Win rate vs expectancy vs payoff ratio

What this page is for

"I win 70% of my trades" sounds great and means nothing by itself. This page shows how win rate, payoff ratio and expectancy fit together, gives you the breakeven win-rate formula, and proves with numbers why the headline win rate is the least useful of the three on its own. Then plug your own trades into the expectancy calculator.

How it works (the formulas)

Three definitions, then the one equation that ties them together:

Expectancy is just the average dollars a trade makes or loses over the long run. Measured in R (multiples of the amount you risk), it simplifies to:

Set expectancy to zero and solve for the win rate you'd need at a given payoff and you get the breakeven line every system lives or dies by:

Inputs and assumptions

• A sample of trades large enough to trust — a handful of trades won't pin down a real win rate or average win/loss.
• Average win and average loss taken from actual closed trades, not planned targets and stops.
• Costs (spread, commission, slippage) folded into the results, since they eat expectancy directly.

Worked example 1 — a low win rate that wins

You win 40% of trades, with an average win of $300 and an average loss of $150 (payoff ratio 2.0).

• Expectancy = (0.40 × $300) − (0.60 × $150) = $120 − $90 = +$30 per trade.
• In R: 0.40 × 2.0 − 0.60 = +0.20 R per trade.
• Breakeven win rate at payoff 2.0 = 1 ÷ (1 + 2) = 33.3%. Your 40% clears it, so the system is profitable — roughly +$3,000 over 100 trades.

Losing 60% of the time and still making money is completely normal when the wins are twice the size of the losses.

Worked example 2 — a 90% win rate that loses

Now you win 90% of trades, but the average win is $50 and the average loss is $600 (payoff ratio 0.083) — the classic "cut winners, let losers run" profile.

• Expectancy = (0.90 × $50) − (0.10 × $600) = $45 − $60 = −$15 per trade.
• Breakeven win rate at payoff 0.083 = 1 ÷ (1 + 0.083) = 92.3%. You win 90%, below the 92.3% you'd need, so you lose money — about −$1,500 over 100 trades — despite being "right" nine times out of ten.

The win rate went up 50 points versus example 1 and the account got worse. That's the whole point: without the payoff ratio, a win rate can't tell you if you're profitable.

A quick reference

Each row is 1 ÷ (1 + payoff). Win above the right-hand number and you have an edge; win below it and you don't, no matter how good the win rate feels.

Common mistakes

• Chasing win rate. Moving stops wider or taking profit early lifts your win rate while quietly wrecking the payoff ratio — and expectancy with it.
• Quoting expectancy in dollars across different account sizes. Use R so the number is comparable.
• Confusing planned reward-to-risk with realized payoff. The payoff ratio is what actually happened, slippage and early exits included.
• Judging any of these on a tiny sample. Twenty trades won't tell you your true win rate; expectancy on a small sample is mostly noise.

Methodology & limitations

The definitions and formulas on this page are standard, widely used ways to describe these concepts; every worked-example number is computed by hand from the formula shown so you can reproduce it. Where a rule varies by provider (prop-firm limits especially), we say so — treat the specifics as illustrative, not as any one firm's rulebook.

Not financial advice. This page explains a concept for education only. It is not investment, trading, or financial advice, and no example is a recommendation. Every prop firm writes its own rules and changes them — always verify against your own program, broker, or account terms before acting.

Last updated 2026-07-06.