3d20, pick lowest - Apprentice level of skill mastery

>3d20, pick lowest - Apprentice level of skill mastery
>3d20, pick middle - Journeyman level of skill mastery
>3d20, pick highest - Master level of skill mastery

Bad idea or very bad idea?
If you are averse to d20, feel free to replace it with another type of die, as long as it's a Platonic solid.

I feel the difference between the three is way too huge to make this system interesting, at least with d20.
But I like the overall idea.

3d3 exploding

I've had a different idea that's a bit more complex, but more coherent in terms of TN diffculties.

Basically,
>base die is d6
>[Stat Rank] equals amount of dice rolled
>[Skill Rank] equals amount of dice kept
>Stat and Skill ranks range from 1 to 6
So basically, you roll Xd6kY to beat a TN. It seems like a good system on paper, but I never got around to graph it properly.

This way, [Skill Rank] hardcaps your roll, while [Stat Rank] softcaps your roll. So it's always crucial to keep your [Skill Rank] less or equal to your [Stat Rank].
It's pretty interesting to look at, to be honest.

Why do people spend so much time obsessing over random stats generation that then reduces the randomness? Ask yourself why you want random stats in the first place.

>random stats

We're talking about the resolution mechanic, you dummy. Not random stats.

So basically the roll and keep system on a d6.
Which is a system that I love, so no worries.
On a related note, here's a system that I was thinking about:
>stats, number of d10's you roll
>skills, bonus you add to each die. High enough skills also add a few dice when using them.
>compare each die to TN, each one over is a success
To make things easier to get successes, I'm adding Task Chains: you declare a chain and the end result you want, you then roll a few times with different skills (or the same one), count your successes on each roll, and each one adds a die to your pool for the final roll.
So you can intimidate your enemy, test their defenses over a few rounds, then go for the final decisive blow.
What does Veeky Forums think?

While mechanically interesting, I think it fails the smell test for tabletop practicality. It is not interesting enough in either act or resolution to justify spending sequentially more time.

If X = time to resolve one roll
and Y = the number of links in the chain
then I think X(Y) is going to get slow very soon; the payoff for that much tabletime would have to be commiserate.