expected value

Also called: EV, expected payoff

The probability-weighted average of the outcomes: EV = Σ p·x, with the probabilities adding up to 1. It is what you would get on average over many similar bets, not the result of any single one.

The expected value turns a set of scenarios into one number. Multiply each outcome by its probability and add:

$EV = \sum_i p_i \cdot x_i$

The probabilities must cover every outcome and add up to 1. EV adds up across independent bets, which is why a sales pipeline is valued deal by deal (win probability × value) and an earn-out as the sure part plus the uncertain part times its probability.

EV is an average over many repetitions. A single bet lands on one outcome, so always show the range next to the EV. Insurance is the classic case: the premium is always above the expected loss p × L, and buying it still makes sense when the loss itself would be too big to absorb.

Example

A summer intensive: +300,000 UAH with probability 0.25, +120,000 with 0.50, −80,000 with 0.25.

EV = 0.25 × 300,000 + 0.50 × 120,000 + 0.25 × (−80,000) = 75,000 + 60,000 − 20,000 = 115,000 UAH, with a 25% chance of losing 80,000.

Common mistakes

Treating EV as a forecast. No single run pays exactly the EV.
Probabilities that don’t add up to 1. A missing scenario biases the answer.
Ignoring the downside. Show the worst case and its probability next to the EV.
Adding exposures in different units. Days and hryvnias don’t add.

Learn it in the course

Expected value and scenarios · Weighting outcomes by their probabilities, deal pipelines and earn-outs, expected loss against an insurance premium, and risk exposure in matching units.
Conditional probability and the 2×2 table · P(A | B) as a share inside a row, precision, recall and accuracy, relative risk and the odds ratio, and why the direction of a condition matters.