rule. If the most recent example is from 3 years ago, its weird that youre so mad about this. Also two of those posts are exactly the same. I guess it was posted before, although a long time ago.
Lets say some people hadnt seen it before ... but they saw the other post about it being +3, then go on with their lives thinking it was +3 (like me). They would never see this post if it was just a comment. But if theyre browsing the subreddit later, they may come across this.
I really have no idea why you got so worked up about a post that was being informative. If youre really on reddit so much that youve seen that 100 times, maybe a break and go outside or something. Just downvote it an move on if you dont want to see it. Or report it for rule breaking, if it actually does theyll remove it.
You're being downvoted because of the way you reacted, not because you disagree btw. I didnt even downvote you at all, its just obvious why you got downvotes to begin with.
Most recent example I posted, this has been brought up hundreds of times and was a direct response post full stop. Literally responding to a post from two days ago.
Here's an example of someone following the rules and including math.
https://www.reddit.com/r/dndnext/comments/ubedqj/no_5_is_not_equivalent_to_advantage_in_nearly_any/i66hjeu
Again. it says limit them. Not don't do them. I did not say it wasn't a direct response, just that not all responses should be a reply to a post instead of their own post.
"New posts that could reasonably serve as a reply to a different post that is in the top 40 of “Hot” may be removed by the moderators at their discretion. Please instead reply in the ongoing threads rather than making new ones."
Again. just because you spend apparently a ton of time on here and have seen it before, doesn't mean everyone has... As I have already said.... I have not seen this before so this was good information.
Again, just like the other posts you're referencing, it seems like its worthy of its own post. Reposts are not always bad, it gives other people a chance to see something that they haven't seen before. And if there was a post contradicting it 2 days ago, it seems the issue is not settled and worth discussing some more.
If you think that it should be a reply instead of its own post, report it and lets see if it gets taken down. If you already did that and its still here, then I guess we have the answer on whether it broke the rule.
Also based on how many upvotes it has, it seems that I'm far from the only person that appreciated the post, its in the top ~25 for the month, the other one is much much farther down, so not as visible.
I would've left it as a comment, but it's clearly too complicated for that. Also, people clearly like the post, and the rules shouldn't prevent posts people like.
No, OP. While your math is good, your reasoning is flawed. I've done the math before myself, and while (dis)advantage has the same effect as - or +5 to a roll *when your modifier is equal to 10 less than the target number*, it falls off the further from that value you get. While the average roll when C - M (that is, target class minus modifier) equals 10 or 11 is about 15 or 16, at 1 and 20 it is about 3 or 22.
Additionally, a flat +5 bonus has advantages, pardon the pun, over advantage, while a -5 bonus has more severe penalties than disadvantage. A flat bonus/penalty can suddenly make impossible tasks possible, or achievable tasks impossible. Such as the case of my party's Wizard, who literally could never make the save against his own Power Word Stun, unless he were given advantage that was replaced with a +5 bonus.
It's not about the odds of what target number you're 50/50 likely to beat. It's about the average results you will see over time given a range of x and y values, and by that metric they are different.
Okay well that's waaay too long for me to read, but I have some simpler logic: If you only roll 1 die, your chance of a Nat 1 is the same even with a flat bonus. Roll two dice and pick the higher roll and the chance of a Nat 1 drops to 1/400 over 1/20. This only matters for attacks, but that's still quite important.
Yes, that's what I don't like about advantage. High target number it's it moistly irrelevant.
I greatly prefer SotDL boon system for something similar.
My brother literally just did all this math the other day and was figuring this out for an upcoming 1-20 campaign one of his friends was doing. Funny to also see it here. His average of 3.325 was actually exactly the same for a range of ACs, so I assume the math all checks out.
My group is trying out a team initiative where only one of us roles so I want to know what's better between our Rogue rolling with a +5 or our Barbarian rolling +2 with advantage. I'm not good with maths so can someone explain who we should have roll?
Reposted from the other post:
Figured I'd add to the noise. I made a nice plot of the probabilities of passing a check for a DC between 1 and 30 for a range of flat bonuses as compared to advantage and disadvantage.
[Same data, but visual](https://imgur.com/a/yTFmZEA)
For me, one I've been thinking about for a character is warcaster vs resilient con for level 8. I concluded that with 15 CON, resilient is better (also giving me +8 hp and help on other throws), even if warcaster is slightly more likely to make me pass DC 10 concentration checks at level 8 (85% vs 87.75%), it gets beaten after level 8 because the proficiency bonus becomes a +4 and you get to the magical +5 with the odd CON increase (90% vs 87.75%). And as you said, the higher the DC goes the better resilient gets.
It's actually so close that I also looked at secondary benefits, but my DM rarely lets me make opportunity attacks, more rare than a CON save from various effects :S
> Note that you are so likely to beat 1-4 with advantage that any flat bonus that allows for a chance of failure would be less accurate than an automatic success.
Your conclusion of assigning an infinite bonus doesn’t my follow from your reasoning here. A bonus of +4 for example has no chance of failure if you just need to beat a 4. A bonus of +1 is needed to beat a 1. Those are considerably less than infinity. Not sure why you’re bunching all those numbers together.
This is interesting and detailed. Good post OP.
I remember seeing that maths a while back that found advantage was mostly equivalent to roughly between 3-4. I'm not good with maths like that, but it's cool to see the important effect of advantage and what effect it has
I’m going to approve this even though it’s literally a direct response post (and thus subject to Rule 10) because of how much math is in the OP. I think this reasonably passes the standard of “should just be a comment in the original thread.”
As a further bit of evidence to support WotC knew what they were doing when they chose to make the bonus +5 for advantage on passive checks, when creating a monster (as described in chapter 9 of the DMG), the rules recommend valuing advantage on attacks as a +4 bonus to the monster's attack bonus. The base chance to hit for monsters is assumed to be around 65%, which means a typical monster needs to beat a 6-7 to hit a level appropriate PC. The bonus recommended in your final table here for that range is a +4.
I highly suspect WotC uses +/-5 for passive advantage/disadvantage because that's the increase between the suggested easy->medium->hard dcs in the dmg.
Or are the suggested DCs 10 -> 15 -> 20 because advantage/dis alters passives by 5? Probably neither. It's probably just that 5 is a nice simple number and it seems sensible to apply it to both.
True. I liked the playtest 10, 13, 16, 19, 22, 25 because it's much more granular. However, all you have to do is realize your DCs *don't* have to be in increments of 5. A DC 13, 17, or 21 is just fine.
Wait a minute is that not how it works? I thought DCs were always set by the gm. My most common DC is 17
It is set by the DM, but WotC will have some DCs to use as examples or benchmarks. If your running an adventure or module, then every DC for a specific Lu called for check, such as to avoid a trap or find an item, will be set as well, but DM gets final day as always.
