Expected Value

Expected value (EV) is the average outcome you would get if you could repeat a decision many times. It combines how likely each outcome is with how much you win or lose in each case. A trade or bet with positive expected value makes money on average over time; one with negative expected value loses money on average, no matter how often it happens to win. EV is the single most important concept for judging whether a strategy, a bet or a prediction market position is worth taking.

The formula#

EV = Σ (probability of outcome × value of outcome)

For a simple win or lose trade:

EV = (win probability × average win) - (loss probability × average loss)

In trading, EV per trade is often called expectancy. See Expectancy.

Worked trading example#

Prediction market example#

A prediction market share pays $1 if an event happens. If it costs 35 cents and you estimate a 45% chance:

EV = 0.45 × $1 - $0.35 = +$0.10 per share

If your estimate were 30%, EV would be minus 5 cents. Prediction market profits over time come from paying less than the true probability. See Reading Odds as Probabilities and Prediction Market Strategies and Risks.

EV of common gambles#

Casinos and lotteries operate on negative EV for players. Many trading behaviours, such as paying high costs, overtrading and buying overpriced long shots, push traders into negative EV without realising it.

Why positive EV is not enough#

Variance and ruin#

A positive EV bet can still bankrupt you if you bet too much. With high variance, a run of losses can wipe out an account before the average has time to show up. Position sizing matters as much as EV. See Risk of Ruin and Kelly Criterion.

Uncertain estimates#

EV depends on your probability and payoff estimates. If you overestimate your win rate or underestimate losses, your "positive EV" may be negative. Estimates should come from large samples and honest testing. See Backtesting Methodology and Overconfidence.

Costs and slippage#

Small edges can disappear after commissions, spreads, slippage and funding costs.

Using EV in practice#

1. Estimate win rate and average win and loss from a large sample of trades. See Trading Journal.
2. Include all costs.
3. Calculate EV per trade and check it is clearly positive.
4. Size positions so that normal losing streaks are survivable. See Position Sizing.
5. Recheck regularly as markets change.

Frequently asked questions#

What is expected value in trading?#

The average profit or loss per trade over many trades, calculated from the probability and size of wins and losses.

Can a positive expected value strategy lose money?#

Yes, in the short term, because of variance, and even in the long term if positions are sized too large and a losing streak causes ruin.

How do I calculate expected value?#

Multiply each possible outcome by its probability and add the results; for a simple trade, win rate × average win minus loss rate × average loss.

Next, learn why results converge over time in Law of Large Numbers.