In my current D&D system this is how the six standard attributes are arranged (I use willpower instead of wisdom).

The top three attributes belong to the physical realm and measure how good the character is at physical activities.  The bottom three attributes belong to the spiritual realm and measure how good the character is in the spiritual realm (magic and intellect and the like).  Each half of the wheel reflects it's counterpart in the other realm. Thus willpower is the spiritual equivalent of constitution, and dexterity is the physical equivalent of intelligence.

To left we see how easy it is for the character to exert force on the world.  Strength measures the physical force; charisma measures the spiritual force (force of personaility).  Wrestle with someone and use strength. Argue with someone and use charisma.

To the right we see how easy it is for the character to finesse the world.  Dexterity measures how easily they physically dance or weave through the world. Intelligence does the same thing for spiritual/mental aspects of the world.

Constitution measure the raw physicality of the character.  Willpower measures the raw spirituality of the character.

As well as being tested directly, each attribute provides a bonus to doing something to the world and resisting something about the world.

The bonuses to resisting things are, of course, bonuses to saving throws.  Strength gets to resist things that try to stop you moving, so it applies to saves vs petrification and paralysis.  Constitution gives a bonus to saves vs poison and death. Dexterity allows you to get out of the area of effect more easily so it provides a bonus to saves vs Blasts and Dragon Breathe. Intelligence gives a save vs Magical Devices (including Wands and Staves).  Willpower gives a save vs Spells and Magic.  Charisma gives a bonus to saves vs Charm and Fear.  [What happens when you get hit with a Wand of Paralysis?  You get to choose the saving throw based on how you react against the attack.  Avoid where it is pointing?  Save vs Magic Device.  Get out of the area of effect?  Save vs Blast/Breathe.  Resist the magic? Save vs Spells.  Overcome the effects of the paralysis?  Save vs Paralysis/Petrification.   Some save might need you to do stuff to use them though - like actually moving to cover or diving out the way, or resisting the magic.]

Bonus boosts collateral rolls.  So strength increases the damage die the character uses.  Constitution increases the hit die used by the character.  Dexterity increases the ability to avoid being hit.  Intelligence increases the number of Expertises (skills) you begin the game with.  Willpower increases the spell point die, and Charisma affects the number of faithful hirelings you can have and their loyalty.

Direct tests of attributes are a straight d20 or d30 (or even d100) roll against the characteristic, with low being good.  [By custom, using the same die you roll to hit with.]

Normal attributes ranges from 3-18.   Player characters use 4d6/best 3 (with the option of a straight 4d6) for one attribute.  Bonus is +1 for every full 3 points above 12 (and -1 for every 3 full points below 9).  A characteristic above 18 is considered exceptional and notable.  A characteristic of 25 is considered the pinnacle of human development.  Anything above that is superhuman.  As characters increase in level their attributes increase.  Every odd level a random prime requisite goes up by 1.  Every even level a random non-prime requisite increases.  So the basic classes increase in attributes fastest.
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