Skills with Central Tendency and Sliding Scale

A friend of mine dropped by earlier today and we were talking about skill-based experience in RPGs. The example talked about involved the "use-it-to-improve-it" model of skill improvement in computer-based RPGs like Morrowind, Oblivion, and Skyrim (some of those more than others). How might we go about creating a skill-system like that for tabletop RPGs? I spitballed an idea right off the bat. I'm not sure why I went in this direction, but I'm pretty its partly +Adam Muszkiewicz's fault. Mostly, even.

Rolling a 2d6 gives you 2 to 12 with a relatively strong central tendency around 10.5. Extra points may added to base skill in a particular domain during character creation, as a result of experience, or both. You more or less advance at intervals, based on general experience in the game. But how do you get the dice to respect the time you put into a particular skill? I think I've hit upon a solution that not only accomplishes this, but also separates skill advancement from other kinds of advancement based on general experience.

Some games use the 2d6 skill roll and might grant bonuses based on skill in particular domains (e.g., tech use, knowledge skills, athletics, etc.). Stars Without Number is a good example, as it already has great skill system. In that game, players can add up to 4 additional points based on their skill levels, with 4 bonus points being the absolute top, but attribute modifiers apply, based on the particular skill. Targets for skill checks in that game go up to 13. Given that attribute mods in that game only go up to +2/-2, then our sliding 2d6 and slightly higher attribute modifiers (up or down to +3/-3) will allow that 13 to go higher. We also can build in a way to increase skill over time, but only if the skill is used.

What if we add to the 2d6 roll a sliding scale to emulate advancement, and just forget about taking points in the skill during character creation, or after leveling up? Instead, we could use a mechanism to determine when a skill is improved. For now, let's assume that it's a 20-point sliding scale.

Take the 2 to 12 range created by 2d6, and lay that atop the 1 to 20 range of our 20-point scale, like this:

I think you could use this for all kinds of things, from thieves' skills, to riding and piloting, or whatever else. I'm not saying I've tested this. I'm just sort of noodling around these ideas, but I think this is a start on something.

So a quick summary.

• Skill check = 2d6 roll + relevant attribute modifier
• Target number = 1 to 20. This roughly translates to DC check in the d20 system, and the levels of challenge for that system are what I'm assuming here. 
• Possible maximum results for 1st level characters range from 9 to 15, depending on the characters attribute modifier, making any number above 15 is unachievable by a first level character. 
• Players advance in skill when the number on the 2d6 skill check and a d20 roll match up. Then, the 2d6 scale slides one place up the d20 scale, indicating an increase of 1 in that skill, and raising the highest possible challenge that can be overcome. Example: A player with no attribute modifier rolls a 12 on the 2d6. This would allow the character to accomplish a DC 11 skill check. If the character advances his or her skill level, then the 2d6 scale advances one. The same roll can now accomplish a DC threshold one point higher, a 12.

It would be important to avoid extremely challenging skill checks for low-level characters, unless you want to make those checks impossible from the outset. But why would you want that?

What's nifty about it, to me, is that it accomplishes the main goal: To make skill advancement dependent on skill use. It also seems, on the surface, to be able to use existing d20 scaling for task difficulty.