The actual argument that I know of rely on statistical test being the way to determine and not just a simple classification that anyone who beats the market is

The actual argument that I know of rely on statistical test being the way to determine and not just a simple classification that anyone who beats the market is lucky. Roughly speaking, if it's possible to beat the market, then when comparing between the result distribution we have of actual result, against a hypothetical distribution where investor was using coin toss to invest, those two have to be different. The conclusion comes from people saying that those two looks the same. Now, actually make the test and choosing all the variable in question is NOT a simple task, and definitely is a hard problem.