Expected Value in Trading: Why a 40% Win Rate Can Win

The short answer

Expected value (EV) is the average profit or loss of a trade over many repetitions: EV = (chance of winning × reward) − (chance of losing × risk). If your EV is positive, you make money over time — even if you lose most individual trades. It's the only number that decides long-term profitability.

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The formula (it's simpler than it looks)

EV = P(win) × Reward − P(loss) × Risk. Say you win 50% of the time, risking 1 to make 2: EV = 0.5×2 − 0.5×1 = +0.5 per unit risked. Positive → over many trades, you grow. Negative → you bleed, no matter how good any single trade felt.

Why a 40% win rate can win

Lose more often than you win — and still come out well ahead.

With a 1:3 reward-to-risk, your winners are 3× your losers. Win just 40% of the time and the math is strongly positive. This is why chasing a high win rate is a trap: tiny wins and big losses can ruin a 70%-win-rate trader.

Expectancy beats win rate

Win rate alone is a vanity metric. What pays is expectancy — your average result per trade. A strategy that's "wrong" 60% of the time but lets winners run can crush one that's "right" 70% of the time but cuts winners early. Always read win rate next to reward-to-risk.

Hamster's note: I once bragged about a 65% win rate while quietly losing money — tiny wins, monster losses. Expected value doesn't care about your ego or your win streak. It just adds up the math. Respect the math.

Quick check — strategy A wins 70% but R:R is 1:0.5. Strategy B wins 40% at 1:3. Which is better?

Strategy B. A: 0.7×0.5 − 0.3×1 = +0.05. B: 0.4×3 − 0.6×1 = +0.6 — roughly 12× the expectancy. Win rate fooled you; expected value told the truth.

Key takeaways

EV = P(win)×reward − P(loss)×risk. Positive EV = long-term profit.
A low win rate is fine — even great — with a high reward-to-risk.
Optimise expectancy, not win rate.

Glossary: Expected value Risk-reward Win rate Risk management The Money

Hamster keeps it real: Positive EV still loses — often, and in streaks. The edge only shows up over many trades; any single one, even the 'perfect' one, is a coin flip you must be able to survive.

FAQ

What is expected value in trading?

Expected value (EV) is the average profit or loss of a trade over many repetitions: EV = probability of winning × reward − probability of losing × risk. A positive-EV strategy makes money over time even if it loses individual trades, which is why it is the metric that determines long-run profitability.

Can a strategy with a low win rate be profitable?

Yes. With a high enough reward-to-risk, a low win rate is very profitable. At a 1:3 reward-to-risk a 40% win rate has strongly positive expected value, because the winners are three times the size of the losers.

Why is win rate misleading?

Win rate ignores the size of wins and losses. A 70% win rate with tiny winners and huge losers loses money, while a 40% win rate with large winners makes money. Expectancy — the average result per trade — is what actually matters.

How do I calculate expected value?

Multiply your win probability by your average win, multiply your loss probability by your average loss, and subtract: EV = P(win) × reward − P(loss) × risk. Estimate the probabilities from a meaningful sample of past trades (30+), not a handful.