Expectancy combines how often trades win with how large wins and losses are, after costs. Drawdown describes the path: a deeper decline needs a larger gain to recover, and position size scales both.
Reward-to-risk ratios and R multiples
R is the initial risk of a trade: the distance from entry to stop per share, or that distance times the shares in dollars. The planned reward-to-risk ratio divides the distance to the target by R. After the exit, the realized R multiple divides the actual result by the same R, which puts trades of different prices and sizes on one scale.
Reward-to-risk = (target − entry) ÷ (entry − stop)
Realized R multiple = (exit − entry) ÷ (entry − stop)
Dollar result = realized R multiple × initial dollar risk| Outcome | Exit | Per share | R multiple | Dollars |
|---|---|---|---|---|
| Target reached | $55.10 | +$6.60 | +2.00R | +$495.00 |
| Exit before the target | $52.00 | +$3.50 | +1.06R | +$262.50 |
| Stopped at the stop | $45.20 | −$3.30 | −1.00R | −$247.50 |
| Gap below the stop | $43.55 | −$4.95 | −1.50R | −$371.25 |
The planned ratio of this setup is (55.10 − 48.50) ÷ (48.50 − 45.20) = 2.00. Exits that differ from the plan move the realized result away from it in either direction, which is why a trading journal records R multiples, not only dollars.
The expectancy formula
Expectancy is the average result per trade that a record implies if its averages held. Multiply the share of winning trades by the average win, subtract the share of losing trades times the average loss, and express the result in dollars or in R. It describes a past sample, and a handful of different trades can change it.
Expectancy ($) = (W × average win) − (L × average loss)
Expectancy (R) = (W × average win in R) − (L × average loss in R)
L = 1 − W, when every trade is a win or a lossW- Win percentage as a fraction: winning trades ÷ all trades.
L- Loss percentage as a fraction: losing trades ÷ all trades.
average loss- Written as a positive amount, so it is subtracted.
- Trades that end at exactly zero can be counted separately; W and L then add up to less than 1, and the zero results add nothing to either term.
- With no losing trades, L is 0 and the expectancy equals the average win, but a record without losses is usually too short to describe a strategy.
- Expectancy in R needs a defined initial risk for every trade; a trade without a stop has no R.
Worked example: expectancy in dollars and in R
A hypothetical record of 20 trades, each sized to risk $250 (1R), had 8 winners and 12 losers. Winners averaged $560 and losers $240, slightly less than 1R because some exits came before the stop. The table works through both versions of the formula.
| Item | Dollars | R multiples |
|---|---|---|
| Win percentage (8 of 20) | 40% | 40% |
| Average win | $560.00 | 2.24R |
| Average loss | $240.00 | 0.96R |
| Expectancy per trade | $80.00 | 0.32R |
| Net result of 20 trades | $1,600.00 | 6.40R |
Expectancy ($) = 0.40 × $560.00 − 0.60 × $240.00 = $224.00 − $144.00 = $80.00
Expectancy (R) = 0.40 × 2.24 − 0.60 × 0.96 = 0.896 − 0.576 = 0.32R
Check: 8 × $560.00 − 12 × $240.00 = $4,480.00 − $2,880.00 = $1,600.00 = 20 × $80.00A positive expectancy from 20 trades is a weak estimate. Replacing two of the winners with two full 1R losses would turn the same record to −$20.00 in total, or −$1.00 per trade.
Breakeven win percentage for a reward-to-risk ratio
Setting the expectancy to zero gives the share of winners at which a strategy only breaks even. If every win is R units of risk and every loss exactly one unit, W × R − (1 − W) = 0, so W = 1 ÷ (1 + R). Below that percentage the strategy loses money on average; above it, it gains, before costs.
W × R − (1 − W) × 1 = 0
W × (R + 1) = 1
Breakeven W = 1 ÷ (1 + R)| Reward-to-risk R | Breakeven win percentage |
|---|---|
| 0.5 | 66.7% |
| 1.0 | 50.0% |
| 1.5 | 40.0% |
| 2.0 | 33.3% |
| 3.0 | 25.0% |
| 4.0 | 20.0% |
The formula assumes R is above zero. As R approaches zero the breakeven percentage approaches 100%, because wins worth almost nothing cannot offset a loss.