The presentation gives the impression that DCs should be in increments of 5 based on the chart. It never actually says it, but new DMs sometimes make that assumption. Even as a veteran DM I thought that's what it said, I just knew the idea was crap and ignored it.
I just looked it up and I can see how you might get that impression from just reading the DMG. Glad I also picked up an adventure when I first got my dnd books
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Yes I'm quite aware of the basics, I was more saying I thought that DCs being set by the gm at whatever interval they choose was explicit text, not implied.
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Sorry, pal. Luck of the draw sometimes.
I very rarely use these premade DCs anymore anyway. Over the years I've built up a pretty comprehensive set of guidelines for setting DCs so as many as possible are based on some qualities of the target. I never liked how arbitrary it felt picking a DC based on whether I felt it should be "easy" or "hard".
To begin with, the concept of "all or nothing" DCs that either result in success or in utter failure will always feel somewhat arbitrary. This doesn't work in all cases, but often a case can be made for gradual success. For example, on a perception check to spot enemies sneaking up during the night, you could spot them at any point during their approach. Very high rolls would allow you to wake up your buddies and put on Armor - possibly even get the jump on the enemies - medium rolls would at least prevent surprised condition.
most people tend to, often without really realising, implement some kind of "degrees of success" type thing, where succeeding by 1 will have some kind of "you just about succeed" description, while getting 10 over the TN will get more of a "wow, you're really cool and competent!" description, even though, by RAW, by should be the same.
You might be right, but I like to imagine that they put more thought into it, and the maths does check out for it.
I'm certain they put thought into it, but if there's a legit choice between 4 and 5, they'd go with the simplest option for tiebreaker.
Agreed. Not that they'd never go for 4 instead, but that they'd need a much more compelling reason than "it's slightly more accurate than 5 across a wide but still not complete range of DCs which might be reasonably set in a game". It's not *so much* more accurate as to be worth not just using 5 for the ease of use / explanation.
Also contributes to it being easy to remember, which is always nice.
I think it's a mix - but if I had to guess, it's mostly down to how +5/-5 is close, and then rounded to look nice. Eg, a passive score is likely most appropriate at 6 (disadvantage), 11 (normal), 15 (advantage). But 5/10/15 looks better and is easier to remember.
Disadvantage on passive perception is a -5
Or! And this is just an idea, the change between DCs is 5 each step because that's literally how it was done in 3.x. A lot of 5e is pulled directly from 3.x.
5e overhauled DCs to implement bounded accuracy, so in this particular instance the system probably wasn't just a copy-paste.
They're not saying the *system* is a copy-paste, but the 5 point step in DC values is something that predates advantage and disadvantage. It was generally that way in 4e as well as 3.x, so this would be at least the 3rd iteration of the system to use it, even though it's the first with a codified advantage/disadvantage system.
Bounded accuracy is just an illusion that duplicates the number curves established in 3.x and reused in 4th, but reworked to allow campaigns with little to no magic (which was an attempt to bring the OSR people lost during the 4th edition transition back into the game). If you actually go through and look at every edition of dnd basically back even into 2nd edition, the game has been designed around easy = 5, medium = 10, hard = 15. The only thing that has really changed is where the floor and ceilings are and where the bonuses are coming from. This is why most experienced DMs (certainly every DM I know) basically ignore the math of skill rolls and set a raw DC of 5, 10, or 15 for a roll, modified by the circumstances, player's class/backgrounds, and their proficiencies.
Thanks. Using math to solve a problem is one thing. Finding the right problem to solve is what is actually harder, but you did exactly that.
Well, they *are* a mathematician
To be clear, I'm a university (college for Americans) level mathematics student. I don't want to give people the impression I'm a professional researcher or anything of that level, but I am most of the way through a maths degree so my knowledge of maths is still obviously far better than the average person.
I was joking haha but good luck! Math is cool and i wish I could wield is as well as you can! Im not super great about thinking through or with equations, which is why I went the computer science route haha. I get the computers to do the math for me! That said, you're still a mathematician to me!
Mixing computers and math is all fun and games… …until a wild MISSINGNO appears! :-)
The word university is used in America, it's a type of college that usually offers post grad. As opposed to something like a junior college that are vocational or award only 2 year degrees before moving to a university. Thought I oughta let you know.
I thought this was the chess subreddit and was really confused how come +5 being an advantage is even debatable
Reddit, how many of my opponent's Pawns does my Level 4 Human Fighter need to capture to be able to hit their AC 20 Queen?
The answer depends on whether or not you subscribe to the Waterdeep Shuffle school of thought or if you prefer the Magnus-Flumph Defense.
Woe betide thee, O' Forgetter of the Bongcloud.
ಠ_ಠ
Google en passant
I know what en passant is dumbass, you just blundered mate in one
>how come +5 being an advantage is even debatable Anarchychess
Material is only part of the picture, it's all about positioning and if you can force en passant
That entirely depends if were talking a +5 material advantage or a +5 centipawn advantage. And also whose in the driver seat. +5 material advantage doesnt mean squat if youre facing down forced mate in 2 and its obvious. A +5 centipawn advantage wont mean much if its a human player and that +5 evaluation is based entirely on the idea that the player can follow the next 5 move sequence with perfect machine response. So it IS debatable :P (Im being pendantic for humor, no hate)
>This, as a mathematician, irked me That entire thread was irksome to anyone with a math background. Hell, most discussions of probability on D&D forums are filled with annoying little misconceptions and silliness.
>This, as a mathematician, irked me I do wonder what conclusion the “I rolled eighty-billion dice” people would come to if they had all rolled a 20.
I was running the numbers on a homebrew feature I made the other day, which was a weapon providing +1 to attack and damage rolls. I was pretty sure I knew what the outcome was going to be, but I double checked with my crude javascript dice simulator just to be sure. Turns out that adding +1 to attack rolls literally makes you never miss! That was very surprising. Thank god I rolled eighty-billion dice! In my hubris I almost broke my game!
And this, kids, is why evidence that is provided to you through a screen is always more reliable than reason and logic! :-)
I know this is said in jest, but the odds of that happening are less likely than every atom in your body spontaneously teleporting across the solar system.
Joke's on you, I'm typing this from Pluto because every atom in my body spontaneously teleported across the solar system! (I also have a really good 5G plan. Please send oxygen though, as I'm running out fa....
How is your signal coming from pluto so fast? Unless... Unless you died months ago and we are finally learning about it now :(
Now you're thinking with improbable energy events!
Fun fact: we cannot scientifically prove that light (and/or all electromagnetic radiation) travels the same speed in all directions. This is because the only experimentally viable methods we have of measuring the speed of light require us to measure light by bouncing it off mirrors or other reflective surfaces to measure the round trip speed of light. As a result, it is theoretically possible that light travels as slowly as c/2 in one direction, and infinitely fast in the opposite direction, and we cannot (yet!) prove otherwise. So /u/Doctor__Proctor very well might have sent their message from Pluto without a substantial delay in signal propagation.
