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I've mentioned a few times in this thread, part of my desire for clearer wording is that this involves Pathfinder Society, and uniformity in the game experience (individual GMs have less "final word" flexibility) is supposed to be the key thing there. I also mentioned that it's entirely possible for someone to not see the glossary entry and make the natural assumption that you've found the best answer/details. If you're just reading the book normally, you'd not even see the glossary - but you would see the full text entry. But let me reiterate: I favor the DC-10 method, if only because of the simplicity. But I also favor it because failure needs to be more of a potential threat for the PCs, especially coming from PF1e where it's not difficult to get PCs with insane bonuses to the point where they can auto-succeed every possible skill DC, unless you set it so high they're the only member of the party that can succeed. 2) Typically when someone doesn't understand something they ask for help. That is notably missing from the OP. They then don't argue with everyone who disagrees with them. You're right. I wasn't asking for help. I knew about the wording of the entry and the differing glossary entries (they're not even consistent) before posting. I was drawing attention to what I believe to be a flaw in the wording, and made my case as to why it is a flaw, and that it is also entirely possible for someone to miss the wording in the glossary. 3) My post was more about general gaming culture then the OP. The OP has behaved in a way quite consistent with our community. It doesn't mean it's the best way to behave or we should characterise it as "the only rational course" If I ever came across as rude, offensive, or overly-argumentative, it certainly wasn't intended. Like Mathmuse quipped about himself, my line of work and interests also involves being extremely analytical to the point of overthinking. It also involves objectively presenting observations, possibilities, and arguments that run counter to my own conclusions. And, like you observed about gaming culture, I also expected some of the derision and dismissiveness in this thread.
If the DC doesn't succeed or fail, it becomes the middle/fulcrum of the scale. In the actual game system that point exists only theoretically, because you can't have an X.5 value, only X.0 (an integer). Your analogy is false, but you are correct that the odds would be completely equal if the DC was the center and not a success/failure. You have no bonus and the dc is 15. You roll there are only 6 steps between failure and critical success here. According to OPs logic crit success should be more likely but it obviously isn't. That is precisely why it makes more sense to talk only about the scale around the DC, rather than the rolls and/or modifiers. When you use the latter, you can use infinite variables and combinations and make it tell any story you want (such as your example being crit success more likely). It makes even more sense to show probability on the DC scale when you consider that it's not usually just one person that rolling against the DC, meaning whole new sets of possible variables in d20 + modifier rolls, each with their own probability percentages. The origin point of the scale I present is the fulcrum between overall success and overall failure. Because there are only four possible outcomes, the center of the scale is always going to be an (X.5) value, the DC (being a positive/success result) has to be on one side of the origin or the other. When I mention framing, I mention it for a reason. If you start on that center point, zoomed all the way in, then start zooming out, you have to at least zoom out minimally to the point where you can see the all four of the result categories. Yes, you can keep zooming out, but the numbers are literally infinite then, so the optimal cut-off is the minimum data set needed to demonstrate. That is why, when using the DC-10 method, a minimum of two values/points/steps for critical failure will be visible by the time you finally see the first value/point/step of critical success. It's literally twice as probable when you measure it that way. You can't quite measure it by a straight die roll, because with 22 values/points/steps in-frame at that time, a lone d20 (regardless of modifiers) cannot meet every result on that scale. Therefore, 1 out of 22 is 4.5%, 2 is 9%: twice as probable on the minimal scale. That's all that meant. I fully recognize dice rolls change it up and have their own probability percentages depending on the modifier and the DC.
I mean, look how much of a debate this has sparked. I've seen people debate these very things at my tables or neighboring tables. If I'm the GM, then I will temporarily rule on it and move on, addressing it later. I'd rather keep playing. But, in the context of Pathfinder Society, there's a point to be had here when the GMs are supposed to conform to society/paizo standards. The entry itself is not clear and concise, and expecting players and GMs to scour every inch of the book for something that's referenced only in the glossary is a misfire in editing and use of language. The primary entry for any rule should be the most clear and concise of all, not some ancillary reference place.
I do not comply with your graphs. Which is precisely why I'd like Paizo to rule on this. I fully recognize both sides, and I even lean a bit more toward simplicity and a bigger risk of failure for the PCs. But, at the same time, if I'm going to point out a flaw in the system, I'm going to thoroughly explain and support the arguments why it's a flaw. It's the engineer in me.
