The better he got, the worse he knew he was.
The inverse Dunning–Kruger effect: http://en.wikipedia.org/wiki/Dunning–Kruger_effect
The inverse Dunning–Kruger effect: http://en.wikipedia.org/wiki/Dunning–Kruger_effect
And it's because the classic statement of the Dunning-Kruger effect is that the unskilled have an unrealistically high estimation of their own abilities. It doesn't talk about what the skilled think.
D-K effect is "If a person is unskilled, then they have high estimation of their abilities."
Converse is: "If a person has a high estimation of their abilities, then they are unskilled."
Inverse is: "If a person is skilled, then they would have a low estimation of their abilities." <-- this matches silv's assertion