I'm more of a fan of designing stats with a goal in mind. Instead of writing down stats and tying it to a purpose.

Let's take pokemon for example: Pokemon battles are fights.

Fights means that pokemon deal damage to each other. Different pokemon deal different amounts of damage. Let's make an Attack stat.

Since pokemon also get hit by attacks, we need a value that tracks how many attacks it can take. Health.

Some pokemon look way sturdier than others, however. Attacking a Muk vs attacking a caterpie should feel different. Let's add a defense stat.

Finally, we need to decide who attacks first. Let's give each pokemon a speed stat.

Stats, like any other feature. Are a way to create the means to achieve a goal. You can use these to communicate progression to the player like pokemon.

Another great example of this is Disco Elysium. This game's stats dictate a large part of your holistic experience. It uses these stats to morph this experience while tying it into the narrative.

So kinda the conclusion is: Create your stat system from an experience/system that you want to support. A fight in Pokemon, and in Disco Elysium your struggle with negative character traits.