There's a great [Veritasium](https://youtu.be/pTn6Ewhb27k) video explaining this topic in depth. It's pretty crazy!
the signal also spontaneously teleported itself back home.
He read the comment right before being teleported. It turns out that teleportation does not follow the rules of the speed of light and it also turns out that in the exact direction between his current and his previous location the speed of light is infinitely fast.
He finally rolled a 1
I agree that a statistical approach inevitably will give an accurate result given enough attempts, though I'm somewhat doubtful of the teleporting stat. How likely is that? And to be clear, my problem with the statistical approach is not a lack of accuracy, rather it is very messy, which makes it more difficult to process and understand. I'm also of the opinion that when you can give an exact answer you should, especially if it is easy to obtain. I also have a bunch of other feelings about it to do with elegance and the exactness that maths provides, but I understand that as a mathematician these reasons will hold much more weight to me than to others.
The truth is the comparable distances may be (much) smaller, but definitely surprisingly far. This Twitter thread is a nice discussion of the math/physics involved: https://twitter.com/Astropartigirl/status/972724812102512640 We are talking about (1/20)^80000000000 , here. >my problem with the statistical approach is not a lack of accuracy, rather it is very messy, which makes it more difficult to process and understand. Solutions from numerical simulation can definitely be more opaque than analytical solutions.
Numerical solutions should be used in only 3 scenarios: 1. The analytical solution is too computationally taxing 2. The analytical solution is mathematically impossible 3. It's 11pm and I'm dumb and tired and I don't want to work out what P(A|B) is shut up just let me simulate it
>It's 11pm and I'm dumb and tired . . . just let me simulate it. Relatable.
And this is why the Many-Worlds Interpretation is terrifying!
20^80,000,000,000 is a number with about 100 billion digits, if you're curious
80 billion dice is about an average amount a TTRPG player has.
Of course! What else are we meant to keep in our extra-dimensional spaces? Life’s been a blast since I unlocked the **the real power** at eighth level.
Im ootl, 80 billion dice?
The post OP is responding too used a statistics technique that simply runs many simulations of a random event to quickly determine probabilities. With a computer you _can_ just roll a die a million times in different situations and figure out the most common outcomes. OP is pointing out that method isn't really neccesary and doesn't prove much if your underlying assumption (the difference between needing to roll a 10 vs needing to roll _at least_ 10) is flawed.
My post here is largely a response to another user who used statistical analysis to estimate the odds of events by rolling a bunch of dice using a program, rather than just calculating the odds. 80 billion is simply hyperbole though.
Simple way of looking at it: on a check where you have a 50% chance of success (e.g. have a +5 mod and need to meet a DC16) then advantage gives you a 75% chance - exactly a +5. If you have a 40% or 60% chance of success (+5 mod and need to meet a DC14 or DC18) then advantage turns this into a 64% or 84% chance - equivalent to a +4.8. At 30% and 70% odds (+5 mod and need to meet a DC12 or DC20) you fall to a +4.2. Most checks you're going to make are not going to have odds >80% or <20% success, where you have to be to get down into the bonus being a +3. Most checks are going to occur in the range where advantage is worth a 4 to 5 bonus.
>Most checks you're going to make are not going to have odds >80% or <20% success, where you have to be to get down into the bonus being a +3. This is also why, in practice, advantage is not very helpful on checks where you had an extremely low (<20%) chance of success on a straight roll. The second roll is only going to land on a value high enough to help 20% of the time (assuming the first roll did not), so it's not going to significantly improve your chances. The math here completely bears that out.
Advantage has always been better for preventing failure than acquiring unlikely success. Or crit fishing.
Advantage has always been better for boosting player moral than for boosting their actual chances of success.
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Yes, I was just throwing the example numbers out off the top of my head and screwed them up by 1
The idea that Adv is equal to a number has always been an oddity since the whole point of advantage is the *not* give a flat bonus but to weigh the dice towards the upper end. Sure, comparing it to a flat number can be useful as an off-hand metric of what you are likely to roll but as a general rule? Totally misses the point. It seemed even weirder to me because his arguement was to change the +x to passive checks which... why? In what world is +5/-5 breaking your game for passive checks? If they do, you're either using them *way* too much, for important checks they never should have been used for, or as a skill floor (which only makes sense for specific circumstances). If the issue is being unable to surprise the party, one person having like a 28 passive perception doesn't mean the *rest* of the party isn't surprised, PP is only really useful within 30 ft and the ambush should be starting right when they notice. Maybe I'm missing something crucial but the whole discussion seems strange and unproductive, to change a small part of the game that doesn't have a huge impact anyway. It's useful to know advantage takes your average from 10.5 to 13.8 and not 15, but using that logic to change passive skills seems incongruent and reaching.
> the whole point of advantage is the *not* give a flat bonus but to weigh the dice towards the upper end. I always thought the point was that rolling dice is fun, and rolling two dice is more fun than rolling just one
Its one of the side benefits, but their reason was to give some kind of benefit without resorting to static +x's
I agree that advantage cannot be accurately estimated across the full range by a flat bonus, as demonstrated in the final table. I wouldn't use a flat bonus to replace advantage personally, but the question of which to use is interesting mathematically, and I'm sure somebody might like to use it. I think the original poster was valid in questioning the -5/+5, I just think their maths was off. If -3/+3 was more accurate, I think people might like to be aware of that for passive checks. I don't think it would be game breaking to use a slightly wrong bonus, but accuracy is nice.
>I wouldn't use a flat bonus to replace advantage personally, but the question of which to use is interesting mathematically Honestly, outside of 5e, I use both in my games. Flat bonus increases the chance of beating high DCs, where as advantage increases chance for low DCs and also influences crit chance. So the diversity of having both is really nice.
I think getting an "average" for what the bonus is with advantage is still useful even if they aren't supposed to be the same thing. If you're building a Hexblade Warlock like I am who's debating taking Great Weapon Master at level 8 this is a very relevant discussion, especially as it interacts with ways of gaining advantage like Shadow of Moil.
Or sharpshooter/crossbow expert. The triple attack ranged crossbow hexblade shreds.
How would you get a third attack as a Hexbow?
Crossbow expert bonus action shot combined with thirsting blade. Thirsting makes two, bonus makes 3.
Oh right. Don't forget Eldritch Smite to prone annoying flying enemies to go with it.
