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Is this considered ambiguous? I thought it was obvious that if you need an 11 to succeed, rolling 10 is "fail by 1", rolling 9 is "fail by 2", and rolling 1 is "fail by 10".
I've never heard of anyone saying, "fail by zero".
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.
So, what we've established is that different combinations of DC and skill modifier will have varying rates of occurrence for crit fails and crit successes.
Not at all. What has been established is the range of results that result in "basic success" is higher than the range for "basic failure" before either becomes critical. This means you basic succeed 1 earlier than intuition would say or crit fail 1 earlier, depending on point of view.
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So if I had to summarize this thread, I think it's:
Everything works fine, it's as intuitive as your expect it to be when someone says "DC+10" or "DC-10" and the only "problem" is that some people are annoyed that the probabilities for crit success and crit failure aren't equal (but they we're never actually expected to be equal once you start adding bonuses).
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So if I had to summarize this thread, I think it's:
Everything works fine, it's as intuitive as your expect it to be when someone says "DC+10" or "DC-10" and the only "problem" is that some people are annoyed that the probabilities for crit success and crit failure aren't equal (but they we're never actually expected to be equal once you start adding bonuses).
But the rule for critical failure does not explicitly state "DC-10" - it states "... fail by 10"
Does "fail by 10" mean:
a) "Failure, and 10 less" or
b) "Success, and 10 less"
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.
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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:
Errata > Specific Rule > Other Rules > Other References (glossary/index/etc.) > Other Materials.
If a rule is clearly defined in two different places, and it is defined differently such that the two are in conflict, you use the more specific one.
If a rule is ambiguously defined in one place (as you are asserting) and clearly defined in another place, and it is defined differently such that the two are in conflict, shouldn't you use the one that's clearly defined? Especially if that clearly defined rule exactly matches one of the two interpretations of the ambiguous rule?
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.
Sorry, but I can still not agree to this, because beat by 10 and fail by 10 are equidistant IF we considering that exactly matching the DC is considered our starting point.
Lets take the referenced DC15 check.
If you roll 14 you fail the DC by 1, i.e. you are one result worse than you needed to be.
If you roll 16 you beat the DC by 1, i.e. you are one result better than you needed to be.
Continue in both directions and you will end up with.
If you roll 5 you fail the DC by 10.
If you roll 25 you beat the DC by 10.
And yes, if you count total sucesses going from 15 to 25 that is 11, while counting total failures from 5 to 14 are only 10.
However both 5 and 25 are equidistant to 15.
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So I figured the heuristic I'm going to use:
DC+10 is the number you need to match or exceed to critically succeed (DC+10 ≤ x)
DC-10 is the number you need to be less than to critically fail. (x<DC-10)
The asymmetry is explained by having "meeting the DC" being a success rather than a failure.
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True, but the statement that DC+-10 makes critical failures more likely than critical success across the entire spectrum of possible DCs is objectively true. It is only noticeable when you need to roll a 12 or higher on the die, but it is always present.
The assertion that DC+-10 makes Critical Failures twice as likely as Critical Success is flatly wrong.
If you need a natural 12 to succeed, you have a 10% chance of critical failure and a 5% chance of critical success.
If you need a natural 9 to succeed, you have a 5% chance of critical failure and a 10% chance of critical success.
Both of these are 1 number off from the 10/11 "middle" part of the d20. Seems pretty balanced to me.
There is no middle part in this scenario. Or more precisely, the middle is an actual value:
With no die modifiers:DC: 11 (5% critical fail / 45% Fail / 45% success / 5% critical success).
DC: 10 is (5% Critical fail / 40% Fail / 50% success / 5% critical success.)
which would be symetrical to a DC of 12 in a balanced math system.
DC 12 is (5% critical Fail / 50% Fail / 40% success / 5 Critical Success)
Interpreting the system as a +/-10 system of DC as the center point value results in
DC: 12 is (10% Crit fail / 45% Fail / 40% success / 5% critical success)
and that 5% shift towards critical failure remains present through flat checks against DC 19.
