Crazy arithmetics.

All numbers below are my estimates. Let's divide s/w engineers to two halves - 50% of "good" and 50% of "bad". For simplicity, I don't account for average ones, ignore the continuum and reduce the problem to one dimension. These three omissions make results almost absolutely unreliable, but still fun.

80% of bad engineers want to switch to management. (The rest think they are good engineers - D-K).
20% of good engineers want to switch to management. (Different reasons).
50% of bad engineers who want to switch to management, do become a manager. (Persistence is key, but some bad engineers still won't make it).
80% of good engineers who want to switch to management, do become a manager. (They are good engineers because they are smart and can reach their goals).
20% of bad engineers who switched to management, are good managers. (Being a manager is a different skill).
50% of good engineers who switched to management, are good managers. (It is a different skill, but being smart helps).

Few multiplies, and voila:
Percentage of managers with "bad engineer" background ~= 71%, and ~29% were good engineers in their previous life.
However, with numbers above (I swear I didn't tune them) half of good managers were formerly good engineers.