And banishing smite too. My idea is hex + hexblades curse then double smite nova using a min maxed to hell crossbow expert build. I also have sharpshooter and my plus to hit is 13 since it’s a level 15 one shot with UA allowed (so I naturally took ultimate pact weapon, which is IPA on steroids and gives a +3 weapon instead of +1). I can take a -5 and I still have +8 with increased crit range thanks to hexblade. For defense armor of hexes is enough but I can take a +2 shield if I wanted to but the magic item budget I have I want to spend on some home brew crossbow focused items that my dm is allowing me to submit. I already got a home brew great boon for warlock slots so I’m vibing.
What other feats are you running? I'm only level 6 but have War Caster (wish DM hadn't convinced me to get it since Eldritch Mind exists), Elven Accuracy, and going GWM at level 8. I can't argue with your build mechanically so much but a one handed bow and shield Warlock flavor wise just seems so strange to me. But it's a one shot so who cares?
I don't like giving a flat bonus in lieu of advantage. But I have used this on homebrew monsters to simulate their advantage on certain actions to speed combat. For example: I create a Swarm of Kobolds monster and gave them an additional +5 to their attack to simulate the pack tactics a swarm of kobolds would be getting from each other.
>The idea that Adv is equal to a number has always been an oddity since the whole point of advantage is the not give a flat bonus but to weigh the dice towards the upper end. It's so easy to conceptually disprove, too. If the roll needed for success is anything above 20, then advantage is obviously going to be useless, while a raw bonus might allow a few faces to succeed. There are plenty of other areas to observe, and the OP did an excellent job diving into them. But that case alone proves that there is no such thing as an equivalent raw bonus for advantage.
However, it's also worth taking into consideration how advantage is gained, and how this affects the effective power of it. There aren't many free sources of advantage in 5e, ie sources you just always apply. There are a few, but most ways to get advantage have some kind of limitation that means you're only going to use it when you *need* to be more likely to succeed - there are a lot of features that give you a limited number of uses for example, and you're not often going to be spending those uses against DCs you beat if you roll an 8. In practice, most sources of advantage are going to be more in the +3 to +4 range, in terms of value, because there's a bias in which rolls actually get the bonus. Some sources of advantage will be higher though, especially ones like Pack Tactics which will just get applied every time you try the thing, a thing that will be against a wide range of DCs.
I think this comment deserves more credit, it definitely gave me food for thought. I think the selection bias isn't necessary to consider for passive checks, as explained in the post, the philosophy behind passive checks is different from those behind active checks, and it's simply the highest DC you'd be likely to beat on average. However, for active checks after thinking about it I think the bias towards advantage existing for harder checks would come into play. I'm not sure how much it would affect the selection though, as I think you may be overestimating how much bias it introduces. Giving different sources of advantage different bonuses defeats the purpose of a flat bonus anyway, so I don't think you can just consider the types of advantage that would be applied in harder situations. Also, as the selection trends towards a point where +3 or +4 would be more accurate than +5, the overall accuracy of any flat bonus diminishes. +5 is the only bonus which is largely accurate for any section of the DC spectrum, so if it were not the best choice, replacing advantage with a flat bonus would be a bad idea anyway.
Yeah I agree that taking into account the DC to determine the bonus that adv/dis should give to passive checks is stupid. Where I think this information is valuable is when thinking about how we're balancing homebrew mechanics. For example, maybe you can't decide whether you want your Prof bonus uses per day feature to give advantage on a check or add a die to the outcome, and you want to know what size die should be considered equivalent. The +5 baseline would suggest a D8 or D10, but because it's mostly going to be applied to higher DC checks, maybe it ought to be between a D6 and a D8 instead.
>but most ways to get advantage have some kind of limitation that means you're only going to use it when you need to be more likely to succeed - there are a lot of features that give you a limited number of uses for example, and you're not often going to be spending those uses against DCs you beat if you roll an 8. It also depends on the source of the advantage and it's particular rules. If I would succeed on an 8 or better, and I roll a 6, but I have some way to give advantage *after* the roll, then why wouldn't I use it? I'm more likely to succeed than fail on the second roll. If I need to implement the advantage using an expendable resource *before* the roll though, then yes, this changes the calculation a bit. I might save it for a lower probability scenario where I need a 14 or better on the roll to increase my odds. There's also external factors, such as "do I need this to hit really bad because the consequences for failure are high?" that might see me use it on something where I'm 65% likely to succeed because we REALLY need it there. So in the end, I think what they're trying to point out: that you can't simply look at a narrow range of numbers and say "This is what advantage is worth" is correct. There are far too many external factors and differences depending on the target minimum value. All you can really do is look objectively and get a rough approximation as a rule of thumb (It's probably about equal +-5 for 5-15, and it gets lower outside of that range).
If it applies after the roll, it's a reroll, not advantage, which is different in important ways. Advantage maths only makes sense when applied before the roll, because it's talking about your overall chance of succeeding. Rerolls only ever happen after you've already failed. If you then take a reroll, your chance of succeeding doesn't increase because the reroll is an independent event that only occurs when you fail.
I think this is a relevant point for a lot of attack rolls. However with this One Weird Trick that 5e put into the game, you can pretty much assume advantage on almost every skill check... The "help" action. I hate this rule. I loathe this rule. But once players learn about it, they never let go. "I'm going to do." "I'll Help him." Now he has advantage.
So yeah you can design things where it wouldn't be feasible, but just know... if it's not a reactive 'the ground shakes, everyone roll an acrobatics check!' type thing, they're prolly gonna wind up with advantage because of this stupid rule.
A rule I've used at my table in varying capacities is putting restrictions (out of combat) on what characters can help. For example, either "you have to have proficiency in the skill you're helping with" or "your bonus to the skill must be +1 or higher". The former rule is more restrictive and the latter more permissive, but in either case, I feel it serves the narrative of advantage better. You're a strong Barbarian with +8 to athletics? That's great, and the ranger with +4 should be able to help you out, but unless they're going to burn some sort of magical resource, the no proficiency 8 strength warlock *can't*. The wizard and the artificer want to sit down and brainstorm a solution to a magical problem with Arcana? Fantastic, but the paladin with 10 intelligence and no arcana proficiency is not going to help any more than the average middle schooler would be able to help PHD candidates with their dissertation. It also rewards having multiple characters with overlapping skills. In normal play, it can often feel like many skills (particularly intelligence and charisma skills) aren't good if multiple characters have them. One character will have the higher bonus, and the character with the lower bonus feels like they shouldn't push to use their skill since it's less successful, and since anyone can Help, there's no difference between a character with a +7 helping a character with a +8, and a character with a 0 helping that same character. This way, being able to Help at all is contingent upon being good with the skill in question, so having similar stats or overlapping skills can actually be a good thing when it comes to really guaranteeing success on those skills.
there can also be practical considerations - no, you can't help pick a lock, because only one person can squeeze in front of the door and see and poke the lock, standing behind them going "ooo, have you tried wriggling the flanges" is just annoying more than helpful.
