Risk-to-reward and expectancy
Why this lesson exists
"What's your win rate?" is the wrong first question to ask a trader. A 70% win rate can be a slow bleed. A 30% win rate can be a Mercedes by year-end. The number that separates them is risk-to-reward — how much you make on a winner versus how much you lose on a loser.
Pair R:R with win rate and you get expectancy: the average rupees you make per trade, across many trades. Expectancy is the only number that tells you whether a strategy is worth running. This lesson derives it, walks through three worked examples on a ₹5,00,000 xtree Standard account, and shows the exact line where good strategies become bad ones.
R:R defined
Risk-to-reward is the ratio of how far you're aiming for the win to how far you'd let the loss go:
R:R = target_distance / stop_distance
You enter xBTC long at ₹85,00,000. Stop at ₹84,50,000 (₹50,000 below). Target at ₹86,00,000 (₹1,00,000 above).
R:R = ₹1,00,000 / ₹50,000 = 2:1
You're risking 1 unit to make 2. A 2:1 R:R does not mean you will win — it just means if you win, you make twice what you lose if you don't.
R:R is decided at entry, not at exit. The stop and target come from the chart. You write them down before you click buy. You do not move the target up because the trade started working, and you do not move the stop down because the trade started not working. Both are the most expensive habits in retail trading.
Why win rate alone is meaningless
Two traders. Same ₹5,00,000 account. Same ₹5,000 risk per trade (from position sizing).
Trader A wins 40% of the time at 2:1 R:R.
expectancy_A = (0.40 × ₹10,000) − (0.60 × ₹5,000)
= ₹4,000 − ₹3,000
= +₹1,000 per trade
expectancy = (win_rate × avg_win) − (loss_rate × avg_loss)
100 trades: roughly +₹1,00,000. Profitable.
Trader B wins 70% of the time at 0.5:1 R:R (small targets, wide stops).
expectancy_B = (0.70 × ₹2,500) − (0.30 × ₹5,000)
= ₹1,750 − ₹1,500
= +₹250 per trade
Same 100 trades: +₹25,000. Profitable but a quarter the size. And one bad week of variance — five losses in a row, which is unremarkable at a 30% loss rate — costs ₹25,000. Trader B's entire 100-trade edge.
Trader C wins 70% of the time at 1:3 R:R (tight targets, very wide stops — the classic over-confident scalper).
expectancy_C = (0.70 × ₹1,667) − (0.30 × ₹5,000)
= ₹1,167 − ₹1,500
= −₹333 per trade
Negative. A 70% win rate, losing money. The R:R is killing them. Trader C will fail the xtree evaluation — not because they don't know what they're doing on individual trades, but because the math under their strategy is broken.
The expectancy formula
The general form:
expectancy = (win_rate × avg_win) − (loss_rate × avg_loss)
Where win_rate + loss_rate = 1 (we treat breakeven exits as losses for safety). If your risk per trade is fixed at R rupees (your stop distance × position size — the constant you decided up front), then:
expectancy = (win_rate × R:R × R) − (loss_rate × R)
= R × [(win_rate × R:R) − loss_rate]
The strategy is profitable when the bracketed term is positive. Set it to zero to find the breakeven win rate for any R:R:
breakeven_win_rate = 1 / (1 + R:R)
A few useful pairs to memorise:
| R:R | Breakeven win rate | Comfortable win rate | |---|---|---| | 1:1 | 50% | 55%+ | | 1.5:1 | 40% | 45%+ | | 2:1 | 33% | 38%+ | | 3:1 | 25% | 30%+ | | 5:1 | 17% | 22%+ |
A 3:1 strategy only needs to win 1 trade in 4 to break even. A 1:1 strategy needs to win more than half — which is harder than most people think.
On xtree's Standard tier, the profit target is ₹30,000 (6% of ₹5,00,000). At ₹5,000 risk per trade with 2:1 R:R, your average win is ₹10,000. Net expectancy of +₹1,000/trade means you reach ₹30,000 in about 30 trades. That's roughly a month of disciplined, selective trading — not a sprint.
Why 1.5:1 is the practical floor
In theory any positive-expectancy strategy works. In practice the assumptions break down at low R:R:
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Slippage and fees. xtree charges 5 bps entry + 5 bps exit. On a 0.5:1 trade with a ₹2,500 target, that's ~₹85 of fees on a ₹2,500 win = 3.4% of the win. On a 2:1 trade with a ₹10,000 target, the same fees are 0.85% of the win. Low R:R amplifies the cost of friction.
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Win-rate drift. Your true win rate is unknown — you estimate it from a sample. The smaller the cushion above breakeven, the more sensitive your strategy is to estimation error. A 0.5:1 strategy needs ≥67% win rate to make money; a real 64% rate is unprofitable. A 2:1 strategy needs ≥33%; a real 30% is unprofitable but the gap is wider and more forgiving.
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Drawdowns. Five losses in a row happen often enough that you must plan for them. At 1.5:1 R:R with 1% risk per trade, five straight losses costs 5% of the account. At 1:3 R:R with 1% risk per trade, five wins followed by one loss is roughly breakeven — the variance dominates.
Use 1.5:1 as a soft floor. Aim for 2:1 or better. If your average R:R is consistently below 1.5:1, your strategy is most likely scalping, in which case win rate has to be much higher and discipline on losing trades has to be perfect.
Worked example: a month of momentum
Standard ₹5,00,000 account. Strategy: 1h momentum continuation entries with a 1.8:1 average R:R, ₹5,000 risk per trade. Observed win rate over 40 trades: 42%.
expectancy = 0.42 × (1.8 × ₹5,000) − 0.58 × ₹5,000
= 0.42 × ₹9,000 − 0.58 × ₹5,000
= ₹3,780 − ₹2,900
= +₹880 per trade
Over 40 trades: ~₹35,200 of expected gross P&L. Net of fees (~₹100/trade × 40 = ₹4,000): roughly ₹31,000. That clears the ₹30,000 profit target.
What this hides: the path. A run of 6 losers early in the month draws down ₹30,000 (6% of the account) before a single winner. The trader has to keep sizing correctly during that drawdown. Most traders don't — they cut size after losses, miss the winners that come, and end the month at expectancy times 0.6.
Position sizing and R:R are paired skills. The expectancy math is meaningless if you abandon the sizing rule mid-streak.
Common misunderstanding
"My win rate is 80% so the strategy is good."
A win rate by itself tells you nothing. The trader running 80% wins on 1:5 R:R has a breakeven win rate of 83% — they're losing money. The trader running 25% wins on 5:1 R:R has a breakeven win rate of 17% — they're making money.
Always ask the second question: what's your average R:R, and what's your breakeven win rate? If the trader can't answer both, they don't know whether their strategy is profitable; they just know whether their last few trades were.
Recap
- R:R = target_distance / stop_distance, decided at entry from the chart.
- Expectancy = (win_rate × avg_win) − (loss_rate × avg_loss). Negative expectancy is a slow bleed regardless of win rate.
- Breakeven win rate = 1 / (1 + R:R). Memorise the table.
- 1.5:1 is a soft floor; 2:1 is a sensible target. Below 1.5:1, friction and variance eat the edge.
- Strategy evaluation needs three numbers, not one: win rate, R:R, and expected number of trades.
Next up: the floor that ends accounts on xtree — what the Maximum Loss Limit is, why it trails, and the drawdown-recovery math behind it.
Test yourself
Next lesson: Maximum Loss Limit (MLL) explained — the floor that ends accounts on xtree, why it trails, and the drawdown math behind it.