A +1 that moves you from requiring a roll of 12 to a roll of a 11 is the most valuable bonus in the game, and is wildly more valuable than a +1 that moves your from an 11 to a 10 which has no impact on your critical success or failure.
This shift means that you are 5% more likely to Critically fail, rather than Fail for every DC between 12 and 19, while you do not get the same benefit from DCs with values between 1 and 9 to critical success. Hence why critical failure is the result that benefits from this interpretation of the math, NOT success.
Which everyone seems fine with until they are having to make flat checks to not die and the likelihood of death just got tangibly more real.
Arguing that critical fail is not important to the game is ignoring saving throws, skill checks and flat checks, all of which are very important to not critically fail. And the kicker is that +/-10 is not simpler or more elegant than understanding that "ties always go to the roller."
So I figured the heuristic I'm going to use:
DC+10 is the number you need to match or exceed to critically succeed (DC+10 ≤ x)
DC-10 is the number you need to be less than to critically fail. (x<DC-10)The asymmetry is explained by having "meeting the DC" being a success rather than a failure.
this heuristic is the balanced mathematical model:
For DC 15x<DC-10 = less than and not including 5.
DC+10 ≤ x = 25
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Regardless of what the official ruling is on this, making it crystal clear in the example text starting on page 14by including exact numbers that demonstrate the intended method would be a great way of avoiding this confusion.
This shift means that you are 5% more likely to Critically fail, rather than Fail for every DC between 12 and 19, while you do not get the same benefit from DCs with values between 1 and 9 to critical success. Hence why critical failure is the result that benefits from this interpretation of the math, NOT success.
Why do you not get the same benefit to critical success?
Natural 9 needed to succeed: 10% critical success chance
Natural 8 needed to succeed: 15% critical success chance
Natural 7 needed to succeed: 20% critical success chance
And so on.
Because 12 matches 10 not 9. You are one number off. The mistake was mine in the original post when I listed 1-9 instead of 1-10.
There is no middle part in this scenario. Or more precisely, the middle is an actual value:
With no die modifiers:DC: 11 (5% critical fail / 45% Fail / 45% success / 5% critical success).
DC: 10 is (5% Critical fail / 40% Fail / 50% success / 5% critical success.)
which would be symetrical to a DC of 12 in a balanced math system.
DC 12 is (5% critical Fail / 50% Fail / 40% success / 5 Critical Success)...
DC 11 ist not the average. This is only the check result or DC that allows for a parity of failures and sucessess including critical failures and successes.
The average roll or DC would be 10.5, which means that your example is flawed as DC10 is only 0.5 away from the average, whereas DC12 is 1.5 away from the average.
DC12 is equivalent to DC9, not in terms of results, but in terms of distance.
Natural 9 needed to succeed: 10% critical success chance, 5% critical failure chance
Natural 12 needed to succeed: 5% critical success chance, 10% critical failure chance
How do 9 and 12 not match?
Natural 9 needed to succeed: 10% critical success chance, 5% critical failure chance
Natural 12 needed to succeed: 5% critical success chance, 10% critical failure chance
How do 9 and 12 not match?
Obviously because 9+1 is 10
And12-1 is also 10.
(Less sarcastically: if 9 and 12 match (one success and one failure), then 10 and 11 match, centered around the midpoint of success. Except that 10 is a success! It can't be "paired" with 11 in the same way.)
Less sarcastically: if 9 and 12 match (one success and one failure), then 10 and 11 match, centered around the midpoint of success.
Yes, I agree. Needing a natural 10 to succeed and needing a natural 11 to succeed match, and they both have an equal 5% chance each to critically succeed and critically fail.
Except that 10 is a success! It can't be "paired" with 11 in the same way.
10 is a success on... what?
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The existing rule (DC+-10) is more balanced with regard to crits than DC+10, DC-11 would be.