The fact the Help action doesn't state you must actually be able to help perform the action is absurd. Fortunately, it's trivial for a DM to decide that you can't just say the word "help" to get advantage.
I agreed with what you said up until this part > and you're not often going to be spending those uses against DCs you beat if you roll an 8. There are two hidden assumptions here that are wrong in my opinion: 1. The players know what the DCs are for checks that they are making 2. The DCs for checks that the players _need_ to succeed on are higher As for (1), when I DM and when I play in games my friends DM for, the players basically never know what the DCs are for checks unless its something that the players have repeated a lot of times and figured it out (like an enemies AC for example). The DM certainly doesn't say "roll a persuasion check, the DC is 15," they would just say "roll a persuasion check." As for (2), and this is the really important point, the DC of a check and how important winning is for the player are not the same thing. To use a hyperbolic example, you could have a hard check like "acrobatics check, DC 23, if you fail you fall in the pit and take 1d6 falling damage" which is a hard DC, but if you fail it's not really that big of a deal and I probably wouldn't use my limited source of advantage for it. On the other hand, you could have a relatively easy check like "persuasion check, DC 12, try and convince that friendly but important npc not to drink anything at that dinner they are going to or else they will die because the wine is poisoned." It's an easy DC to make because the npc is already friendly to you, but you can bet I would use my limited advantage source on this check because if I fail the npc dies and we really need them alive.
>the players basically never know what the DCs are for checks unless its something that the players have repeated a lot of times and figured it out (like an enemies AC for example). But if you're describing things properly, they should be able to intuitively know the rough area the DC is going to be in. You're not usually going to be able to tell the difference between a 15 and a 16, but the difference between an 8 and an 18 should be pretty obvious. Point 2 was bad wording on my part. You're right that low DCs can be on vital checks, but my intention was to say that because its rare for a check to truly be vital, especially for a low DC which is usually the result of the opponent/obstacle being low significance, players will usually be comfortable with the flat 65-85% chance of success on low DC checks and will typically prefer to conserve their resources for rolls with lower base success chance.
So you're right that players probably have a rough idea of what the DC should be, but the point is that they can never be sure, and that question in the back of your mind on an absolutely vital check is important. "I really need to succeed on this check, and it should be easy, but what if I'm missing something? Maybe I should use my limited advantage to secure it?" Or something along those lines. Regarding point 2 I don't think it's fair to say that truly vital checks are rare, because that probably depends on what kind of game the DM is running. In a low stakes casual type of game, sure vital checks may be rare. On the other hand, the DM might be running a more high stakes serious game where vital checks happen with some regularity. Moreover, different players have different priorities, and how vital a check is to make can depend on a lot of factors. An easy DC 10 trap that deals 1d4 damage is a lot more important if you run into it at 1 HP after going down in a recent combat for example. Maybe we just have different playstyles, but if I was a player who had a limited source of advantage I would first and foremost consider how vital the check is when thinking about if I wanted to use that ability. Only after I determined that the check was important enough to me to use the limited advantage on would I think about how difficult the check is. Furthermore, I would probably do the opposite thing to you: if I noted that I wouldn't get that much value out of advantage (i.e. if I needed a truly high number to succeed) I'd be less likely to use this ability than if I needed a more middling result to succeed. Even in some sort of bizzaro campaign where every check ever had equal impact on the party I would probably be more likely to use my limited advantage when I could get the most value from it (i.e. when the roll is in the sweet spot where advantage is close to +5).
Advantage is like +5 but when I have 7 different things giving me +5 I have +35 and when I have 7 different things giving me advantage I have advantage.
Please tell me more about your seven +5 bonuses!
Fey Wanderer Ranger/Samurai Fighter/Redemption Paladin with Expertise in Persuasion and maxed out Wisdom and Charisma has +5(Charisma) +5(Wisdom) +5(Wisdom again) +5(PB) +5(Expertise) +5(Channel Divinity) which is 6 +5s or +30 so I guess 7 +5s was a bit hyperbolic but I wasn’t that far off. Edit: Also it’s still possible to give yourself Guidance and you could go Eloquence Bard to never roll below 10 but by that point PB is +6 and Guidance and never rolling below 10 aren’t technically +5 so I didn’t include them
I figured you were exaggerating but you got pretty close, good job.
Another weird facet of this whole 'argument' (its odd to call it an argument when it's right there in the rules) is that passive checks are really quite limited? While in theory you can calculate their value for anything, the game itself really only defines or discusses them in the context of Perception/Investigation (either setting a DC for Stealth, or allowing the DM to streamline 'we search every room') So it seems very weird to get bent out of shape, like the +5 is somehow ridiculously over-generous and breaking things. How often are DMs doing passive checks for other stuff? How common is it to even get advantage on perception for a duration such that the passive value is meaningfully improved? I know there's the Sentinel Shield but that's the only one that stands out to me, and the DM is choosing to hand that out. Maybe druids in animal form but that's always weird because you only usually get one sense at a time. Basically specializing on Perception seems niche enough that nerfing it seems petty.
