Expected value
How do you compare possible outcomes when each one has a different chance of happening?
In plain words
Expected value is the probability-weighted average of possible results. Each outcome is multiplied by its chance of occurring, then all are added together. It compresses a spread of possible futures into one figure, and it need not match any outcome that actually happens.
Why it matters
It gives a common scale for judging decisions whose results are uncertain. A favourable expected value can still lose this time, and an unfavourable one can still win; the figure describes an average over repetitions, so any single week can land far from it.
In a real week: ETH, week of 21 June 2021
In the week of 21 June 2021, ETH moved between a high of 2260.16 and a low of 1700.48, a range of 32.91%, closing at 1982.28 for a weekly return of -11.64%. Its best day, 2021-06-27, gained 8.33%, and its worst day, 2021-06-21, lost -15.96%. Turning such a spread into one expected value requires a probability for each outcome, and the realised week shows how far a result can sit from any average.
A common mistake
Treating the expected value as the result to expect in any one period. It averages across possibilities, and a single week can fall anywhere inside or beyond the range those possibilities cover.