We can calculate the exact probabilities for Flat Checks (no modifier).
The probabilities for a DC:X Flat check is the same for any situation in which you need X on the die to meet the DC.
Therefore by calculating all the probabilities of Flat Checks 1-20, we can see all the probabilities for any check except the most extreme edge cases in which even a 1 or a 20 would not be enough to get to the DC.
We can see that there is a higher chance of success over all, but in terms of Crits they are almost identically probable across the distribution, with actually a tiny tiny edge in favor of Critical Success.
The assertion that Crit Fails are more likely is just not true.
Note: I don't want anything I have said to be taken as an insult, the confusion is very understandable, but I hope the visual helps.
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This is a problem that had not escaped my notice, being the math nerd that I am (although I imagine we'll be seeing Mathmuse in this thread shortly, leaving me quite outclassed :P ).
Sorry about being late to the discussion. I had three separate errands to run today.
Whole lotta overthinkin' goin' on.
Overthinking is my way of life.
Outrider is correct. The way the Pathfinder 2nd Edition Core Rulebook describes critical success and critical failure on page 445, a d20 check has at most 10 different d20 outcomes that are regular success, with fewer if the DC is higher than average or if the DC is so ridiculously low that critical success is more likely than regular success. In contrasst, a a d20 check has at most 9 different d20 outcomes that are regular failure, with fewer if the DC is lower than average or if the DC is so ridiculously high that critical failure is more likely than regular failure.
Nine is less than ten, so in general regular failure is 90% as likely as regular success.
This does not change the ratio of critical failure to critical success. The exact value of the DC could give that apparently missing chance of regular failure to critical failure, but if the DC were lower by one than that apparently missing chance goes to regular success instead--and if regular success is already maxed out at 10 chances then it goes to critical success.
I am embarrassed that I did not spot this during the playtest. I checked the wording in the Playtest Rulebook and it is even clearer: "If you fail and roll a 1 on the d20 (also called a “natural 1”), or you fail and your result is equal to or less than the DC minus 10, you critically fail instead of just failing." I performed over 4 dozen calculations during the playtest where I assumed that the maximum chance of regular failure was 10 out of 20, yet the playtest rules blatantly gave a cutoff that gave only 9 chances out of 20.
I am especially embarrassed because spotting such gaffes has been part of my work. I wrote technical documentation and knew how to describe mathematics accurately to the layman. Moreover, I was a grader for the USA Mathematical Talent Search high school mathematics contest and I cringed every time some bright student made a mistake because a problem was phrased badly. I became a problem evaluator for that contest—and I still do so in retirement—and regularly point out how to reword mathematical language so that high school students will interpret it correctly.
The language in the rulebook is symmetrical. However, DCs are asymmetrical, so symmetrical language that falsely assumed the numbers were symmetrical created an asymmetry of its own.
Difficulty Class (DC) treats success and failure differently. If the DC is 15, then rolling a 15 or higher (after modifiers are applied) is success. Rolling a 14 or lower is failure. But where did that 14 come from? It is the cutoff for failure just like 15 is the cutoff for success. In order to have 10 chances out of 20 for failure, we would need that the rules mention the 14. But the rules don't.
Let me compare the cases symmetrically.
(1a) Rolling DC+10 is the lowest result for critical success. (1b) Critical success has no highest result.
(2a) Rolling DC exactly is the lowest result for regular success. (2b) Rolling DC+9 is the highest result for regular success.
(3a) Rolling DC - 9 is the lowest result for regular failure. (3b) Rolling DC - 1 is the highest result for regular failure.
(4a) Critical failure has no lowest result. (4b) Rolling DC - 10 is the highest result for critical failure.
The DC - 10 in sentence 4b reflects the DC+10 in sentence 1a. The DC - 9 in sentence 3a reflects the DC +9 in sentence 2b. The DC - 1 in sentence 3b does not reflect the DC unmodified in sentence 2a. The symmetry is broken and regular failure is shortchanged out of one of its rolls.
