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[Guest 6801328]

GAH! Advantage/disadvantage is never actually like +/-5 at any point on the scale. It has a similar OUTCOME at 11 as a normal roll with a + or - 5, yes, but having a similar outcome is not at all being the same thing. And that difference becomes very apparent the further from the center you get.

Sorry, pet peeve when people try to turn a normal distribution into a shifted flat one. You hide information for no added clarity. It's a disservice.

What other meaning of “like” is there in this case, other than a similar outcome?

 

[Fenris-77]

GAH! Advantage/disadvantage is never actually like +/-5 at any point on the scale. It has a similar OUTCOME at 11 as a normal roll with a + or - 5, yes, but having a similar outcome is not at all being the same thing. And that difference becomes very apparent the further from the center you get.

Sorry, pet peeve when people try to turn a normal distribution into a shifted flat one. You hide information for no added clarity. It's a disservice.

It's also a nice easy touchstone for the less mathematically inclined. As long as I know that's roughly similar to +/-5 at DC 11, and that its value declines as it heads toward 20, I have enough to make reasonably well informed decisions, up to a point. Past that, I'll ask someone who knows more than I do. If you have a better description I'd love to hear it.

 

[Guest 6801328]

It's also a nice easy touchstone for the less mathematically inclined. As long as I know that's roughly similar to +/-5 at DC 11, and that its value declines as it heads toward 20, I have enough to make reasonably well informed decisions, up to a point. Past that, I'll ask someone who knows more than I do. If you have a better description I'd love to hear it.

The math is pretty straightforward. With advantage your chance is equal to the chance of both dice failing, right? So it’s the chance of one die failing, squared. The chance of one failing with DC 11 is 0.5, which squared is 0.25.

So, what DC gives you a 25% chance of failing with one die? DC 6. But since our DC is actually 11 we need a +5 bonus.

So DC 11 with a either +5 bonus or advantage both result in a 75% chance of success.

Q.E.F.D.

What you find at higher or lower DCs, if you do the same calculation, is that the +5 (or -5 for disadvantage) gets smaller and smaller in magnitude.

 

[Ovinomancer]

The math is pretty straightforward. With advantage your chance is equal to the chance of both dice failing, right? So it’s the chance of one die failing, squared. The chance of one failing with DC 11 is 0.5, which squared is 0.25.

So, what DC gives you a 25% chance of failing with one die? DC 6. But since our DC is actually 11 we need a +5 bonus.

So DC 11 with a either +5 bonus or advantage both result in a 75% chance of success.

Q.E.F.D.

What you find at higher or lower DCs, if you do the same calculation, is that the +5 (or -5 for disadvantage) gets smaller and smaller in magnitude.

This is the same logic that tries to argue that a scaled and recentered 2d6 is the same as a d20 -- because you can get them to cross at the middle and the curves look kinds the same if your graph them on a stretched enough x-axis.

The PDF of ad/disad is not a flat distribution, even a shifted flat distribution. Just because the two intersect is not a good enough reason to claim similarity. You're hiding the wealth of information in the rest of the distribution when you do this.

Or, are you fine with saying any two things are "like" each other if they happen to have the same probability of occurring for a specific use case? If so, we have a wealth of other things we can say. Like Advantage is like 3d6+2, if you need an 11.

 

[Esker]

This is the same logic that tries to argue that a scaled and recentered 2d6 is the same as a d20 -- because you can get them to cross at the middle and the curves look kinds the same if your graph them on a stretched enough x-axis.

The PDF of ad/disad is not a flat distribution, even a shifted flat distribution. Just because the two intersect is not a good enough reason to claim similarity. You're hiding the wealth of information in the rest of the distribution when you do this.

Or, are you fine with saying any two things are "like" each other if they happen to have the same probability of occurring for a specific use case? If so, we have a wealth of other things we can say. Like Advantage is like 3d6+2, if you need an 11.

Oh god, not this again.

 

[Esker]

Without intending to directly reply to Ovinomancer because I don't want to get sucked in to that again, but for the benefit of anyone else reading this thread, the point about advantage/disadvantage being "like" +5/-5 is that when your roll is converted to a binary outcome (success vs failure), the only thing that functionally matters is the probability of success (and the probability of failure, which is determined by the probability of success). The business about whether the PDF is flat or curved or whathaveyou is immaterial as long as you are always converting the result to a binary thing at the end of the day.

