Normal Distribution Resolution

This is part of the Echelon RPG Development series. Here are links to other articles of the series:

The design calls for a resolution mechanic that simulates a normal distribution, which when graphed looks like a bell curve. This means at least three dice must used. A dice pool using 3d6 is currently the chosen configuration. The 3d6 dice pool has a range of 3-18 and a mean of 10-11. A strong reason to use the 3d6 dice was for ease of determining Difficulty Ratings (working from a mean result of 10).

A mechanic with a normal distribution was chosen because I believe it more accurately reflects success in real life. With most single die implementations, you have the same chance of rolling any of its values, which does make sense to me. This method provides more consistent, if not cinematic, results.

Difficulty Ratings

A Difficulty Rating, abbreviated DR, is a target number that must be met or exceeded to attain success whenever a roll is required. Some DRs are static numbers derived directly from traits of the target. For example, it is always a DR 20 to pick an average lock. Other times, the DR may be the result of an opposed check.

Determining Success

When an action requires a roll to be resolved, three six-sided dice are rolled and the results are tallied. In addition to the total value presented by the dice, modifiers are also added to the total. If the final total meets or exceeds the Difficulty Rating, the action is successful.

Critical Success & Failure

With single die mechanics, critical success or failure is usually achieved by rolling the maximum and minimum die values respectively. Such die results also usually infer automatic success or failure. This method could be used in a multiple die system effectively making critical successes and failures very rare (requiring all three dice to display the maximum or minimum values).

Echelon uses the combination of open ended rolls and variance. While this means there are no automatic successes or failures, there may always a chance to succeed with open ended, or exploding, dice rolls.

Open Ended Rolls (Six Again)

In Echelon, characters may specialize in certain abilities. When rolling to resolve an action related to an ability a character has specialized, the player may designate a single die as an exploding die. Anytime the exploding die shows a value of 6, roll it again and add the new value to result total. If the new value is also a 6, repeat the process until anything but a 6 is rolled.

For example, if a player rolls the resolution dice and gets a 6 & 3 on the normal dice, and a 6 on the exploding die, he would add the results and get a 15. Then he re-rolls the exploding die and adds the result to his total. He continues re-rolling and totaling the result until the exploding die does not result in a 6.

A character may also spend resources to swap an exploding die into his dice pool for a single roll. Only one die may be added to a character’s dice pool in this manner. It is possible for a character to have more than one exploding die in his pool by having both types of exploding dice. The best way to distinguish the exploding dice is by denoting them with a different color.

Variance

Variance is the difference between the final sum of the roll after all modifiers have been applied and the DR. Some actions provide additional benefits if a roll exceeds the DR by a specific amounts. For example, if character casts fireball on a pack of wolves, and his roll has a variance of 5 more than the Difficulty Rating, he might gain an additional die when he rolls damage. This is called an Exceptional Success.

Variance also works in the other direction. For instance, if the same character had rolled 10 less than the DR while casting fireball, the roll would have a variance of -10. This is called an Exceptional Failure, and in this case would result in the character losing additional resources. The exact benefits and penalties of Exceptional Success or Failure is defined in an ability’s description.

Other Options

Another possibility includes using a 3d8 dice pool that has a range of 3-24 and a mean of 13-14. However, calculating DRs become unintuitive since the mean result is a 13. Another thought would be to use a mechanic similar to Savage Worlds where players roll two dice and take the higher of the two results.

Listening to: Ghoultown – Mistress of the Dark – Mistress of the Dark

5 thoughts on “Normal Distribution Resolution

  1. Been itching to put together some ideas for a d6 variant myself for some reason. Between you and Wyatt though I’ve got a lot to learn from.

    Eagerly looking for more.

  2. @The Last Rogue: Yeah, Wyatt’s NAA d6 stuff is a good read. You might also be interested in Michael Wolf’s Gears which is also using a 3d6 core mechanic, though it’s a roll-under paradigm.

  3. Have you concidered positive/negitive die options such as 2d8 – 2d8 it has a range from 14 to -14, an average of 0 and a standard deeviation of around 5 (4.5). This makes figguring out difficulty rateings really easy given the relativly easy given the nice numbers.

  4. I haven’t given them much consideration. Mostly because I’d like to limit the amount of dice being used and I’m really looking for a normal distribution. Add open ended rolls (required since I would like there to be that chance of anything can happen), and it would become a mess. Besides, everything is going to get complex real quick, thus I would like players to be concerned only about going one direction (addition) when calculating integers.

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