You keep saying pg. 445 is open to interpretation. There is no such openness to pg. 630. And if you're fine with interpreting the glossary to give the foolproof definition while the main entry, related main entries, and even other glossary entries have no such language... that's your choice. Again, this is Paizo's editing we're talking about here. I love them and their products, but their history of copy editing isn't exactly pristine... If a person doesn't happen to read that particular part of the glossary, but instead reads the main entry like most people would, then it's open to interpretation. Rules lawyers gonna rules lawyer. And again, I recognize ALL of this - I stated it from the very beginning - I just would like Paizo to define it once and for all. Maybe even correct the PDF later down the road - preferably before any pocketbook versions get released (I hope so!).
If you fail a check by 10 or more. Rolling equal to the check is not failing. Right? Without a explicit example/calculation/reference in the entry, it's subject to interpretation. Part of me wants to go with DC-10 because of simplicity, and because it seems like success is so much more common - at least it was with PF1e and the power players. I will say, after some test runs and a scenario in PF2e, it does feel like failure and especially critical failures happen a whole lot more often, noticeably so, and outweighed the critical successes. The math proves this, too. EDIT: I will add that part of this is due to some players wanting to skill check when they shouldn't (due to being PF1e veterans), so that definitely impacts things a bit, but there is something to it feeling more common, for sure.
It's a minimal frame around the reference point. The reference point is the DC.
In DC + or - 1, you need 4 points on the scale, absolute minimum. The die you use to roll against it is 100% irrelevant. You can use a d4 and be spot-on to my point. You can use a d100, and it still scales, you just need to adjust the framing. The percentages will change, but the fact remains that the scale is skewed to one side. The reason I use minimal framing is because any other number of points than the minimum is completely arbitrary (the number line stretches to infinity both ways).
The issue with "fail by X" meaning "DC-X" is that it becomes significantly more pronounced when you lower the value of X. https://i.imgur.com/8NbuXMc.png In this example, you can see that Fail by 1 or more means you just critically fail, with no chance of a regular failure. Ignoring d20 rolls, just looking at pure probability: At "Fail by 5" you critically fail 16.7% of the time as opposed to critical success at 8.3% At "Fail by 1" you critically fail 50% of the time, with critical success at 25% (regular success at 25%, too).
Thanks Mathmuse. It can be complex to convey, as I write below: Really this has taught me never to try to teach children probability with a number line. Yeah it's difficult for people to wrap their heads around when the starting point begins on a positive or negative point. I think it also stems from the fact that we all learn counting by starting positive, too (with 1), then we later learn about zero. Any time I teach students how to count binary, octal, and hexidecimal it blows their minds that we count decimal "wrong" - that we should really begin counting at zero (i.e.: zero is assumed). Decimal, using ten numbers for a single digit, is from 0 to 9, not 1 to 10 as we are initially trained.
A is 10, B is 11, .. F is 15... "Wait, what?" my students usually ask. Yeah, because 16 total places, starting with 0, all the way to "15" as F. I find the odometer is the best method to teach this, seeing the numbers "roll over" to the next digit helps people connect the dots. Minds begin to explode when "F" (15) rolls over to "10" (16).
But the rule for critical failure does not explicitly state "DC-10" - it states "... fail by 10" Does "fail by 10" mean:
It matters, because we already know that "succeed by 10" means "Success, and 10 more" - in the success scenario we moved 11 points away, in the failure scenario we move... 11 as well? or 10? That's the problem. That's it.
True, but you also don't hear of people saying "succeed by zero" either, but that's exactly what you are doing when you meet the DC. So, DC+10 is "succeeding by 10," yet it is technically the 11th success point on the scale: the DC and then 10 more points. If we kept things equidistant, "failing by 10" in your example would be the same distance away from the frame of reference (the DC) as "succeeding by 9." Your version of "failing by 10" counts the DC as one of the 10 points, but your "succeeding by 10" ignores the DC and moves an additional 10 points. It's wonky, I know.
Or have I just made up that rule and there is no special rule for a natural 1 and a natural 20? Nat-1 and Nat-20 just move the category of success down or up one, respectively. You still determine what the total is first, and where it lands on the scale, then step it down/up. I'm working on a GUIDE for my Pathfinder Society group, where I have some good (I hope) visual aids.
