Physical
• Athletics (jump, climb, balance, reflex, speed, dodge, tumble, grapple, melee weapons)
≈ Strength, while agile
• Size (hit points, stamina, carrying capacity, long reach, heavy weapons)
≈ Constitution, while Tiny Pixie has low and Huge Ogre has high
Mental
• Perception (physical senses, rational intuition, investigation, knowledge, deception)
≈ Intelligence, while aware
• Precision (cautious sensitive motion, stealth, disabling trap, crafting, sharpshoot weapons)
≈ Dexterity, while methodical
Social
• Charisma (social skills, charm, intimidation, empathy, artistic beauty, psychic interaction)
≈ Charisma, while emotionally insightful
• Willpower (will save, mental resilience, soul, sense of self, psychic size)
≈ Wisdom, while mentally tough
Thoughts about the above experiment ...
The above hexad seems the closest possible to the D&D tradition while being about equally useful and minimizing overlapping redundancies.
I am happy with the Physical Athletics/Size and Mental Perception/Precision arrangement. It even seems possible to assign the combat bonuses to each of the four.
Physical
• Athletics: attack bonus to melee/thrown weapons
• Size: damage bonus to melee/thrown weapons
Mental
• Perception: attack bonus to sharpshooter/sneak weapons
• Precision: damage bonus to sharpshooter/sneak weapons
There are two Social abilities. Willpower is soul and mental size, and Charisma is mental interactivity. It is impossible to be charismatic without also being emotionally intelligent and sensitive, so Charisma necessarily includes empathy and emotional insight. This also helps toward making the two aspects about equally useful. Willpower gets all mental saves. Persuasion gets all social checks.
Note that Mental Perception gets the Deception checks to forge, disguise, and bluff because you have to know what you are talking about to create a convincing forgery or disguise, or illusion.
The fact that the attack bonus and damage bonus can split up into different abilities helps prevent any particular ability from becoming too overpowered.
It might make sense to make the two Social abilities responsible for all magic? In this sense, magic means being in an interactive personal relationship with the phenomena of the cosmos.
Charisma in the sense of psychic interactivity gets the attack bonus (or spell DC) for spells. Willpower in the sense of psychic weightiness gets the damage bonus (or spell effect boosts) for spells.
Social
• Charisma: bonus to spell attack/DC
• Willpower: bonus to spell damage/effect
That said, Illusion magic needs Perception (sensory detail) and Precision (crafting of exact duplicate). Similarly, other kinds of magic may benefit from the nonsocial abilities, even tho magic itself is Social.