This involves a lot of poking numbers, wrangling probabilities, and dusting off some high-school probability and statistics lessons. I've found AnyDice to be very useful for visualising things.
The basic mechanism by which tasks are resolved; this part is pretty simple, the complexity comes with working out how and when to apply modifiers, and how to interpret the results.
d20 + modifiers vs. Target Number
There are a number of choices to be made here.
Use an attribute, or a modifier derived from that attribute?
The mean (average) value of a d20 roll is 10.5, so a target number of "more than 10" gives a chance of success of 50%. Assume the average attribute to be 10.5 (the mean result of rolling 3d6).d20+attribute gives a mean result of 21, so a target number of "more than 20" gives a chance of success slightly above 50%.
If rolls are modified based on an attribute (for example, +/-1 point for every point above/below the average of 10-11) then as long as average attributes give a modifier of zero, a target number of "more than 10" gives a chance of success of 50%. For example:
| Attribute | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10-11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Modifier | -7 | -6 | -5 | -4 | -3 | -2 | -1 | 0 | +1 | +2 | +3 | +4 | +5 | +6 | +7 |
Using attributes keeps things simpler on the character sheet; modifiers generally use smaller values that are easier to deal with, but there may be more of them involved. For example:
14 (d20 roll) + 16 (attribute) + 2 (situational modifier), target number >20
vs.
14 (d20 roll) + 5 (attribute-derived modifier) + 2 (situational modifier), target number >10
Conclusion: Undecided at present; on the one hand using modifiers means adding smaller numbers together, which is less taxing from a mental arithmetic point of view; on the other hand I'm advised that players hate negative modifiers, even if the underlying mathematics are the same.
Use a flat modifier, or additional dice?
Even if we use "d20+attribute", there are circumstances in which we might still want to apply modifiers - skill tests, situational advantage, that kind of thing. So is it preferable to just apply a flat modifier, or roll extra dice?
1d20 gives a mean value of 10.5, with results between 1 and 20.
1d20+5 gives a mean value of 15.5, with results between 6 and 25.
1d20+1d10 gives a mean value of 16, with results between 2 and 30.
So while both of those modifiers give a similar mean result, the range of possible results is wider when using dice rather than a flat modifier, though the results are on a bell curve (higher likelihood of rolling values closer to the mean than to the extremes).
Conclusion: I quite like the idea of rolling extra dice, but that may dilute the "roll a d20" core mechanic. Also, rolling multiple dice can be quite "swingy" - +1d10 will on average act as a +5.5 bonus, in practice it can be anything from a +1 to a +10. Meanwhile a +5 bonus is always a +5 bonus. Using flat modifiers most of the time with extra dice in special circumstances might be a decent compromise.
Using dice instead of modifiers is kind of a neat idea.
ReplyDeleteOne could have everything be dice actually. A Wizard would have d4 STR, while a Barbarian might be as high as d12. Same with attacks, a Wizard would have a d4 BAB, while a Fighter would be rocking d12.
One could then modify the dice to represent great skill with things like exploding dice, or brutal dice (the 4E mechanic). Lots of room to build feats and features that modify the dice, and that's way more interesting and deep than getting flat numerical bonuses.
The d20 is still king, and used for task resolution to hit the target number, but the dice can modify it. If you don't have a value in a relevant task, it's a flat d20.
I like polyhedral dice as a distinctive part of RPG culture, and would love to find ways to fit them into the system. My general goal is to create a "typical" D&D-style RPG, in the same way that Dungeon Grind is based in a "typical" D&D-style setting. Not a carbon-copy or retroclone, but with enough points of similarity to feel familiar.
DeleteOne idea I've been toying with is using different sizes of dice to represent attribute-based modifiers, with the second digit of the attribute being the size of die you add to the roll - attribute 14 gives +1d4, 16 gives +1d6, 18 gives +1d8. Maybe having skill/proficiency slots could be represented by rolling extra dice, with each additional slot boosting the size of the die.
Why even have numbers for your ability scores?* Why not just the dice? Str 1d6 Con 1d4 Dex 1d10 Int 1d6 Wis 1d4 Cha 1d8 for a Rogue, for instance.
ReplyDeleteThen with every skill being linked to an attribute, your rank in a skill could determine how many bonus dice you get. So the Rogue above would, when first training in Stealth, roll 2d10 for Stealth (1d10 from Dex + 1d10 from Stealth) and add that to the d20 roll.
*yeah, I know it's a sacred cow. When was the last time anything but the modifier actually mattered? But we still haven't gotten rid of the entire number.
Last time D&D used the actual attributes rather than a modifier was 2e AD&D, I believe - proficiency checks involved rolling under the relevant attribute. Which was kind of inconsistent (roll high for combat, roll low for proficiencies) so I can see why they changed it in later editions.
DeleteI'll be talking about the attributes I have in mind in the next design diary post, but yeah, abandoning the numerical ability scores entirely may be an option. One advantage it does have is that it's fairly intuitive to most gamers, while working out how much better it is to roll a d10 than a d8 is slightly less intuitive.