If you have cases where the amount by which you succeed or fail by matters (which sometimes it does, but rarely), then it's more complicated, but for most d20 rolls in 5e*, all that matters is whether you rolled high enough or not. And if "high enough" is rolling an 11, then you can roll with advantage or roll a single die and add 5 and it changes nothing.

*Setting aside crits and crit misses in addition to anything that says something like "If a creature fails the save by more than 5... [some additional effect]"

 

[Ovinomancer]

Without intending to directly reply to Ovinomancer because I don't want to get sucked in to that again, but for the benefit of anyone else reading this thread, the point about advantage/disadvantage being "like" +5/-5 is that when your roll is converted to a binary outcome (success vs failure), the only thing that functionally matters is the probability of success (and the probability of failure, which is determined by the probability of success). The business about whether the PDF is flat or curved or whathaveyou is immaterial as long as you are always converting the result to a binary thing at the end of the day.

If you have cases where the amount by which you succeed or fail by matters (which sometimes it does, but rarely), then it's more complicated, but for most d20 rolls in 5e*, all that matters is whether you rolled high enough or not. And if "high enough" is rolling an 11, then you can roll with advantage or roll a single die and add 5 and it changes nothing.

*Setting aside crits and crit misses in addition to anything that says something like "If a creature fails the save by more than 5... [some additional effect]"

Yes, because sub-posting is always a good look.

The issue with the +/-5 is that it's easily confused by people who don't know better. That's been often seen on these very boards by people who confusing this single point of intersection between two graphs as holding for broader cases, or the people that average intersections of multiple graphs or just wing it to say it's +/-3. When people that know better use it, it's frustrating. Math shouldn't be a matter of being unwilling to part with your comfortable, but incorrect, assumption.

 

[Guest 6801328]

This is the same logic that tries to argue that a scaled and recentered 2d6 is the same as a d20 -- because you can get them to cross at the middle and the curves look kinds the same if your graph them on a stretched enough x-axis.

The PDF of ad/disad is not a flat distribution, even a shifted flat distribution. Just because the two intersect is not a good enough reason to claim similarity. You're hiding the wealth of information in the rest of the distribution when you do this.

Or, are you fine with saying any two things are "like" each other if they happen to have the same probability of occurring for a specific use case? If so, we have a wealth of other things we can say. Like Advantage is like 3d6+2, if you need an 11.

Whoah.

Um, yeah. I/we were only saying that at the middle of the curve (DC 11), +5 to a normal roll is equivalent to advantage. Nothing more than that.

You're right; that might be misinterpreted by people who don't read carefully or think about what it means. I'm not sure a more sophisticated answer is going to accomplish anything, though.

So maybe a better response is, "Yes, but overly simplistic, misleading explanations are how we of the technocratic high priesthood keep the unwashed proletariat under our thumbs." If you tell them to "take the red pill" while feeding them those simplistic half-truths, it comes across as inviting them into the inner circle, and they run eagerly to their dooms.

Fools.

 

[TwoSix]

Math shouldn't be a matter of being unwilling to part with your comfortable, but incorrect, assumption.

Yea, but this isn't a math question, really; it's a question of what's the best way to communicate a mathematical idea to those who don't have the disposition to work it out themselves. Precision has no place in coining a useful aphorism that 90% of the gaming population understands. Bell curves aren't intuitive to most, telling people that "it's about a +4, as long as you're not in everything hits or everything misses territory" has worked well for me in the past when talking to bright but not mathematically strong players.

 

[Esker]

Bell curves aren't intuitive to most, telling people that "it's about a +4, as long as you're not in everything hits or everything misses territory" has worked well for me in the past when talking to bright but not mathematically strong players.

The issue isn't (just) that bell curves are too complicated, the issue is that looking at the curve (which isn't even bell-shaped if we're talking about advantage/disadvantage) is irrelevant if you are just going to compare to a threshold. All that matters is the probability of hitting the threshold; and adding a modifier or using a non-uniform distribution of rolls both modify that probability. Focusing on the means of adjustment when the ends are the same is sort of like saying that rolling a d6 and checking for 4 or higher is an unacceptable substitute for flipping a coin. Yes the physical process is different, but the properties that matter are the same.