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Jan 25, 2013 -- 5:27AM, Pyromantic wrote:

A further illustration:

Suppose we are defining a mechanic for death saves, and selecting between two options.

Option A:  Each round a player makes a d20 check (DC 11).  After 4 failures the player dies.
Option B:  Each round a player makes a d20 check (DC 6).  After 2 failures the player dies.

Suppose also that we are deciding between them on the basis that advantage may exist for these checks, and we want to minimize the significance of advantage.  Which one should we choose?  You might say B, because both involve a d20 check, but option A's check is at 11, where advantage equates to the larger flat bonus of +5.

Let's first note that for each option the expected number of checks until death is 8.  (And no, I'm not saying that makes the distributions identical, or that one objectively favours players more than the other without consideration of context.  I'm saying they are comparable in the sense that they have a quality--expected number of rounds until death--that can be used as a point of comparison, that in this case that quality begins the same, and that we can thus analyze the impact of advantage on this basis.)

Option A with advantage:  Your probability of failure on the d20 check goes from 0.5 to 0.25.  The expected number of rounds until death doubles from 8 to 16.
Option B with advantage:  Your probability of failure on the d20 check goes from 0.25 to 0.0625.  The expected number of rounds until death quadruples from 8 to 32.

Jan 24, 2013 -- 10:21AM, JihVed wrote:

Well, yes, by changing the metric from "flat percentage increase in success" to "proportional increase in success" you have also changed the meaning of "matters" in that context.

It isn't that I'm "changing" the metric.  It's that I'm bothering to (a) specify the metric, and (b) consider whether that metric "matters" in terms of measurable in-game consequence.

Edit: I'd have to think on this some more, but my initial impression is that it is very defensible to say that the significance of advantage is actually more stable across the contexts of various target numbers than a particular flat bonus, rather than less so. 

I feel like you're being intentionally nit-picky here.

Throughout the thread (and every other thread that discusses advantage) the comparison has been in the flat percentage shift in probability for advantaged accross target rolls, versus the flat percentage increase in probablility for a flat numerical bonus to the roll.

What you're discussing is the the game impact of ANY bonus and how it effects character action.

The problem with that comparison is that you have no baseline to compare it to.  Yes, advantage by your defenition "matters" more at high TN's, because ANY bonus matters more at high TN's.

The only way to understand the impact of the advantage mechanic is to compare it to the only other mechanic that represents what advantage is meant to achieve. (ie the flat bonus ).   The whole point of comparison is to guage which mechanic has a greater impact at various TN's.  And the only meaningful way to do that is to compare the flat percentage in probability increase.

You examples above only compare advantage with itself.  Those results are not useful in a comparison of where advantage matters because there is no baseline.


Don't get me wrong here.  Your evaluatiopn of the in game effects of advantage have a lot of merit.  You just seem to be ignoring that the rest of the thread has been discussin advantage as compared to a flat bonus.  That is the implied portion of my statement which spawned you to counter a point I didn't make.

No one is arguing that having a bonus to your roll matters more for difficult rolls.  The point of confusion with advantage is that it's effective bonus is a bell curve based on the target roll.   

That is the only point people have been attempting to clarify. And again, that is what I mean when I say that advantage "matters more" an TN 11.  It means that for that one specific roll (not the in game effects of that roll, but the roll itself) the difference in pass/fail probability is more greatly effected at TN 11 than at the extremes.

Wasn't really able to respond for a few days, but I do wish to do so.

As far as I'm concerned, I'm not being nit-picky (deliberately or not) or ignoring what has been said in the thread.  I actually appreciate that the OP asked specifically when advantage is more powerful than particular flat bonuses rather than a more vague description.  That isn't the point though.  The relevant portions of the post that spawned yours, and of your post that I quoted, are:

Jan 24, 2013 -- 3:58AM, OrKKiller wrote:

The closer you are to needing to roll an 11 on the dice, before bonuses and penalties, the more advantage and disadvantage matter. The further away the less it matters.

Jan 24, 2013 -- 5:33AM, JihVed wrote:

And yes, you both make essentially the same point.  Advantage matters more when the target roll is closer to 11.

