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Bell Curve or Linear?

Chris J

Registered User
Validated User
What gives a more accurate representation of a character improving her skills, 2d10 bell curve or 1d20 linear?

Also, what are the pros and cons of using a linear dice mechanic?

Thanks all.
 

Extrakun

Tinker of Games
Validated User
If we are talking about reality, and I am using learning software development as a benchmark here.

I think we can safely break skill levels into novice, journeyman, accomplished, expert, master and grand-master. Now, the gap between the first three can be staggering. However, after that , people specialize. It's impossible to be a master or grandmaster at everything (save for a few exceptional ones). From what I observe, it is usually a bell curve. A novice programmer takes a week to do what a journeyman can do in a few days, an accomplished developer takes one day, while an expert takes a few hours.

I don't know if this applies to other fields, though.

Now, a linear dice mechanic doesn't mean that that a journeyman is linearly more accomplished than the novice. If I assign the rung as such -- novice gives a +1 to the dice roll, journeyman +3, accomplished +6 and expert +8, there is sort of a curve there. A linear dice mechanic just means that a +1 increases the chance of success by 5% more increment (but as others may point out, the improvement is more than 5%. If you have a roll a d20 and need to roll a 1 to success, having a +1 bonus means your chance of success has doubled).

A linear curve is easier to figure out the probability of success. If I need to roll below 13 on a d20, I figure out that my chance of success is 60%. If I have to roll below 2d10, then it's harder for me to calculate the probability.
 

Heavy Arms

Registered User
Validated User
Just a note: 2d10 isn't a true bull curve. You need at least three dice for a proper curve.

The biggest practical difference is what you assume "improvement" means.

If you want improvement to mean increasing your maximum potential, it's probably easier to go for 1d20.

If you want improvement to mean more consistent performance around average, it's probably better to go for XdY.
 

Alban

Registered User
Validated User
It heavily depends on the experience system.
You won't have the same results if your skill levels all cost the same XP, or if skill levels are more an more expensive.
See also how the Basic Roleplaying experience system works. In order to improve a skill, you need to roll under your skill during an adventure, and over that same number after the adventure. Which means skills tend to grow faster the closer they are to 50%.

With completely linear systems,the difference between 2 skill levels is independent on difficulty. If 2 characters have a 4 points difference in skill level, then the one with the highest skill level will always have the same +X% chance of success when compared to the other one.

With bell-curves, or semi-bell-curves, the difference between 2 skill levels will also depend on the difficulty of the task. If A and B have respectfully skill level 10 and 11 in a 2d10+skill system, A will have 94% chance to beat Difficulty 14, and B 97%. Only a 3% difference.But versus difficulty 21, A has 45% chance of success and B has 55%. 10% difference.

Note, however, that chances of success should not be the only way to examine a resolution system. Past a given skill level, chances of success will only be a concern versus unusually high difficulties. Quality of success should then be a more interesting parameter.
 

PeteNutButter

Registered User
Validated User
I would say using "bell-curve"/nonlinear dice makes a game harder to balance. Things that take off in the extreme need to be carefully limited. In a 3d6 system for instance having more than 5 over your opponent in the roll or DC makes things very unlikely. I'm using a 3d6 system, but it has created headaches for me as well. I've had to create systems to allow characters ways to help close the gaps at a cost. "I.e. Spend x resource and get advantage..."
 

Chris J

Registered User
Validated User
This post is in relation to the other post I made concerning dice pools. I’m having a real headache trying to figure out a decent difficulty system that doesn’t screw with the probabilities.

Initially it was-1 success, -2 success, etc. But even that -1 seemed huge
 

Mister Gridlock

Registered User
Validated User
I don't think you should look at a dice mechanic in a vacuum. Example: in D&D, typically you're starting at level 1 with a +1 bonus to hit. The D20 is linear (5% chance to roll any number). This is a feature because it's so swingy. If you had a bell curve and were faced with an AC (target number) beyond the median, you'd miss more often than not; the linear die gives you a chance.

On the flip side, if you're playing hyper-competent supers, having a swingy die can mean you generate "failures" unpredictably--that's unsatisfying with the idea they rarely just fail at stuff; the dice pool is more reliable.
 

phatonin

Chaos is a bladder
Validated User
A bit late for the party, but here's my fancy: I much prefer linear. Chances are easier to grasp, scores are easier to balance, and modifiers are uniform.

Moreover linear is emulated with a single die, which reads without summing or counting. Only drawback, imo, is that a single die imposes hard boundaries to scores and modifiers.
 
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