(1) before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar and

(2) after costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar
William F. Sharpe-
The Financial Analysts' Journal Vol. 47, No. 1, January/February 1991. pp. 7-9

You can get as cute as you want with how you define passive and active management attempting to avoid these truths, but they are self evident, and those who fail to acknowledge them are simply self interested.