It centers around 4d6. I call it Base14.

Basically, your chance of success is a roll of 14 on 4d6. It is the most common roll, but still something like 11% chance. Your skill bonus gives you lower and higher numbers on either side of 14. For example, if your skill bonus is +5, your range of success is 9 – 19.

I have to double check the percentages to see if this is viable.