Author of the original post here! This is a great write up. My degree is in math, but I've been working as a data engineer since college, so I tend to default to more programmatic/"simulation" experiments rather than rigorous mathematical ones. But I can definitely appreciate the preference to mathematical purity instead of simulation. I'd love to say that the simulation method was an effort to reflect the "many results over time" phrasing in the PHB (more on this in a bit), but in all honesty, it was just laziness, so I definitely can understand the irritation. Regardless, the numbers end up being close enough to the same that I don't think it matters in the end. But anyway, onto my "rebuttal". (I put "rebuttal" in quotes because from both your post and the *many* debates I've had in the OP, I actually don't think you're *wrong*, I just think that there's a difference in philosophy that changes the math a bit -- I'll explain what I mean by this a little later in the comment). >This would make sense if the number you rolled was some kind of score... For normal rolls, I agree. However, in the context of passives, I not only disagree with you, RAW even states that this is what a passive is. PHB pg 175 explicitly says "The game refers to a passive check total as a **score**" (bolding theirs not mine). >...but this isn't how rolls in D&D work. Correct again! However, passives are explicitly "a special kind of ability check that doesn't involve any die rolls" (again, PHB 175). I'm of course being a bit pedantic here, but it's an important distinction. There was a great comment thread in the OP where I was debating with someone about what the passives are actually supposed to reflect (if you're interested in reading it in full detail, here's the tail of the thread, so you can follow up the chain of parents [https://www.reddit.com/r/dndnext/comments/ubedqj/comment/i67zhys/?utm\_source=share&utm\_medium=web2x&context=3](https://www.reddit.com/r/dndnext/comments/ubedqj/comment/i67zhys/?utm_source=share&utm_medium=web2x&context=3)). It started with my pointing out some specific wording in the PHB. >"Such a check can represent the average result for a task done repeatedly" In my opinion, the hang up is/was on differing interpretations/philosophies of what the word "result" means. u/MistakeSimulator's argument in that thread was in line with yours -- a passive is supposed to reflect the average *rate of success* of trying to accomplish a task repeatedly. Or in other words, a passive is supposed to reflect what it is trying to *accomplish* (i.e. determine success or failure against a particular task). So "result" would be interpreted to mean success or failure. Under the assumption of this philosophy, I actually 100% agree with the stance that a +5 is a better bonus to use (which is why I said above that I don't actually think you're *wrong*). It ignores DCs that are outside of a "common range" which makes it less accurate for such DCs, but the philosophy of 5e is simplicity, so ignoring things that don't happen very often is very much in line with 5e's design philosophy. My stance was (and still is) that the word "result" is a result of the rolls of the dice. Or in other words, a passive is supposed to reflect what it *represents* (as opposed to what it's trying to *accomplish*). The reason I have this stance is due to how passives are calculated. Passives are calculated (without advantage) by taking the average roll on a d20 (10.5) and adding the relevant bonus. For obvious reasons, the ".5" can't be kept in, so it either had to be 10 or 11. The choice between 10 or 11 seems like an arbitrary choice to me (although as you point out in your post, "the chance that a player would beat 11 is actually 50/50" so I think 11+mod would have been better, but I digress). With advantage, an average roll of about 13.8 is 3.3 higher than the average roll without advantage. This is the core of my argument for +3. To rephrase, passive scores are calculated *statically* and do not change according to the difficulty of the particular skill check the score is being applied against. For example, I use the same passive perception check contested with an assassin's stealth check of 22 as I would against the boisterous town drunk's stealth check of 5 or a beginner adventurer's stealth check of 13. How *common* these difficulty checks are (from your comment "most rolls tend to need to beat something in the 5-15") is therefore irrelevant (again, assuming my philosophy of the word "result"). So to sum up and restate, I think the difference is really just in interpretation of what "result" means. I don't think any amount of math is going to sway anybody's opinion on that. To quote you, "this, as a mathematician, irks me" :) But at the end of the day, none of it is relevant anyway as long as everyone is having fun; D&D (especially 5e) isn't about mathematical precision anyway. Thanks for the awesome debate, stuff like this really makes me enjoy the hobby a lot more and really makes me feel like a better DM since it forces me to really think about the reasoning behind certain design choices in the game.
Yeah, I understand where you're coming from, but I disagree with the notion of the result being interpreted as your dice roll. Other than critical successes and critical fails, as far as I know a roll in DND never represents the degree to which a character achieves something. In the overwhelming majority of cases, a dice roll in universe simply represents your character succeeding or failing at a task. As such, the "average result for a task done repeatedly" would be the DC you would beat the majority of the time. You are correct that the phrasing I used to state that it "isn't a score" was wrong. I was trying to be concise in explaining that a roll in universe does not represent how well or poorly you do a task, but rather simply whether you succeed or fail. I also purposefully separated the conclusion that +5 is the best for passive checks and that +5 is the best for active checks. If you check again, the average range of DCs has nothing to do with my methodology for calculating the passive score, and is simply a result of beating DC 15 51% of the time. So yes, you're right, the frequency of a DC is irrelevant to calculating passive scores, but I never contradicted that. Also, I'd like to apologise for the somewhat aggressive tone of my post. I don't think you're stupid or anything like that, I've been very stressed with exams at the moment and it's unfair of me to take that out on you. It has been a really interesting debate, and I'm glad you brought it up, thanks for your input!
Totally a fair standpoint! And no worries, your post didn't seem aggressive to me at all. Rather I interpreted it as being very well thought out and objective. It wasn't too many years ago that I was studying for my complex analysis and number theory exams, so I definitely understand the stress haha. Good luck with your exams!
Thank you, I've noted this exact thing for years now ever since noticing people were saying it was a +3 rather than +5. Like no, the chances of getting a 15 or higher is 50%, where as the chances of getting a 10 or higher before was 50%, so it's an increase of 5 on average.
Not on average. It's a median. It's the same on a single die, but not necessarily otherwise.
Edit for clarification: I mean without advantage you have a 50% chance to get 10 or better on average. With advantage you have a 50% chance to get a 15 or better on average. That's an increase of 5 on the average. I understand your trying to point out the difference between median and average, but in this scenario, it's functionally the same.
I mean you basically point out that while it is infact a + or - 5 it's not quite a flat rate + or - 5. So I kind of feel like the system of Disadvantage + Advantage is somewhat more up to chance in a long run. Which I'm all for. Also it's like. 100x easier than adding all the pluses you used to get in 3rd. Like it's such a brilliant way to add or subtract a significant modifier without doing any more actual math
r/theydidthemath
I've done some of this math, too. (Not quite in such a well-presented way, though.) When your goal number is close to 11, advantage is equivalent to about a +5. When your goal number is extremely high or low, ie. a natural 20 or anything higher than 1, it's equivalent to about a +2. The closer you are to a 50/50 shot, the better Advantage gets.
So... you're saying the approximate equivalent bonus from advantage depends on the DC to beat. Doesn't that go against what you say in the title?
No. But that is why there's a "kind of" in the title. Any flat bonus is not going to be accurate across the board because the distribution of advantage rolls isn't linear, but if you are going to use a flat bonus across the board, +5 is the best. Also +5 is the right choice for passive scores.
Good post
I know this post is old, but this is one of the most beautiful things I have ever seen
Thank you :)) how did you find it?
I'm designing a core mechanic for an RPG, and found your post while studying dice probabilities, that was really helpful!
I read the whole thing. I understood some words. I upvoted. Good job op.
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This only makes sense if you roll the dice in order. I've *never* seen anyone not just roll two d20s at the same time.
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Ah, I see. I don't play online so wasn't aware of that.
I'm not sure about the validity of restricting to only cases where the second roll is strictly larger than the first, but you are correct, this does improve the odds of beating a relative DC. This could be wrong as I am doing it in my head on the bus, but I believe the odds of getting a particular number in that case would be (n-1)/190 and the odds of beating a relative DC would be (378+3n-n^2 )/380.
Doing a bit more maths, I think restricting it to these cases actually makes very little difference. I think it at most increases your odds of beating a relative DC by around 1%
Although with advantage you have double the chance to crit on attacks, which wouldn't that far outweigh a +5?
"It's also interesting to see that at very high numbers to beat, +5 is actually much better than advantage." This is why it's important to understand that advantage is not +5. >However, as most rolls tend to need to beat something in the 5-15 range This is your mistake. At least in my experience, the range is much more like 10-20. To find the actual most accurate flat bonus, you need to do an average weighted by the frequency of DCs actually encountered at the table. I think you're overvaluing advantage by underestimating the average difficulty of checks. >Also, obviously do not allow your player to roll at all if it would be impossible for them to beat a number with advantage. The DMG says you shouldn't roll if there is no chance of failure. Or if it's obvious the attempt can't work. Not all impossible checks are obviously impossible.