How win percentage and reward-to-risk trade off
Neither number means much alone. A strategy that wins 60% of the time still loses money if its wins are half the size of its losses, and one that wins 30% of the time can come out ahead if its wins are three times its losses. The grid shows expectancy in R for combinations of the two, with every loss at exactly 1R and no costs.
| Win percentage | 0.5R wins | 1R wins | 2R wins | 3R wins |
|---|---|---|---|---|
| 30% | −0.55R | −0.40R | −0.10R | +0.20R |
| 40% | −0.40R | −0.20R | +0.20R | +0.60R |
| 50% | −0.25R | 0.00R | +0.50R | +1.00R |
| 60% | −0.10R | +0.20R | +0.80R | +1.40R |
In practice the two are linked. With the stop fixed, a farther target is reached less often, so raising the reward-to-risk ratio tends to lower the share of winners. Comparing a record’s win percentage with the breakeven percentage for its average reward-to-risk says more than either figure alone.
How commissions and slippage change the result
Costs come out of every trade, winners and losers alike. Commissions and fees are charged per order or per share, and slippage is the difference between the expected price and the fill. A fixed cost per trade lowers each win and deepens each loss by the same amount, so expectancy falls by exactly that cost and the breakeven win percentage rises.
Cost per trade (R) = (commissions + fees + slippage per share and side × 2 × shares) ÷ 1R in dollars
Expectancy after costs = expectancy before costs − cost per trade
Breakeven W with costs = (1 + c) ÷ (1 + R)c- Cost per round trip, in R.
R- Average win in R, with every loss at exactly 1R before costs.
| Item | Dollars | In R |
|---|---|---|
| Commissions, $1.00 per order × 2 | $2.00 | 0.008R |
| Slippage, $0.05 per share × 2 sides × 100 shares | $10.00 | 0.040R |
| Total cost per trade | $12.00 | 0.048R |
| Expectancy before costs | $80.00 | 0.320R |
| Expectancy after costs | $68.00 | 0.272R |
| Net result of 20 trades after costs | $1,360.00 | 5.440R |
| Reward-to-risk R | No costs | Cost 0.048R | Cost 0.20R |
|---|---|---|---|
| 0.5 | 66.7% | 69.9% | 80.0% |
| 1.0 | 50.0% | 52.4% | 60.0% |
| 2.0 | 33.3% | 34.9% | 40.0% |
| 3.0 | 25.0% | 26.2% | 30.0% |
Slippage is charged per share, so its weight in R depends on the stop distance. Five cents per side, ten cents a round trip, is 0.03R on a $3.30 stop but 0.25R on a $0.40 stop, which makes strategies with tight stops and small targets the most sensitive to costs. A fixed commission per order works the same way: it weighs more on a small position than on a large one.
TradeClever’s Backtest Scan, inside the CleverScan editor, is an event study: it selects a rule’s matches on a start date, keeps them to an end date and reports their price returns and equal-weight average, without position sizing, costs or exits. Subtract realistic costs from any such return before comparing it with a breakeven threshold; strategy testing explains how an event study differs from a trading simulation.
Drawdown and the gain needed to recover
A drawdown is the decline of account equity from its running peak, the highest value reached so far. Because the recovery starts from a smaller base, the gain needed to return to the peak is larger than the loss: a 50% decline needs a 100% gain. For a decline d written as a fraction, the required gain is d ÷ (1 − d).
Drawdown (%) = (running peak − equity) ÷ running peak × 100
Gain needed to recover (%) = d ÷ (1 − d) × 100running peak- The highest equity value reached so far.
d- The drawdown as a fraction, at least 0 and below 1.
| Drawdown | Gain needed |
|---|---|
| 5% | 5.3% |
| 10% | 11.1% |
| 20% | 25.0% |
| 30% | 42.9% |
| 50% | 100.0% |
| 75% | 300.0% |
At a 100% drawdown, 1 − d is zero and the formula divides by zero: there is nothing left to recover from.