The way bonuses are converted into DCs exaggerates the asymmetry even more. The average of a d20 roll is 10.5, halfway between 10 and 11. If we wanted a 50-50 chance of success, the DC ought to be 11, since that gives 10 numbers, 11 through 20, that would be success. I presume that most people think that an attack bonus equal to an armor bonus ought to be a 50-50 situation. But if the bonus to weapon attack is +7 (+4 Strength bonus, +3 trained 1st-level proficiency) and the bonus to armor is +7 (+1 light armor, +3 Dexterity bonus, +3 trained 1st-level proficiency), then we have d20+7 versus AC 17, so the attacker succeeds on a roll of 10 or more, 11 chances out of 20 for regular or critical success. The equal chances, combined with the natural 1 and natural 20 system, mean that out of 20 possible outcomes, we would have 1 critical failure, 8 regular failures, 10 regular successes. and 1 critical success.
If we increased the DC by 1, then out of 20 outcomes we would have 1 critical failure, 9 regular failures, 9 regular successes. and 1 critical success. If we instead decreased the DC by 1, then out of 20 outcomes we would have 1 critical failure, 7 regular failures, 10 regular successes. and 2 critical successes.
The good news is that for these three DCs, the shortchanging of regular failure does not matter. It only matters when we increase the DC by 2 more than the balanced-bonus case: 2 critical failures, 9 regular failures, 8 regular successes. and 1 critical success. The opposite case, reducing the DC by 2 less than the balanced-bonus case is 1 critical failure, 6 regular failures, 10 regular successes. and 3 critical successes.
I suspect that the ease of counting is going to have more of a positive effect on play than the slight inaccuracy of the math will have a negative effect, though.
We can still have ease of counting with more symmetrical math. It is just a matter of changing "less than or equal to" to "less than."
You critically succeed at a check when a check’s result meets or exceeds the DC by 10 or more. If the check is an attack roll, this is sometimes called a critical hit. You can also critically fail a check. The rules for critical failure—sometimes called a fumble—are the same as those for a critical success, but in the other direction: if you fail a check by 10 or more, that’s a critical failure.
A wording that would give proper symmetry between regular success and regular failure would be:
You critically succeed at a check when a check’s result exceeds the DC for success by 10 or more. If the check is an attack roll, this is commonly called a critical hit. You also critically fail at a check when the check's result is 10 or more below the result for failure, that is, less than DC - 10. A critical failure is sometimes called a fumble.
NOTE: I realized that the current definition of critical success, "You critically succeed at a check when a check’s result meets or exceeds the DC by 10 or more," is erroneously worded. Since it is impossible to meet a check's result by 10 or more, since "meet" means "have the same value as," the modifier "by 10 or more" cannot be applied to "meet." Therefore, the literal interpretation is that rolling the DC exactly also counts as a critical success, though rolling 1 through 9 more than the DC is only a regular success.
Really this has taught me never to try to teach children probability with a number line.
Rolling a single die does not match up to numbers on a number line. The average (as mean) is useless in this scenario because it does not exist.
No one sets a DC of 10.5 (although perhaps it would be easier if they did).
In a probability system determined by a single die roll with more than 2 ranges of significance (in this case 4) you cannot model the equation around a number line unless you are willing to admit that equal to only matters when trying to move into the next range of values.
Apparently I am not good at explaining matrices, ranges and arrays, because I am not a mathematician and I am sorry for that, but it is clear to me that the center point of understanding checks vs DCs would be the point where the scale is perfectly balanced.
In PF2 that point is DC 11, because it yields a perfectly distribution (5/45/45/5).
A balanced model would see that moving 1 space from that number should result in equal symmetry:
10 - (5/40/50/5)
12 - (5/50/40/5)
It takes a deliberate effort to push the entire scale towards critical failure to move the posts to
10 - (5/40/50/5)
12 - (10/45/40/5)
for a net result of what: assuming that +/-10 does not require understanding the difference between greater than or equal to, and less than?