There is slightly more critical failure territory? GOOD. The game is stacked in favor of success as it is, failure needs to have some teeth to it. Hehe, agreed! I'm a bit torn on this one, but leaning slightly for the DC-10 method. Stil, the other side has something to offer and I wanted to argue the case thoroughly. I've had enough rules-lawyers at my tables to know what is headed my way... lol :)
It's uneven, but it matches what's stated on pg. 630 of the Core Rulebook. The problem is that specificity always outweighs other references. In order:
The entry for critical failure only says, "if you fail a check by 10 or more". The weapon critical hit entry does give some weight to DC-10... but at the same time, we've seen Paizo's history with copy editors has not always been the best. Looking at this being used in Pathfinder Society, I'm not sure which route to go. For now, I accept that DC-10 works and it's simple, but we have a ton of super geeks that play Pathfinder, and I know people will argue it, even if my chapter has decided DC-10 for now (until ruling from Paizo). I'm making my arguments from an "Arbiter" point of view. I see reasons for both, but I'll be damned if I can't make an argument for an unpopular but technically possible position. I just want clarification from an official source so we can cite it and be done with it.
This is probably the most simple way you can narrow this down: If a DC10 is a Success, and an 11 (DC+1) is a Critical Success, then if we strictly go by DC minus the window, then you could Critically Fail on a 9. There would be no failure window, only a critical failure window. That is why DC-10 is unbalanced.
If the Failure-10 method were applied to the same problem, then it makes a whole lot more sense.
Well I think most of this discussion is centering about the beat by / fail by definitions. That is indeed the crux of it: the book doesn't state explicitly that it is DC-10, only, "If you fail a check by 10 or more, that’s a critical failure" But if failing starts at DC-1... do we count from the start of failing, or do we count from the start of succeeding? One method is simpler, but unequal. The other is equal, but can cause a brief delay/complication. I see good reasons for both solutions. Failing by 10 or more results in a critical failure. The 5 is a critical failure. But this is never stated explicitly, you assume intent to mean one way. This is why it is an issue; the language isn't clear.
Here's another way to put it:
Instead of "positive result" think "right side" Instead of "negative result" think "left side" No matter how you cut it, if your starting point is a finger (an integer), then the distance from the far side of that hand to that reference finger will never, ever be equal to the distance from the opposite hand's far side to the reference finger.
There cannot be a "middle" with no value. You're conflating several things here. Yes, the number zero can obviously exist on the number line, like so:
That is not what I'm talking about here. You are treating the DC as if it were a zero in the sense of a NULL. It's not. It is a positive result, from the standpoint of a success vs. a failure. Again, my graphic chart illustrates this perfectly, where DC=0 but it also equals Success 1. Thus DC = DC+0 = S1. These things can all be true at the same time, I really don't understand why you chose to split hairs here on semantics when my points are clear. So if our reference point, the DC, or DC+0, or S1 is equal to a SUCCESS, which is a positive result, then it follows that DC+10 is 11 total points on a the number scale. The reference point is POSITIVE, not NULL. Period. Where it gets wonky is that the failure scale begins at DC-1, or F1. A negative result; a FAILURE. The question about this entire thread is whether or not the DC of a critical success is measured as DC-10, or F-10 (which is DC-11). The former method is easier, but it is not even-scaled, with only 10 points on the Failure scale, vs 11 points on the Success scale. You even got the set portions of this all correct, but you're skipping places: In my first example (DC15):
In my second example (DC0):
(the font type made it not line up, I tried to ease that a bit with leading zeros)
https://i.imgur.com/dXEIEtX.pngYour number line illustrating this problem contains 22 numbers. We are not rolling 22-sided dice. This is not a problem for 20-sided dice. Because this isn't about d20s alone, this is about the spectrum of results that can mean one of four possibilities: critical failure, failure, success, and critical success. The absolute minimum number of points on a scale to represent this is 22 points. Because we're using DC+10 as the high end of the spectrum, that means the DC (a number) + ten more numbers. That's 11 points on the positive end of the scale. The negative side of the scale needs an equal number of points. 11 + 11 = 22. But your reference of a d20 does have a point: as NA Palm put it, you cannot have a DC where it is possible for you to critically succeed and fail, not without the special nat-1 and nat-20 rules.
Zero is an integer. Obviously, but we're not measuring "nothing" in this application of number lines - we're measuring EITHER/OR, POSITIVE or NEGATIVE, that is, FAILURE or SUCCESS. There cannot be a "middle" with no value. Your starting point is on the SUCCESS side. A DC is a success. Therefore, a DC must be on ONE SIDE of the scale, NOT the middle. Your own graph states clearly, zero is neither negative nor positive. A total of a DC is a success, not nothing. If you absolutely must place a zero, you put it on the line between the two sides and you can't actually reach the number; It is the fulcrum of the scales. It only occurs when the two sides are balanced. EDIT: It's like the d20 rolls we mention. "Zero" as a middle point (10.5) theoretically exists as a division between measurement categories, but it cannot happen in reality. You will always end up rolling a low-end number (1-10, a failure on the scale), or a high-end number (11-20, a success on the scale). Negative or positive. Failure or success. There is no "null," a "nothing" roll is not possible.