I don't see how you can take the first of those to be anything other than a comparison of advantage with itself across two different contexts; it's a question of the change in significance of advantage rather than a question of magnitude.  Further, it seems to be based entirely on saying that advantage equates to a larger flat bonus in one context than another, and rather than leaving it at that, making a logical leap that advantage is more significant in the first context using the equivalent flat bonuses as a measuring device.  I acknowledged that that might not have been what you meant (the point you didn't make).  It might not be the point meant by any particular quote; I really don't know.  But I think it is the most reasonable interpretation of that particular language, and it has appeared in almost exactly that form enough times over the forums for me to think it is meant precisely that way quite frequently.  If the language of the thread really was restricted to measuring the equivalent flat bonus for any particular target number then fair enough, but I don't believe the language of the thread (along with many others) is so restricted.

I also don't see any particular reason that it shouldn't be discussed in such a fashion.  Why can you only talk about the significance of a bonus relative to flat bonuses?  Why is that the only way to understand the impact of the advantage mechanic?  I would presume that we similarly want to consider the significance of using flat bonuses for certain situational benefits if they are in use, rather than leaving it as the end of the discussion.  I'm not breaking entirely new ground here; the very first response in this thread made a distinction between relative changes in probability of both success and failure, and people have otherwise talked about how much is gained with the implicit indication that you can determine significance more or less directly from a flat bonus.  You can make the comparison for the purpose of determining which mechanic (advantage vs. particular flat bonus) is more powerful at various target numbers, but I see no reason to stop the discussion there, and I'm quite sure that others haven't.

I will also say that I am certainly not suggesting that proportional decrease in the chance of failure is "the" or "my" definition of significance, though I think in many situations it's a very good one.  However, even taking that as the measure of significance of a bonus for a moment, it is not true that any bonus is more significant at higher probabilities of success than lower; you could certainly construct modifiers to a probability distribution such that it is not the case.

Edited slightly for clarity.

Jan 29, 2013 -- 11:36PM, OrKKiller wrote:

The answer to your question is that mainly everything you describe can be equally applied to every other mechanic and set of rolls in the game. Advantage/disadvantage doesn't alter the results you are talking about compared to regular rolls. Yes it has an effect, but that same effect happens when you use a normal roll across multiple rolls.

I assume that the question(s) to which you are referring is/are "Why can you only talk about the significance of a bonus relative to flat bonuses?  Why is that the only way to understand the impact of the advantage mechanic?"

I never said that advantage and a flat bonus are categorically different in this regard; indeed I'm pointing out the exact opposite, that advantage and a flat bonus are categorically similar here.  Once you move into language comparing "significance" or how much something "matters" across different contexts, using flat bonuses as a point of comparison is largely pointless since there is no basis for thinking flat bonuses provide a stable measurement of such things, and taking flat bonuses to be so leads to some pretty questionable conclusions.  However, saying that they are in the same category does not mean that the discussion ends; that would be like saying all increasing functions are essentially the same and you can't analyze them any further.  Even if you were to determine that two bonuses behave in a qualitatively similar fashion that doesn't mean you can't consider quantitative differences. 

For example, if you compare probability of success with or without advantage, or with or without a +2 bonus, you will find that as your target number decreases (and your base chance of success goes up) the ratio of probability of failure with the bonus to probability of failure without the bonus gets smaller and smaller in each case.  In other words, from a certain (perfectly reasonable) point of view, the significance of both bonuses is larger as you change the context to one of a larger base probability of success.  However they certainly don't do so in the same way.

I'm not sure if every current mechanic behaves qualitatively similar; in order to check I'd have to look at every current mechanic.  However, it is certainly possible to construct dice mechanics that do not.  It's a bit tricky to go in this direction; it's generally much harder to determine a suitable dice mechanic from a desired behaviour than to determine behaviour from a mechanic, but here's one example:

I'll call it the "1 in 4" bonus.  When you make a d20 check with this bonus, you also roll a d4.  If the d20 check passes, you succeed.  If the d4 results in 1, you succeed.  This is behaving in a categorically different manner: the ratio of probability of failure with the bonus to the probability of failure without the bonus is always 0.75, except where it is undefined for no probability of failure.