When I submitted my Sociology M.Phil study proposal, the adviser wrote in the comments section:
Very good in theory, not at all very good in practice.
That sounds odd. What creates dissonance is the juxtaposition of "not at all" and "very good" which are opposite in meaning to each other. I suppose "not very good", "not so good" or "not at all good" would have been more typical constructions.
Research done: I Googled the exact phrase and found a few examples, usually in reviews. It's definitely not commonly used.
[...] I am not at all very good at this game as many here like to point out [...]
Another recent example for "not at all very":
[...] the way they treat their workers is completely unfair and not at all very professional [...]
Is "not at all very good" correct usage? Also, how should it be logically interpreted on an arbitrary 6-point scale of quality from 'very good' through 'good', 'not very good', 'not at all very good', and 'not good' (I am not sure those 4 points are sequential) to 'not at all good' which basically means 'bad'? Please give your reasons why or why not and try to support them with adequate references to avoid any objection of being "primarily opinion based."
Note: I am not sure I used the appropriate tag. Please advise or edit.