A win rate says how often trades finish ahead, not whether the trades make money. Profit depends on the win rate together with the size of the average win and the average loss, which is why a 75% win rate can break even and a 35% win rate can earn a steady profit. The numbers below are computed, and every example is hypothetical.
Key takeaways
- Expectancy per trade is the win rate times the average win, minus the loss rate times the average loss. A win rate on its own cannot give it.
- The break-even win rate is 1 / (1 + R), where R is average win divided by average loss. It runs from 75% at R = 0.33 down to 25% at R = 3.
- A flat $5 round-trip cost per trade (5% of a $100 risk) pushes each break-even win rate up by 1.25 to 3.75 percentage points in the table below.
- With 200 trades, a run of 8 or more losses has a 53.0% chance at a 45% win rate and a 7.4% chance at 60%, so streaks alone are weak evidence.
- 55 wins in 100 trades gives a 95% Wilson interval of about 45.2% to 64.4% for the true win rate, which includes 50%.
Win rate, payoff and R-multiples
Four terms carry the whole discussion. Win rate (p) is the share of trades that close with a profit. Average win (W) and average loss (L) are the mean dollar results of the winning and losing trades, with L entered as a positive number. The reward-to-risk ratio used here is R = W / L, the average win measured in units of the average loss.
An R-multiple restates a trade result in units of the amount risked at entry, usually the distance from entry to the initial stop-loss times the position size. That amount is called 1R. If 1R is $100, a $200 profit is +2R and a full stop-out is -1R. Expressing results this way removes position size from the comparison, so trades of different dollar sizes can be averaged.
The letter does two jobs below. Written alone, R is the ratio W / L; written after a number, as in +0.40R, it is a result in units of 1R. The two match only when the average loss equals 1R, which holds when losing trades are full stop-outs. If stops are moved, gapped through or exited early, the average loss drifts away from 1R and the ratio should be computed from the actual average loss.
Expectancy: the number that pays
Expectancy is the average result per trade. It combines all three inputs and has one form in dollars and one in R:
Expectancy ($) = p × W − (1 − p) × L
Expectancy (R) = p × R − (1 − p) where R = W / L, results in units of L
Here p is the win rate as a decimal, W the average win, L the average loss and R their ratio. A positive value means the average trade made money over the sample, and zero means it broke even.
Illustrative example: two traders, before costs
Both traders are hypothetical, and the arithmetic is exact.
- Trader A wins 75% of trades with an average win of $40 and an average loss of $120. Expectancy = 0.75 × $40 − 0.25 × $120 = $30 − $30 = $0 per trade. Taking the average loss as 1R ($120), the average win is 0.33R and expectancy is 0R.
- Trader B wins 35% of trades with an average win of $300 and an average loss of $100. Expectancy = 0.35 × $300 − 0.65 × $100 = $105 − $65 = +$40 per trade. With the average loss as 1R ($100), that is 0.35 × 3 − 0.65 = +0.40R.
Trader A is right three times out of four and earns nothing on average. Trader B is wrong almost two times in three and earns $40 per trade. The win rate ordered them the wrong way round.
Break-even win rate by payoff ratio
Setting expectancy to zero in the R form gives p × R = 1 − p, so the win rate at which a system exactly breaks even is:
Break-even win rate = 1 / (1 + R)
The "after cost" column below assumes 1R = $100 and a flat $5 round-trip cost on every trade, win or lose. It solves p × W − (1 − p) × L − $5 = 0, which gives p = ($100 + $5) / (W + $100).
| R (average win / average loss) | Average win with $100 risk | Break-even win rate, no cost | Break-even win rate, $5 cost |
|---|---|---|---|
| 0.33 (exactly 1/3) | $33.33 | 75.0% | 78.75% |
| 0.5 | $50 | 66.7% | 70.0% |
| 1 | $100 | 50.0% | 52.5% |
| 1.5 | $150 | 40.0% | 42.0% |
| 2 | $200 | 33.3% | 35.0% |
| 3 | $300 | 25.0% | 26.25% |
Trader A sits exactly on the top row: a 75% win rate at R = 1/3 is break-even before costs. Win rate and payoff are also not independent in real trading. As a matter of reasoning rather than measurement, a profit target set further away is, other things equal, reached less often, so changing one input usually moves the other, and the table shows only where the line sits, not which pairs are achievable.
Costs move the break-even line
Commissions, fees, the bid-ask spread and slippage are paid on every trade, so they come off the average result whatever the outcome. FINRA's day-trading page says frequent trading can carry higher costs that erode returns, and it does not give amounts. The $5 figure here is an assumption chosen for round numbers, not a typical cost.
The same two traders after a $5 round-trip cost
- Trader A: $0 − $5 = -$5 per trade, or about -0.04R with 1R = $120. Over 100 trades that is -$500.
- Trader B: $40 − $5 = +$35 per trade, or +0.35R with 1R = $100. Over 100 trades that is +$3,500.
The same $5 turned a break-even system into a losing one and trimmed 12.5% from the other's edge. A fixed cost matters most where the average win is small, because the cost is a larger share of each win. For a planned trade, the position size calculator turns an account size, a risk percentage, an entry, a stop and a target into a share count, the reward-to-risk ratio and the matching break-even win rate before costs.
