jmucchiello
Hero
Let me start by saying there are no right answers to this question.
In most d20 games, there are two circumstances for d20 rolls: rolls vs DC and opposed rolls. But math-wise, this means that some rolls have linear probability distribution with 20 discrete results and some rolls have triangular distribution with 39 discrete results where central results are more frequent. Is there a reason combat and saving throws are always linear rolls while SOME skill rolls are linear and SOME are triangular? Why is Stealth sometimes done against passive perception and sometimes done against an active perception roll?
Should there be two different random distributions in the same game system? And why not use the triangular one in more places? Why is AC fixed at 10+? Why not roll it? Why are saving throw DCs fixed? why not roll it for each spell? In both cases, the normal roll is linear but it could be triangular. We don't do it, my guess, because it would be too many die rolls: Announce casting a spell, roll d20, calculate DC, target rolls d20 to meet the target. Fixed DCs skip the roll and calculate steps.
And if triangular rolls are "bad" for combat and saving throws, why are they appropriate for SOME skill checks? What is special about skill checks? Is it because there are no auto failure/auto success in skill checks? Why is that so important that the range of the roll needs to expand from 20 to 39 result states with a different probability distribution?
That's a lot of questions but at the root the question is why are there two different probability distributions used in a system where the rules say there is one roll mechanic: roll d20, add mods, check if you reach the DC.
It's easy to "fix". Just use passive skill values for all skill check DCs. If the player is being stealthy, they roll against the guard's passive perception. If the player is being sneaked up on, they make a perception check against the sneak's passive stealth value. (Let the player make the rolls that affect their characters, right?)
But ultimately, does it even need "fixing"? I don't know. It was just something I noticed and it's been bugging me. I just want to hear some folks plea the case of having the two different die rolls. Maybe there's something I'm overlooking.
In most d20 games, there are two circumstances for d20 rolls: rolls vs DC and opposed rolls. But math-wise, this means that some rolls have linear probability distribution with 20 discrete results and some rolls have triangular distribution with 39 discrete results where central results are more frequent. Is there a reason combat and saving throws are always linear rolls while SOME skill rolls are linear and SOME are triangular? Why is Stealth sometimes done against passive perception and sometimes done against an active perception roll?
Should there be two different random distributions in the same game system? And why not use the triangular one in more places? Why is AC fixed at 10+? Why not roll it? Why are saving throw DCs fixed? why not roll it for each spell? In both cases, the normal roll is linear but it could be triangular. We don't do it, my guess, because it would be too many die rolls: Announce casting a spell, roll d20, calculate DC, target rolls d20 to meet the target. Fixed DCs skip the roll and calculate steps.
And if triangular rolls are "bad" for combat and saving throws, why are they appropriate for SOME skill checks? What is special about skill checks? Is it because there are no auto failure/auto success in skill checks? Why is that so important that the range of the roll needs to expand from 20 to 39 result states with a different probability distribution?
That's a lot of questions but at the root the question is why are there two different probability distributions used in a system where the rules say there is one roll mechanic: roll d20, add mods, check if you reach the DC.
It's easy to "fix". Just use passive skill values for all skill check DCs. If the player is being stealthy, they roll against the guard's passive perception. If the player is being sneaked up on, they make a perception check against the sneak's passive stealth value. (Let the player make the rolls that affect their characters, right?)
But ultimately, does it even need "fixing"? I don't know. It was just something I noticed and it's been bugging me. I just want to hear some folks plea the case of having the two different die rolls. Maybe there's something I'm overlooking.