To me, the phrase "beating the market" means getting a higher expected return than average
Its standard meaning is "achieve a return higher than that produced by buying and holding an portfolio of all assets in the given market".
Excellent point -- I tried using the fuzzy words "higher expected return than average" to drive home the zero-sumnes of the issue, but that phrasing does not reflect actually people mean by "beat the market".
Let's get concrete. What do you think are specific and realistic scenarios for an individual investor, with at most a few hundred thousand dollars in capital, to attempt to beat the market?
First counter-question: why should an individual investor care? Unless you perceive yourself to be in some sort of ranked competition (which is actually the case for professional money managers), why would you care about beating the market?
On a purely rational basis, you have a universe of investment opportunities. You evaluate, to the best of your ability, the future probability distributions of returns from all of them and some kind of a dependency structure (in the simple case, a covariance matrix). From these, you form a portfolio that best matches you...
P/S/A: There are single sentences which can create life-changing amounts of difference.