The problem with a DC is that meeting it is a success, meaning it puts it on one side of the scale. It is not the fulcrum of the scale, it is the first weight placed on one side. Literally, the reference point (DC) is the first success point on the outcome scale. To make an equal counterpart for the scale to balance, there must be a reference point as the first failure point on the scale, which is DC-1. S1 = DC+0 and F1 = DC-1, right? Then it can only follow... S2 = DC+1 and F2 = DC-2
That's the only way the scale doesn't tip in one direction or the other. 11 points on both sides. 22 points/numbers/places total. That's it. DC-10 is not equal in scale to DC+10. It can't be.
The center of the scale is not a whole number (an integer). It cannot be. You must start on an integer, which means that an equal number of points must be on either end of the scale. Just like the center for any normal, even-sided dice is not a number that can be rolled. The middle of a d20 is 10.5, it is not an integer. But because 20 is an even number and you start on 1 (not 0), then the lower half is 1 through 10, the higher half is 11 through 20. That means each half has ten numbers, or ten points on each side of the scale.
It's kind of like looking at a 5' grid. You can't be on the line, you have to be in a square (Medium creatures, assumed). No, sorry. See this as for why. The reference point isn't a middle point, the reference point of a DC is already on one side of the scale. https://i.imgur.com/VH3taTN.png You are conflating the reference point and the center of the scale, which is simply not true.
Yeah, that's what I meant when I say there's no "zero" in this. The DC is on the "positive" side of the scale; there has to be a negative counterpart/reference-point. Both sides of the equation need balanced for the scale to be equal. It's kind of like looking at a 5' grid. You can't be on the line, you have to be in a square (Medium creatures, assumed). If you start measuring inside the house at the first 5' square (with the door on the threshold line), then +10' inside is just 2 squares from the door. Just because you're standing in the first square, doesn't mean that 10' outside the house is the first square outside, because 10' inside is only 1 square away. No, outside begins at square 1 as the first frame of reference, and is 2 squares from the door.
That's the whole purpose of all of this: what's the reference point when starting to determine failure? Critical Success is the DC+10, the reference point is the DC, where success starts, meaning Critical Success begins on the 11th point of the Success scale. Inversely, Critical Failure is "failing a check by 10 or more," but do we start with Failure as a reference point? That technically begins at DC-1, not at DC-0. Put it this way: Critical Success begins on the 11th point of the Success scale. Wouldn't Critical Failure also (because it's "the same") begin on the 11th point of the Failure scale, then?
Yes, maybe, but you see the problem, don't you? Success is also the DC, meaning DC and 10 more, 11 total places on a number scale. In the method you describe, means 10 less and minus the DC itself, 9 total places on a number scale. You hit critical failures sooner than you hit critical successes. https://i.imgur.com/dXEIEtX.png This is why it's a conundrum, and I really hope Paizo answers this. One method or the other, there is a loss: a loss of simplicity, or a loss of equal statistical outcomes.
For those trying to wrap their heads around the number scale problem, I tried to clarify a bit better here. https://i.imgur.com/dXEIEtX.png Pay special attention to the Success and Failure + or - in comparison to the DC + or -
But then the mirror of that would also be true. i.e.:
So at a 15 DC, failure is from 5 to 14, and critical failure at 4 and below. No matter how you cut it mathematically, there isn't a "zero" to start from; you have to be positive or negative in your number line. I just hope Paizo will clarify their intent. I'm fine with either answer, I see good reasoning for both points. I just want to know: are we officially going for simplicity, or are we going for even odds?
If we did that on the other side, then DC+0 = Success by one.
i.e.: 15 DC would critically succeed on a 24, not a 25, using that same reasoning.
Please see:
Essentially, the problem is this: The CRB (pg 445) states:
But that raises the question: since failing STARTS at the DC minus 1 (DC-1). Does that then mean critical failures start at DC-11, which is failure minus 10, ... or DC-10? First glimpse, it's easy to say DC-10, but you've got to remember that the success STARTS at DC+0. My visual aid demonstrates this much better. If it's DC-10, then you have TWICE as much of a chance of critical failure (9%) than you do of critical success (4.5%).
If it's DC-11, then it's all equal.
In an edition where simplicity is the goal, part of me wants to err on the side of simplicity and say critical failure is just DC-10... but I know the rules lawyers love these games, too. The math nerd in me hates this, as well - especially when +1 or -1 matters in everything else we do. |
Venture-Captain, Idaho—Boise 33 posts. No reviews. No lists. No wishlists. 33 Organized Play characters. 