System Design Notes: Percentage Based Systems

The Basics

There are two major ways to handle percentage rolls: use a d100 and modify the score rolled under, or modify the die type used to accomodate different situations. The both have very different probability distributions. The modifier based system simply shifts a constant distribution, making each +1 and increase by at most one percent. Obviously if the score is an automatic success or failure this won't change things much. For the dice varying version and increase of +1 can cause a 5 to .5 percent increase, depending on the difficulty die. The other major difference is that a low score can always succeed with a die based system, where as a small negative difficulty can invalidate a low score easilly. In either case scores above a certain level (based on difficulty) are automatic successes. While addtions can be made to provide "fluke" effects, these are typically add-ons, rather than consistant with the percentage based system.

Another question of a percentage based system is what to base the degree of success on. Usually this is some variant of the amount rolled under, but a few other options exist, such as those in Unknown Armies.

Probability Fitness

The major difficulty in deciding if a mechanic is well suited to a segment of skill familiarity is to distinguish between the class of actions that are "easy" and the class that are "hard". The simplest way to do this is to describe a set of actions that are reliable at a skill level (around 100%) and a set that are unreliable (around 50%), and if desired a set that are flukes (around 5%). For the purpose of this analysis I'll just ignore the flukes, especially since these typically rely more on the "fluke" effects mentioned above, than difficulty modifiers. Essentially we can assume that if flukes are desired they will occur whenever the probability is effectively 0%.

Another major concern is defining the segements, again for our purposes I will take a simple three tiered route: Natural, Skilled, Mastered. This provides up to six different difficulty levels. What defines the strata of characters in a game is how much separation there exists between actions that are unreliable for the lower tier and reliable for the upper tier. The two adjustable quantities are between Unreliable Natural and Reliable Skilled actions, and between Unreliable Skilled and Reliable Mastered actions. In these two cases the easiest choice is to make each pair equivalent, either in terms of modifier or die type. For the purpose of this analysis I will do just that. Hence we have: Reliable Natural (RN), Unreliable Natural (UN), Unreliable Skilled (US), and Unreliable Mastered (UM), as our four key levels of difficulty.

Additive Modifers

When we have an additive modifier system the key choice is what will the 0 modifier difficulty be. In order to demonstrate the ramifications of a zero point I'll show what happens when 0 is chosen for each of the difficulty classes.

0 modifier (RN) (UN) (US) (UM)
Average Natural 100 50 0 -50
Average Skilled 150 100 50 0
Average Mastered 200 150 100 50
(RN) 0 +50 +100 +150
(UN) -50 0 +50 +100
(US) -100 -50 0 +50
(UM) -150 -100 -50 0

Dice Based Difficulty

One of the key problems using dice based difficulties is that there is a rather course range:

Die Type: Set 1 picks: Set 2 picks:
d10
d20 X
d30
X
d40 X
d50*
d60
X
d80 X
d100
X
d120 X
d150*
d200
X
d300 X
* - harder to roll, so not preferred for a default difficulty value.

Based on this table we can start the four tier difficulty list at any of four main values. So we can look at (RN) being 1d20, 1d30, 1d40, or 1d60:

Average Natural 20 30 40 60
Average Skilled 40 60 80 100
Average Mastered 80 100 120 200
(RN) d20 d30 d40 d60
(UN) d40 d60 d80 d100
(US) d80 d100 d120 d200
(UM) d120 d200 d200 d300

Fixed Difficulty Systems

More a setting choice than a system choice, you can simply ascribe the vast majority of actions to a single difficulty tier. Set the modifier or die type to 0 or d100 respectively and play the game. This tends to be abusable if outs are not provided. For example, actions significantly easier than the tier should simply be automatic, where as actions significantly above the tier are not possible. Perhaps this can be situationally avoided due to resource use, or perhaps this is simply a setting appropriate constraint. In either case this allows the intuition of the percentage to be more direct for the player, as in a 39% chance is always a 39% chance, never more or less.

Percentile Systems

A percentile system is very different from a percentage system, even though they both rate a like number. In a percentile system a character's ability is determined relative to a difficulty or an opponant, rather than a percentage of success. This is more reminiscent to standardized test result, and provides a stronger sense of statistical meaning to the character's ability. If he has a 99 percentile he is in the top 1% of the population, and will tend to dominate the field. In case given a normal task he will perform it with near certainty, but even some one with 95 percentile is not going to fail that same task five times more often. Rather they will be nearly indistinguishable until a harder task is used, and even then the 4 percentile difference may not be enough to distinguish on a single action.

The simplest way to perform a percentile system to have two numbers: the difficulty and the breadth. The roll is performed by taking the difference, if positive then the each full breadth provides a another die. Any successes will cause the roll to succeed. Likewise if it is negative any roll as many extra dice as each full breadth and if any one of them fails the roll fails. In this case degree of success should be decided in advance, i.e. how much will be risked, so it is based on the difficulty of the roll. Opposed rolls use the opponant's percentile, plus any difficulty additions. In developing this system I tended to use coin flips, with heads as success and tails as failure. This seems to work fairly well, but modifications can be performed especially if the dice will be changed instead of changing the breadth value. As far as breadth a value between 5 and 10 seems good, with variance based on ability.


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