I’ve been digesting the rules and find myself stumbling over the idea that advantage with a zero attribute involves rolling 2d20 and keeping the high one. Whereas advantage with a 1 in an attribute (1d4) is 1d20 + (2d4 keep the highest 1). It makes sense keeping in line with the mechanics but the maths seem a little off. Advantage with a zero attribute gives a 51% chance to success on a CR 15, up from 30% for a straight 1d20 roll. To get that same chance with an attribute 1 you would have to have your attribute die explode. Said a different way, 75% of the time you’re better off having a zero in an attribute than a one, provided you have advantage on the roll.
Also, because you are rolling 2d20 and keeping the highest you are doubling your odds of rolling a 20 and having the d20 explode. This is actually a pretty big deal as an extra 5% chance of exploding a 20 with the way damage is calculated is a huge advantage.
Is this just a quirk of the system or am I missing something (very possible)? I’d be inclined to just give a player with a zero attribute a +1 in a situation where they had advantage. Definitely less interesting, but helps to keep attribute scores of 1 worthwhile.
However, a Score of 0 has a MAX of 1 advantage or disadvantage, whereas every other is without limit.
Also, an attribute score of 0 is very unlikely to be used for a damaging attack (OL is about what make sense, and the GM can rule that it makes sense you can’t use a weapon to attack with a Score of 0 without disadvantage), and the sheer amount of higher average of rolls with any other attribute, not even counting higher advantage amounts, makes having a 0 score far less likely to be used.
Can it explode, sure, so can anything, but the averages and the math end up better for any other attribute then 0 when more advantage is applied.
There have been a lot of people that have done graphs and math about it in the past.
TLDR;
Yes, it is known, and it is in the design, but not a real concern in the bigger scope.
Not suggesting that I discovered anything, just pointing out that it seems problematic in an otherwise decently wrought system. Mostly wanting to clarify that I wasn’t missing anything else as I’ve just discovered the system.
I get that it was easier to make the rolls consistent than to move mountains for a small balance in the math. It seems like a simple, and well known, flaw that is easily worked around. Good to know. Thanks!
Yes, you’re right on the money here. It’s a small discrepancy that wasn’t worth the complications in the rules to fix for an “issue” that very rarely comes up in actual play. No need to even work around it in my experience, I’ve played with mathematicians who didn’t notice that this was a thing.
I think the only thing that you are missing is that the average roll for an attribute score of 1 is still always higher than any equivalent roll with an attribute score of 0. Otherwise, you are spot on. You can find more detailed results of the average rolls here: Average Roll Breakdown by Attribute Dice
This would obviously change if you’d allow more than 1 advantage on the d20, but that’s why the attribute score of 0 has a cap, while no others have.
Everyone here talking about advantage, but just in case I want to say that this also applies with disadvantage.
Attributes with a 0 in their score can only accumulate a maximum of 1 advantage or disadvantage die.
As the online rules said: You are so untrained and inefficient at the skill you can’t use the cumulative advantages that arise, as well as disadvantages that occur.
A 1d4 + 1d20 can still end up rolling higher than a flat d20 due to explosions. The d4 has 25% chance of exploding, and even more with even just 1 advantage dice. Also…
Statistically speaking, correct me if my math sucks here, but the benefit of getting to a score of 1 is that it sucks less to have disadvantage. since you are keeping the lowest d4 and keeping the 20, rather than the lowest of the 2d20’s.
Using my rough estimation of the probability, you should roll higher with disadvantage 1 on a score of 1 than a score of 0. More frequently higher at least…
And also, keep in mind extraordinary attributes cannot be used if you have a score of 0 in it so the little discrepancy shouldn’t matter.
I think this makes sense that the probability is a little skewed when transitioning from no training (0) to having minor training (1).
Obviously those without any experience in the extraordinary attributes (A generic representation of your campaigns power system whether it be magic, or technology, or what have you) cannot ever use them.
And for the attributes that anyone can have, the Physical, Social, and Mental sense.
I think it makes sense untrained people are unpredictable with just their flat d20 rolls and can sometimes roll higher than a person with a score of 1 if they get even the slightest advantage in their side.
There are just some times where people get that noob luck.