Many years ago I did a comprehensive analysis of Canadian mutual fund returns over about 20 years, and found that the average return per year was dead on the market. The distribuiton of returns was Guassian and had a width of about 1%. I concluded from this that in fact fund managers can beat the market... by precisely amount they pay themselves.

This is evidence for the "second order version of market efficiency" your mention: it was uncanny, and put me into index funds for life (that, and the fact that there was no way of predicting from year-to-year which funds would beat the market the following year.)