DGRPG Design Diary #5: Primary Attributes

Another crunchy Design Diary today, in which I flail around with numbers some more.

Each character has six primary attributes loosely mirroring the STR/DEX/CON/INT/WIS/CHA characteristics of D&D, slightly tweaked for the sake of symmetry. The names of the attributes are provisional at this point, and may change if I find more appropriate or flavourful synonyms.

The primary attributes are divided between Physical and Mental; in each category, one attribute of each type:

• Action - Doing stuff.
• Evasion - Dodging stuff.
• Resistance - Enduring stuff.

Attribute	Type	Description
BRUTEishness	Action, Physical	Strength, physical power, ability to hit things and break stuff.
DEFTness	Evasion, Physical	Dexterity, physical agility, ability to jump out of the way, juggle, manipulate objects.
GUTSYness	Resistance, Physical	Constitution, physical resilience, ability to absorb damage, endure pain, resist disease or poison, perform acts of extended physical exertion.
CLEVERness	Action, Mental	Intelligence, mental power, ability to outsmart opponents, recall facts, notice details, present persuasive arguments, focus magical energy.
WILYness	Evasion, Mental	Wisdom, mental agility, ability to navigate bureaucracy, think on one's feet, react quickly, bend the rules, shirk responsibility, divert blame.
STUBbornness	Resistance, Mental	Charisma, mental resilience, strength of personality, ability to issue orders to subordinates or resist orders from superiors.

Direct vs. Derived Values

It'd be good to find a way for these values to be directly relevant to gameplay; this could be achieved by using the attribute values themselves in task resolution (as described in the previous Design Diary), but that can lead to cumbersome mental arithmetic in-game. It might be that attribute values are best left as a way of gauging relative ability between characters, with derived values being used in-game for the sake of speed and simplicity.

What kind of derived values could be used?

Assuming primary attributes follow the D&D model (usually between 3 and 18, with some outliers), a number of options are available.

• Flat modifiers - an unchanging numerical modifier depending on how far the attribute value is above or below the mean. Modifiers may be positive or negative, and are applied to the result of the task resolution roll.
• Dice modifiers - additional dice are rolled depending on how far the attribute value is above or below the mean. Results may be added to or subtracted from the result of the task resolution roll.

My current model has the primary attributes determined directly, either randomly by dice-roll (ie: 3d6 or some close variant), or (possibly) through a point-buy mechanic.

So some example attribute-derived modifiers might look something like this:

Attribute	Dist.	Flat 1	Flat 2	Dice (mean)
1	-	-9	-5	-1d10 (-5.5)
2	-	-8	-4	-1d10 (-5.5)
3	0.46%	-7	-4	-1d8 (-4.5)
4	1.39%	-6	-3	-1d8 (-4.5)
5	2.78%	-5	-3	-1d6 (-3.5)
6	4.63%	-4	-2	-1d6 (-3.5)
7	6.94%	-3	-2	-1d4 (-2.5)
8	9.72%	-2	-1	-1d4 (-2.5)
9	11.57%	-1	-1	0
10	12.50%	0	0	0
11	12.50%	0	0	0
12	11.57%	+1	+1	0
13	9.72%	+2	+1	+1d4 (+2.5)
14	6.94%	+3	+2	+1d4 (+2.5)
15	4.63%	+4	+2	+1d6 (+3.5)
16	2.78%	+5	+3	+1d6 (+3.5)
17	1.39%	+6	+3	+1d8 (+4.5)
18	0.46%	+7	+4	+1d8 (+4.5)
19	-	+8	+4	+1d10 (+5.5)
20	-	+9	+5	+1d10 (+5.5)

The modifiers here are pretty arbitrary for now, and presented to illustrate the options available.

The "Dist." column shows the probability distribution for each attribute value assuming they're generated by rolling 3d6 - this gives a normal distribution of results, in which you're much more likely to end up with a value close to the average than near the extremes. For example, the chance of rolling a 10 or 11 is 25% (and the chance of rolling between 9 and 12 is just shy of 50%), whereas the chance of rolling 17-18 (or 3-4) is only a little over 2%. This distribution is skewed if you use an alternative method of generating attributes (for example, roll 4d6 and ignore the lowest die, or roll 10 times and pick the best 6 results) but as a general guideline it's useful enough.

Adjusting the relationship between attributes and modifiers allows the value of each point of modifier to be increased or decreased. For example, an item that gives a +1 bonus is equivalent to a single extra attribute point under Flat 1, but two attribute points under Flat 2, so it makes a bigger difference.

Meanwhile the mean modifiers given by the Dice column are similar to those in Flat 2, except there's a much wider range of possible values - an attribute of 18 gives a reliable +4 bonus under Flat 2, and while +1d8 gives a mean value of +4.5 an individual roll could give a result anywhere between +1 and +8. There's a potential for it to make a really big difference to the outcome - or hardly any difference at all. This could be positive (as it means that even a sub-optimal attribute might still has a chance of success) or negative (as it means that even high attributes have a risk of failure).

Either way the additional randomness could be a desirable feature, as it encourages the player to rely on more than just having large numbers on their character sheet - every roleplayer knows how fickle the dice gods can be.

DGRPG Design Diary #4: Task Resolution

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.