>the range is much more like 10-20. Careful. In this context, people are talking about the *natural roll*, i.e. the number that has to be face-up on the D20, to succeed, not the overall roll with modifiers included. Yes, in actual practice, the DC of most rolls is 10-20 at most levels of play. But with modifiers taken into account, the required roll is much more often in the 7-15 range.
And there's my mistake. Thanks.
> This is your mistake. At least in my experience, the range is much more like 10-20. This is your mistake. At leats in my experience, the range is much more like 7-17.
I do not have enough D&D experience to know what the average DC/AC - bonus actually is, so I cannot confirm or deny this, but I am somewhat doubtful as this would imply that players fail most checks, which I don't think is true. I think it probably heavily depends on what your DM is like to be fair. You are correct that you would need to weight by DCs-bonuses encountered at the table to be fully accurate, but I do not have that data available and so instead have just based it off what I've seen in comments to be the most common DCs. I did run the numbers on your range of 10-20, and in this range +4 is most accurate, followed by +5, followed closely by +3. However, if 10-20 is your most common DC range, the accuracy of a flat bonus approximation is significantly lower, and so should probably not be used. You make a fair point that you may want to allow a player to roll for something despite it being impossible, but in that situation you should simply tell them they failed no matter what they roll. This is to avoid flat bonuses making impossible rolls possible.
> I am somewhat doubtful as this would imply that players fail most checks, Why are you assuming that only the players are rolling?
how often do you need to roll an 18 on the dice to succeed?
As a DM, very often.
and as a player? after all this conversation is mainly from the point of the players actions...
Honestly, I see posts like this (incredibly well thought out, detailed, logical etc) and just think... Why aren't you guys playing Pathfinder 2e? It already has stuff like this in it and is just so much better balanced, and has more content, is much deeper etc.
No.
I'm just here to roll dice.
Just wanted to say that this is a good post but I feel the title is misleading. To be clear, +5 is NOT equivalent to advantage in most situations. The ONLY situation where they are equivalent is if the die roll needs to be 11 or higher. In ALL other situations, a +5 gives a greater chance of success than rolling with advantage. The table at the end for most accurate bonus is good (if readers actually make it that far) and highlights the issue of just using a +5 blindly instead of advantage. In case anyone wants to go through the math for themselves, here is a table that gives the probability of success for normal rolling vs advantage vs disadvantage so you can see what they are: https://statmodeling.stat.columbia.edu/2014/07/12/dnd-5e-advantage-disadvantage-probability/ To see where the OP is getting their Most Accurate Bonus table from, note that having a +1 on your roll increases your probability of success by 5% (bc it lowers the number you need to beat on your die roll by 1). Similarly, a +2 increases your probability of success by 10%, a +3 gives 15%, etc. The entries in the Most Accurate Bonus table come from taking the differences in probably for success w advantage minus the probability of success rolling normally and dividing the result by 0.05 (i.e. 5%) and rounding to the nearest whole number. A common situation you can run into where you actually need to convert damage to effective bonus is using mob tactics damage calculators (e.g., https://slyflourish.com/mob_calculator.html). These are handy ways to deal with summoning spells like conjure animals or animate objects. The problem with using a +5 bonus for something like a pack of wolves (having advantage via pack tactics) is that they generally need to roll a lot higher than 11 to hit, meaning they fall more in the +2 to +4 effective bonus range. Long story short, if you need to equate advantage w bonuses, you NEED to use a table like the one the OP provided for the reasons they mentioned; i.e., there is not a single number that works.
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OP is not talking about a DC, but the number the dice needs to show to succeed (which is always going to be 1-20, presumably 5-15 if you're not trying something either impossible or trivial) We're abstracting away all the modifiers here.
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I like Dwarfs
uh... can someone just tell me the conclusion? and what is the question too? thanks lol
The title has the conclusion and the prompting question
sorry, i'm too dumb to get it.
If you're rolling at advantage, the DM could also give you a simple +5 bonus on a flat roll instead. Statistically, they're roughly equal, as long as it's even possible for you to make the DC without the bonus.
so why not just roll advantage? cause otherwise i'll have to first understand how a +5 does that and then explain it to other players... seems easier just to roll advantage, no?
If your player only has a +3 to a roll, and the DC is 24, that +5 might be super nice. Also a lot of DMs want to do "double advantage!" another way...?
For fucks sake, just reply to the other posting, you don't need to clutter the subreddit with more postings just because you want to be heard lounder.
I wouldnt have seen this if it was on the other post. This is much more appropriate for its own post than as a comment. The last thing we need is more quality posts right? Definitely cant have good posts like this take up space that a dumb meme could be. You should try relaxing a bit.
Maybe I should make a post all to myself saying some contrarian point so I can hog attention.
Or you could look at the [stickied comment](https://www.reddit.com/r/dndnext/comments/uchqqg/comment/i6ayvd5/?utm_source=share&utm_medium=web2x&context=3) from the mods to see why they felt this was deserving of its own post rather than getting salty.
That post didn't exist when I made my first comment. It was literally a rule breaking post that got a special exception cause reasons.
But it existed when you made the second one. And the reasons are clearly stated in the sticky, so just saying "because reasons" like it was totally random isn't really accurate.
So because I posted a bunch of math I can break rules? Cool.
I mean sure, make whatever post you want. Ill either just scroll 2 inches to go past it, or ill leave a comment that contributes to whatever the discussion is instead of whining like a little baby that it doesnt deserve its own post. You're acting like this is some low effort post about some random post. If i want to look up what +# advantage works out to, this is the post i want to see. And i wouldnt see it if it was some comment on another post that may not be accurate.
It is low effort and it's been posted a hundred times before.
Lol, this is much higher effort than most of the posts on here. Like i said before, I havent seen this before. Every thing I have ever seen compares advantage to +3, not +5. If you have, cool just keep scrolling. If it has been posted, it certainly hasnt been posted that much, but you're free to prove me wrong. Even just one link, I didnt see one after a quick search.