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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.
Binary, using two numbers for a single digit, is from 0 to 1.
Hex, using sixteen numbers for a single digit, is from 0 to F.
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).
10 is a success on... what?
Except that 10 is a success! It can't be "paired" with 11 in the same way.
On a DC 10 with a +0 modifier.
Why a +0? Because the + is irrelevant when talking about natural d20 values.
By the way, I love how you decided that "these are a pair" (9 & 12, failure & success) "the same way these are a pair" (10 & 11) "and also 10 is identical to 11" (success & success) without throwing a Exception.
The place where the argument that failure (not counting critical failure) should have a maximum range of 9 breaks down for me is when I look at the simple case of the flat check to avoid dying.
In theory, it makes the most sense to me that each time your dying condition increases by one, the probability of you dying should increase by an equal value.
At Dying 1
You are making a check vs a DC 10+1 for 11.
that fits the 5% Crit Fail, 45% fail, 45% Success, 5 Crit Success. We are all on the same page.
If I fail this check, I gain Dying 2 for a DC of 12.
Suddenly the 5% shift in probability jumps straight from success down to critical failure:
10% critical fail, 45% Fail, 40% success, 5% Critical success.
That is a 100% increase in the crit fail value right at the point where getting a critical failure would kill me, when a balanced model should see a DC 12 scale of
5% Crit fail/ 50% failure / 40% success, 5% Critical success.
Even though it might feel like those odds are the same 55% bad/45% good, it is a brutal jump in lethality that does not make the game better for players in any way.
I yield to Mathmuse on the wording of the rules as speaking clearly about math is his job, and so I guess the CRB does have an asymmetrical system because of the inclusion of that "equal to" in the sentence about critical failure, but I strongly contend that it is a mistake that should be corrected and not the intention of the developers, who are also fairly good with math themselves.
This is a pressing and serious issue. Or else I am too soft on players and thought that the math system should always give benefit to the roller/encourage better results, not worse ones.
10 is a success on... what?
Except that 10 is a success! It can't be "paired" with 11 in the same way.
On a DC 10 with a +0 modifier.
Why a +0? Because the + is irrelevant when talking about natural d20 values.
By the way, I love how you decided that "these are a pair" (9 & 12, failure & success) "the same way these are a pair" (10 & 11) "and also 10 is identical to 11" (success & success) without throwing a Exception.
Yes, rolling a natural 10 with a +0 modifier on a DC 10 check is a success. I do not see how "it can't be paired with 11" follows from that.
And thank you for complimenting my ability to not throw an exception.
Yes, rolling a natural 10 with a +0 modifier on a DC 10 check is a success. I do not see how "it can't be paired with 11" follows from that.
So, then how does it pair-up-with-the-opposite-result (9 is a failure and "matches" with 12 which is a success) with an 11?
How do 9 and 12 not match?
Wait a minute. Page 10 of the PF2 CRB says: "Similarly, failing the check by 10 or more is a
critical failure (sometimes called a fumble)."
It actually does specify that your roll would be failing by 10 or more, not that the number you rolled is equal to 10 less than the DC. There is nothing to see here.
Failure has a range of 10 just the same as success.
with no bonuses against a DC of 12
a 22 or higher is a critical success.
a 12 is a success.
a 2 is a failure.
Less than 2 (so 1 or less) is a critical failure.
@Unicore
You may want to check out this reddit thread explaining the probabilities of the dying condition.
At dying 2 you are looking at DC 12 and only crit fail on a 1. My concern has passed since I saw the clarification in the rule book that the range on failure is 10.
Yes, rolling a natural 10 with a +0 modifier on a DC 10 check is a success. I do not see how "it can't be paired with 11" follows from that.So, then how does it pair-up-with-the-opposite-result (9 is a failure and "matches" with 12 which is a success) with an 11?
How do 9 and 12 not match?
The pairing is based on the chances of critical success and critical failure.
