A few posts from Bogleheads.org:
https://www.bogleheads.org/forum/viewtopic.php?t=319283
On Investment Goal
I don't manage other people's money for living. Alpha, beta, or whatever Greek letters mean nothing to me.
The only thing I care about is ensure that the total value of my portfolio is more than the alternative (buy and hold the market) for every single day after the first couple of years.
Let M0 be the market at t0, and Mn at tn, and my portfolio is P0 at t0, and Pn at tn, my relative performance is pn = (Pn/P0)/(Mn/M0).
My definition of beating the market is prob(pn > 1) -> 100% and pn >> 1 if n is sufficiently large (20, 30, or 40 yrs).
I think the definition matters more to individuals investing their own money for retirements than any Greek letters taught in schools.
The Greek letters are there for the financial industry to justify reaping people off their retirement money