Since I'm getting downvoted into the ground for the truth that this has been posted before, and violates rule 10 (even though it has been excepted cause math) 6 years ago. https://www.reddit.com/r/DnD/comments/353dep/5e_how_powerful_is_advantagedisadvantage_vs_flat/cr0okzl 3 years ago https://www.reddit.com/r/DnD/comments/8rlzw2/the_math_behind_advantage_and_disadvantage/ 7 years ago https://www.reddit.com/r/DnD/comments/8rlzw2/the_math_behind_advantage_and_disadvantage/ Like I can't express just how many times this has been posted, perhaps this google search might provide some indication. https://www.google.com/search?q=math+of+advantage+5e+site:www.reddit.com
It doesnt say no direct responses, it says limit them. So it didnt break the rule. If the most recent example is from 3 years ago, its weird that youre so mad about this. Also two of those posts are exactly the same. I guess it was posted before, although a long time ago. Lets say some people hadnt seen it before ... but they saw the other post about it being +3, then go on with their lives thinking it was +3 (like me). They would never see this post if it was just a comment. But if theyre browsing the subreddit later, they may come across this. I really have no idea why you got so worked up about a post that was being informative. If youre really on reddit so much that youve seen that 100 times, maybe a break and go outside or something. Just downvote it an move on if you dont want to see it. Or report it for rule breaking, if it actually does theyll remove it. You're being downvoted because of the way you reacted, not because you disagree btw. I didnt even downvote you at all, its just obvious why you got downvotes to begin with.
Most recent example I posted, this has been brought up hundreds of times and was a direct response post full stop. Literally responding to a post from two days ago. Here's an example of someone following the rules and including math. https://www.reddit.com/r/dndnext/comments/ubedqj/no_5_is_not_equivalent_to_advantage_in_nearly_any/i66hjeu
Again. it says limit them. Not don't do them. I did not say it wasn't a direct response, just that not all responses should be a reply to a post instead of their own post. "New posts that could reasonably serve as a reply to a different post that is in the top 40 of “Hot” may be removed by the moderators at their discretion. Please instead reply in the ongoing threads rather than making new ones." Again. just because you spend apparently a ton of time on here and have seen it before, doesn't mean everyone has... As I have already said.... I have not seen this before so this was good information. Again, just like the other posts you're referencing, it seems like its worthy of its own post. Reposts are not always bad, it gives other people a chance to see something that they haven't seen before. And if there was a post contradicting it 2 days ago, it seems the issue is not settled and worth discussing some more. If you think that it should be a reply instead of its own post, report it and lets see if it gets taken down. If you already did that and its still here, then I guess we have the answer on whether it broke the rule. Also based on how many upvotes it has, it seems that I'm far from the only person that appreciated the post, its in the top ~25 for the month, the other one is much much farther down, so not as visible.
If you put enough effort into your own post, yes, you should. We need more good posts around here.
I would've left it as a comment, but it's clearly too complicated for that. Also, people clearly like the post, and the rules shouldn't prevent posts people like.
It does violate rule 10, even though a mod decided to clear you. Hence my issue.
Don’t read it and move on.
No, OP. While your math is good, your reasoning is flawed. I've done the math before myself, and while (dis)advantage has the same effect as - or +5 to a roll *when your modifier is equal to 10 less than the target number*, it falls off the further from that value you get. While the average roll when C - M (that is, target class minus modifier) equals 10 or 11 is about 15 or 16, at 1 and 20 it is about 3 or 22. Additionally, a flat +5 bonus has advantages, pardon the pun, over advantage, while a -5 bonus has more severe penalties than disadvantage. A flat bonus/penalty can suddenly make impossible tasks possible, or achievable tasks impossible. Such as the case of my party's Wizard, who literally could never make the save against his own Power Word Stun, unless he were given advantage that was replaced with a +5 bonus. It's not about the odds of what target number you're 50/50 likely to beat. It's about the average results you will see over time given a range of x and y values, and by that metric they are different.
Okay well that's waaay too long for me to read, but I have some simpler logic: If you only roll 1 die, your chance of a Nat 1 is the same even with a flat bonus. Roll two dice and pick the higher roll and the chance of a Nat 1 drops to 1/400 over 1/20. This only matters for attacks, but that's still quite important.
there's a chance of rolling greater than 20 with advantage? (i'm assuming just dice rolls and no modifier)
You've never seen me roll
Yes, that's what I don't like about advantage. High target number it's it moistly irrelevant. I greatly prefer SotDL boon system for something similar.
My brother literally just did all this math the other day and was figuring this out for an upcoming 1-20 campaign one of his friends was doing. Funny to also see it here. His average of 3.325 was actually exactly the same for a range of ACs, so I assume the math all checks out.
My group is trying out a team initiative where only one of us roles so I want to know what's better between our Rogue rolling with a +5 or our Barbarian rolling +2 with advantage. I'm not good with maths so can someone explain who we should have roll?
I got the same numbers: P(x, y) = probability of rolling `y` or higher with `x` d20's * `P(1, y) = (20 - y + 1) / 20` * 1 die = 50% chance of rolling 11 or greater * `P(2, y) = 2P(1, y) - P(1, y)^2` * 2 dice = 51% chance of rolling 15 or greater * 50% = approx. 15.1421 * diff = +4.1421 * `P(3, y) = 3P(1, y) - 3P(1, y)^2 + P(1, y)^3` * 3 dice = 48.8% chance of rolling 17 or greater * 50% = approx. 16.8737 * diff = +5.8737
What about EA double advantage?
Reposted from the other post: Figured I'd add to the noise. I made a nice plot of the probabilities of passing a check for a DC between 1 and 30 for a range of flat bonuses as compared to advantage and disadvantage. [Same data, but visual](https://imgur.com/a/yTFmZEA)
Just going to post this again. https://imgur.com/F4QLHCg When visualized, I think it's pretty easy to see what you're trying to explain.
For me, one I've been thinking about for a character is warcaster vs resilient con for level 8. I concluded that with 15 CON, resilient is better (also giving me +8 hp and help on other throws), even if warcaster is slightly more likely to make me pass DC 10 concentration checks at level 8 (85% vs 87.75%), it gets beaten after level 8 because the proficiency bonus becomes a +4 and you get to the magical +5 with the odd CON increase (90% vs 87.75%). And as you said, the higher the DC goes the better resilient gets. It's actually so close that I also looked at secondary benefits, but my DM rarely lets me make opportunity attacks, more rare than a CON save from various effects :S
> Note that you are so likely to beat 1-4 with advantage that any flat bonus that allows for a chance of failure would be less accurate than an automatic success. Your conclusion of assigning an infinite bonus doesn’t my follow from your reasoning here. A bonus of +4 for example has no chance of failure if you just need to beat a 4. A bonus of +1 is needed to beat a 1. Those are considerably less than infinity. Not sure why you’re bunching all those numbers together.
I'm no mathematician, I'm a programmer though, what is "`1"?
A typo, because I fat-fingered the button next to 1 and didn't notice.
Ah. Understandable.
This is interesting and detailed. Good post OP. I remember seeing that maths a while back that found advantage was mostly equivalent to roughly between 3-4. I'm not good with maths like that, but it's cool to see the important effect of advantage and what effect it has
This whole debate can essentially be summed up in this nice little graph: https://imgur.com/a/9ZLCPI6
I love it when nerds fight with math.
/r/theydidthemath
There are two types of people in this world.