I read "failing by 10 or more" as "if you added 10 to your result, you would still have failed."
So a roll of 5 on DC 15 does not fail by 10 or more, because if you added 10 it would succeed but a roll of 4 does.
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Wait a minute. Page 10 of the PF2 CRB says: "Similarly, failing the check by 10 or more is a
critical failure (sometimes called a fumble)."It actually does specify that your roll would be failing by 10 or more, not that the number you rolled is equal to 10 less than the DC. There is nothing to see here.
So you would also say rolling DC-1 would count as failing by 0?
I would say:
DC+10 Secceed by 10
...
DC+1: Succeed by 1
DC: meet <-- ties go to roller, but are succeeding by +-0.
DC-1 fail by 1.
...
DC-10 fail by 10.
I agree 100% the wording in the book is pretty bad.
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Wait a minute. Page 10 of the PF2 CRB says: "Similarly, failing the check by 10 or more is a
critical failure (sometimes called a fumble)."It actually does specify that your roll would be failing by 10 or more, not that the number you rolled is equal to 10 less than the DC. There is nothing to see here.
Failure has a range of 10 just the same as success.
with no bonuses against a DC of 12
a 22 or higher is a critical success.
a 12 is a success.
a 2 is a failure.
Less than 2 (so 1 or less) is a critical failure.
A result that is 10 lower than the DC has failed by 10.
critical
You can get a greater success—a critical success—by rolling 10 above your DC, or a worse failure—a critical failure—by rolling 10 lower than your DC. 445–446 critical hit (Strike) 471 critical specialization (weapons) 283–284
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This is going to be the new "DC to jump over a 10 foot pit" right?
Did PF1 have this issue with rules that said "If you fail by 5 or more, this bad thing happens"?
Did PF1 have this issue with rules that said "If you fail by 5 or more, this bad thing happens"?
Yes they had similar rules, e.g. climbing, however I am no aware of any issues.
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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).
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).
If we ignore the fact that we're rolling a d20, and ignore the rule that a natural 1 or 20 adjusts the degree of success, then yes, the system would be broken.
But "the system is broken if we ignore the rules" is not a compelling argument.
page 445 from chapter 9 repeats the same language:
"You critically succeed at a check when a check’s result
meets or exceeds the DC by 10 or more. If the check is an
attack roll, this is sometimes called a critical hit. You can
also critically fail a check. The rules for critical failure—
sometimes called a fumble—are the same as those for a
critical success, but in the other direction: if you fail a
check by 10 or more, that’s a critical failure."
If you fail a check by 10 or more. Rolling equal to the check is not failing.
Against DC12, an 11 is the highest roll that would be a failure. Subtract 10 from that to know what would be a critical failure.
The rules are pretty clear.
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It's a minimal frame around the reference point.
The reference point is the DC.
The frame is the minimum window required to show the range of numbers needed to convey all possible outcomes (C.F., Failure, Success, C.S.).
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).
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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.
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You keep saying pg. 445 is open to interpretation. There is no such openness to pg. 630.
It is also important to realize that they deliberately changed the language from the play test to make this clear. THe playtest lists:
"If you fail and roll a 1 on the d20 (also called a “natural
1”), or you fail and your result is equal to or less than the
DC minus 10, you critically fail instead of just failing"
which is what Mathmuse was quoting.
The developers saw this problem and changed the actual text to try to make it clear.
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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!).
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).
I do not comply with your graphs. For me DC-1 IS F-1 as for DC15 a roll of 14 is failed by 1 and not failed by 0.
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You keep saying pg. 445 is open to interpretation. There is no such openness to pg. 630.
This. To quote p. 630 (emphasis mine):
You can get a greater success—a critical success—by rolling 10 above your DC, or a worse failure—a critical failure—by rolling 10 lower than your DC.
If this contradicted p. 445 it would be one thing, but it doesn't because p. 445 is ambiguous. Which means I'd definitely go with it.
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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.