Linear vs non-linear dice rolls

The current pathfinder system for skills has you roll d20 to find out if you did something. There’s some innate problems with this, due to the way a d20 works. Maybe Paizo were going for simplicity (though you wouldn’t know it from reading the Combat Manuevers section), standardizing dice rolls. Maybe they’re not sure how probabilities work (there’s actually some evidence for this). It ends up that by switching from 1d20 to 2d10, everything works a bit better.

This has huge implications by removing the linearity of the d20 roll in lieu of an actual bell curve of probability. What we’re actually checking on a skill roll is [How well you do something (roll) + at your current ability (+skill modifier) +/- the environment (outside modifiers)]. When you do something, you generally do it average for your ability level. Play guitar, work on a car or computer, paint, draw, etc. Whether you’re just starting out or you’re a master, you most often perform average for your ability. Your ability is represented by your +Skill Modifier. How well you do at a given time is your roll.

Yngwie Malmsteen can play guitar really well. He has a +20 modifier to Performance: Guitar Shredding because of this. If he’s having a terrible night because of hookers and blow (omg rolls a 1) he still gets a 21. That’s pretty damn good. Maybe the longhairs in the audience notice something’s amiss, but your mom is still impressed. Maybe he’s having an awesome night (rolls a 20) and it’s a concert for the ages that Rolling Stone can’t quit talking about. Most of the time he rolls a 9-12 and gives what most people consider a virtuoso performance in hair metal wanky guitar.

The problem is, d20 doesn’t do this. The mode of d20 is flat, in mathematical terms. You have the exact same chance to roll a 1 as a 20 as a 10. We want something closer to a bell curve, where things like 1 and 20 are at the extreme, and on average you’re in the 8-12 range. That doesn’t affect your innate ability or training (that’s the +skill mod), but on an average attempt, you perform average for your skill level.

We’re retaining the d20 for combat, because those 1s and 20s are part of the fun, and having them crop up more often leads to more dynamic combat.

Linear vs non-linear dice rolls

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