High win rates and hidden tails
An observed average win and average loss describe the trades that actually happened. A strategy that wins often and loses rarely but heavily can post a high win rate and a positive average for a long stretch before the rare loss arrives.
Illustrative example: each trade wins $20 with probability 98% and loses $1,500 with probability 2%. True expectancy = 0.98 × $20 − 0.02 × $1,500 = $19.60 − $30 = -$10.40 per trade. The chance that a 100-trade sample contains no loss at all is 0.98 raised to the power of 100, about 13.3%, and that sample would show a 100% win rate and +$20 per trade.
Real strategies with this shape include selling options. FINRA's options page says the premium an option seller receives is the maximum profit, that the maximum loss on an uncovered (naked) call is "theoretically unlimited", and that short option positions can require significant additional funds if the market moves against the seller, and that if those funds are not deposited the firm can liquidate positions without notice. By the same arithmetic, any approach that adds to a losing position until it recovers has this shape: many small wins, with the risk concentrated in a few outcomes.
One behavioral link: Odean's study "Are Investors Reluctant to Realize Their Losses?" (Journal of Finance, vol. 53, no. 5, 1998) analyzed trading records for 10,000 accounts at a large discount brokerage and found a strong preference for realizing winners rather than losers. The study did not measure win rates. As arithmetic, though, selling winners early and holding losers tends to raise the share of closed trades that are wins while letting the average loss grow.
Luck, streaks and sample size
How likely is a long losing streak?
The probabilities below come from an exact dynamic-programming calculation over 200 independent trades with a fixed win rate, and a 100,000-run simulation agreed to within 0.2 percentage points for the 8-loss row. Independence and a constant win rate are assumptions that real markets may not satisfy.
| Win rate | Chance of 5 or more losses in a row | Chance of 8 or more losses in a row |
|---|---|---|
| 45% | 99.4% | 53.0% |
| 60% | 71.4% | 7.4% |
A system with a 45% win rate is more likely than not to produce an 8-loss run somewhere in 200 trades, and a 60% system still has about a 1-in-14 chance. Hitting such a run does not by itself show that an edge has gone, and avoiding one does not show an edge exists.
How precise is an observed win rate?
A win rate from a few dozen or a few hundred trades is an estimate with a margin. The Wilson interval is one standard way to bound it; NIST's Dataplot reference gives the formula and notes that the plain normal approximation is meant for relatively large samples with a proportion not near 0 or 1.
Wilson 95% limits = [ p̂ + z²/(2n) ± z × √( p̂(1 − p̂)/n + z²/(4n²) ) ] / (1 + z²/n)
p̂ = wins / n, n = number of trades, z = 1.96 for 95%
| Observed result | Win rate | 95% Wilson interval |
|---|---|---|
| 55 wins in 100 trades | 55% | 45.2% to 64.4% |
| 110 wins in 200 trades | 55% | 48.1% to 61.7% |
| 550 wins in 1,000 trades | 55% | 51.9% to 58.1% |
At 100 trades the interval spans about 19 points and includes 50%. It takes roughly 1,000 trades to narrow it to about 6 points. The interval covers only the win rate; the average win and average loss carry their own uncertainty.
Frequently asked questions
Can a system with a win rate under 50% have positive expectancy?
Yes, when R is large enough. The condition is p × R greater than 1 − p. A 40% win rate at R = 2 gives 0.40 × 2 − 0.60 = +0.20R per trade before costs, while the same 40% at R = 1.5 is exactly break-even.
Is a 45% win rate good or bad?
It depends on R. At R = 1.5 it earns 0.45 × 1.5 − 0.55 = +0.125R per trade, while at R = 1 it loses 0.45 − 0.55 = -0.10R per trade. The comparison that matters is the win rate against its break-even rate.
Does the break-even formula work if trade sizes vary?
The expectancy formula is an average, so it holds for mixed sizes if W and L are the actual averages of the winning and losing trades. Averages from few trades are noisy, so a sample from a handful of trades is a weak basis for either number.
What if a trade has no stop-loss, so 1R is unclear?
1R is normally the initial risk set by the initial stop. Without a stop, 1R has to be fixed some other way, such as a dollar amount chosen before entry as the most the trade was allowed to lose. Whatever rule is used, it should be set before the trade and kept the same across the log, because changing it rescales every R-multiple.
How many trades separate 55% from a coin flip?
With the Wilson method, an observed 55% win rate needs about 400 trades before the 95% interval (about 50.1% to 59.8% at 400) stops including 50%. At 300 trades it still runs from about 49.3% to 60.5%. That covers only the win rate, and it assumes trades are independent.
A short checklist for your own log
- Record, for each trade, the dollars risked at entry, the result and all costs, so each outcome can be written in R after costs.
- Compute p, average win and average loss, then expectancy in dollars and in R, and compare p with 1 / (1 + R).
- Add the per-trade cost to the break-even calculation, as in the table above.
- Attach a Wilson interval to the win rate before drawing conclusions from it.
- Look at the single largest loss in the log. If one outcome decides the total, the average is fragile.
