It turns out I can just post whatever I want here and no one can stop me.
Ability scores are boring in modern versions of D&D. If your ability scores are randomly generated, then they make sense as-is; but if you can arrange them or use point buy or standard array, there is a trivially correct choice for almost all characters, and that's boring. Here are a few different options for how to make them interesting again. These are written from a 5E perspective because I'm just recycling notes out of my ideas file and not really writing them from scratch, you can probably convert them to any D&D-like game without too much effort.
Option 1: Redefine Ability Scores
Redefine the six stats as follows.
Strength - Your ability to project force into the world, whether physical or magical. Whenever you would add an ability score to a damage roll, add your Strength modifier instead.
Dexterity - Your precision and aim. Whenever you would add an ability score to an attack roll, add your Dexterity modifier instead.
Constitution - Your health and survivability. Continues to add to hit points. No changes except based on what the other stat changes do.
Intelligence - Your ability to do skillful things. Whenever you would add an ability score to a skill check, add your Intelligence modifier instead.
Wisdom - Your strength of will and ability to enforce your will on the world. Whenever you would add an ability score to a save DC or use as part of another class feature, add your Wisdom modifier instead.
Charisma - Your sense of self and ability to keep yourself together. Whenever you would add an ability score to a saving throw, add your Charisma modifier instead.
(Wis and Cha could easily be swapped, idk, I wrote this in two minutes)
With this method, suddenly it's no longer just "Wizards want Int, fighters want Str". Every stat becomes useful for every character. (PS - I stole this idea from Pillars of Eternity.)
Option 2: Remove Ability Scores (Flexible Version)
Remove the 1-20 ability scores. Keep the ability score names.
All characters are proficient in two ability scores, and deficient in one, of their choice.
If you are proficient with an ability score; when you make an ability check, attack roll, or saving throw based off that ability score, add your proficiency bonus. (This is separate from adding your proficiency bonus if you're also proficient in that roll, so you'd add it twice if you are proficient in both Strength and Athletics and you made a Strength (Athletics) check.)
If you are deficient with an ability score; when you make an ability check, attack roll, or saving throw based off that ability score, subtract one.
If your class references an ability score for a reason (such as save DC or uses per day), use your proficiency bonus. Optionally, you could require that the character actually be proficient in the referenced ability score in order to use your prof bonus.
You can use an ASI to become proficient in an additional ability score or select a feat.
Option 3: Condense Ability Scores
Remove the six stats. Replace with Fortitude, Reflex, and Will. If the game refers to Str or Con, use Fortitude; if it refers to Int or Dex, use Reflex; and if it refers to Wis or Cha, use Will. Exception: Hit points gained by level are a flat value for all PCs chosen by the GM based on campaign style (+0 for life is cheap, +2 default, +4 for superheroes) and are not gained via Fortitude.
You have proficiency in one of Fortitude, Reflex, or Will based on your class. You are deficient on another one, and neutral on the third, also based on class. Some classes might let you pick between options. You can go from deficient to neutral with one ASI; neutral to proficient takes two ASIs.
When making any attack or replacing any stat in a class feature, use the new stat that you're proficient in. (For example, fighters are proficient in Fortitude; a fighter making an attack would use Fortitude for the attack. Clerics are proficient in Will; a cleric's attack would be based on their Will. This is true whether the cleric is attacking with a spell or a staff. Clerics would also use their Will in place of their Wisdom modifier if a class feature says, for example, you can use this Wisdom modifier times per day.)
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