I think your question starts from the wrong place. I have worked with many shit programmers that have been through formal education.

For me there are two types of programmers

• Those that learnt to code because they think $$$$
• Those that code because they love code

Given the choice I will work along side the second category all day and avoid the first at all costs.

The better question being what is the % of good programmers that are self taught vs formally trained :)