Worked example: maximum drawdown from an equity table
Maximum drawdown is the largest drawdown in the whole record. Track equity after each trade, carry the running peak forward, compute the drawdown on every row and take the largest. The hypothetical sequence below starts at $25,000 and risks a fixed $250 (1R) per trade.
| Trade | Result | Equity | Running peak | Drawdown | Drawdown (%) |
|---|---|---|---|---|---|
| Start | Opening equity | $25,000.00 | $25,000.00 | $0.00 | 0.00% |
| 1 | +2.0R | $25,500.00 | $25,500.00 | $0.00 | 0.00% |
| 2 | −1.0R | $25,250.00 | $25,500.00 | $250.00 | 0.98% |
| 3 | −1.0R | $25,000.00 | $25,500.00 | $500.00 | 1.96% |
| 4 | +1.5R | $25,375.00 | $25,500.00 | $125.00 | 0.49% |
| 5 | −1.0R | $25,125.00 | $25,500.00 | $375.00 | 1.47% |
| 6 | −1.5R | $24,750.00 | $25,500.00 | $750.00 | 2.94% |
| 7 | −1.0R | $24,500.00 | $25,500.00 | $1,000.00 | 3.92% |
| 8 | +3.0R | $25,250.00 | $25,500.00 | $250.00 | 0.98% |
| 9 | +2.2R | $25,800.00 | $25,800.00 | $0.00 | 0.00% |
| 10 | −1.0R | $25,550.00 | $25,800.00 | $250.00 | 0.97% |
The maximum drawdown is $1,000.00, or 3.92%, reached after trade 7: five of the six trades after the $25,500 peak lost, one of them through a gap at −1.5R. Getting back needs a 4.08% gain from $24,500, which trades 8 and 9 provide.
Losing streaks and position size
Losing streaks happen even in records with positive expectancy. If trades are independent and each loses with the same probability, the chance that k given trades in a row all lose is that probability to the power k, and the chance of meeting such a streak somewhere in a long series is much higher. Real trades are rarely fully independent, because market conditions can persist and affect many trades at once, so the figures illustrate the arithmetic rather than describe any strategy.
Chance that k given trades all lose = q^k
Equity left after k full losses at risk f per trade = (1 − f)^kq- Probability that a trade loses, assumed constant and independent of other trades (0.60 below).
f- Fraction of current equity risked per trade.
| Streak length k | Chance for k given trades | Chance of at least one in 100 trades | Drawdown at 1% risk | Drawdown at 2% risk |
|---|---|---|---|---|
| 4 | 12.96% | 99.9% | 3.94% | 7.76% |
| 6 | 4.67% | 87.3% | 5.85% | 11.42% |
| 8 | 1.68% | 49.0% | 7.73% | 14.92% |
| 10 | 0.60% | 20.5% | 9.56% | 18.29% |
| 12 | 0.22% | 7.7% | 11.36% | 21.53% |
A run of 8 losses has a 1.68% chance of starting at any particular trade, yet across 100 independent trades the chance that one appears somewhere is about 49.0%. Position size decides what such a streak costs, and the same sequence of R results scales almost in proportion with the risk per trade.
| Risk per trade | 1R in dollars | Maximum drawdown | Maximum drawdown (%) | Gain to recover |
|---|---|---|---|---|
| 0.5% | $125.00 | $500.00 | 1.98% | 2.02% |
| 1% | $250.00 | $1,000.00 | 3.92% | 4.08% |
| 2% | $500.00 | $2,000.00 | 7.69% | 8.33% |
| 3% | $750.00 | $3,000.00 | 11.32% | 12.77% |
Doubling the risk per trade roughly doubles the drawdown, and the gain needed to recover grows a little faster. Position sizing shows how a chosen risk per trade turns into a share count.
Continue with
- Stock strategy testingEvent studies, simulations and their limits.
- Run a scan for an earlier sessionSee what a rule matched before.
- Trading journal and trade planRecord R multiples trade by trade.
Read our data and methodology notes for calculation context. This guide explains research tools and observations. It does not recommend a trade or investment.