Intuition The core idea in one breathYou cannot control whether a single trade wins or loses — that is noise. But you CAN control your risk unit (R) and measure your outcomes in multiples of that unit . Once every trade is measured in R, wins and losses become comparable "chips", and expectancy tells you how many chips the whole system spits out per bet on average. A positive expectancy system makes money over many trades even if it loses more often than it wins.
R is the amount of money you are willing to lose on a trade if your stop-loss is hit. It is fixed before you enter.
R = ( Entry Price − Stop Price ) × Position Size R = (\text{Entry Price} - \text{Stop Price}) \times \text{Position Size} R = ( Entry Price − Stop Price ) × Position Size 1-unit of risk . Everything else is measured relative to it.
WHY define R at all?
Because dollar amounts across different trades are not comparable. A ₹500 loss on a ₹10,000 position and a ₹500 loss on a ₹1,00,000 position mean very different things. By expressing outcomes as multiples of R , every trade is put on the same scale , no matter the price, share count, or account size.
The result of a trade divided by the risk you took:
R -multiple = Profit or Loss on the trade R R\text{-multiple} = \frac{\text{Profit or Loss on the trade}}{R} R -multiple = R Profit or Loss on the trade
A trade that loses exactly your stop = ==− 1 R -1R − 1 R
A trade that makes twice your risk = + 2 R +2R + 2 R
A trade closed early for half a loss = − 0.5 R -0.5R − 0.5 R
You buy a stock at ₹200 with a stop at ₹190, buying 100 shares.
Risk per share = 200 − 190 = ₹ 10 = 200 - 190 = ₹10 = 200 − 190 = ₹10
R = 10 × 100 = ₹ 1000 R = 10 \times 100 = ₹1000 R = 10 × 100 = ₹1000
Why this step? R is defined by the distance to your stop , not the entry price. The stop is where your idea is proven wrong, so the loss there = 1 full unit of risk.
Worked example Converting an exit into an R-multipleSame trade. You sell at ₹230.
Profit = ( 230 − 200 ) × 100 = ₹ 3000 = (230 - 200) \times 100 = ₹3000 = ( 230 − 200 ) × 100 = ₹3000
R -multiple = 3000 / 1000 = + 3 R R\text{-multiple} = 3000 / 1000 = +3R R -multiple = 3000/1000 = + 3 R
Why this step? We divide by R (₹1000), not by the entry cost, because R is our chosen yardstick of risk. This trade returned 3 units of risk .
Worked example A loss that isn't a full lossYou get nervous and exit at ₹195 before the stop hits.
Loss = ( 195 − 200 ) × 100 = − ₹ 500 = (195 - 200)\times 100 = -₹500 = ( 195 − 200 ) × 100 = − ₹500
R -multiple = − 500 / 1000 = − 0.5 R R\text{-multiple} = -500/1000 = -0.5R R -multiple = − 500/1000 = − 0.5 R
Why this step? Exiting early cuts the loss to half a unit. Notice R stays ₹1000 (defined at entry) — the actual loss can be smaller or larger than 1R.
We want: on average, how much R do I make per trade?
Suppose over many trades:
Win rate = W = W = W = 1 − W = 1 - W = 1 − W
Average winning trade = + A w = +A_w = + A w
Average losing trade = − A ℓ = -A_\ell = − A ℓ A ℓ A_\ell A ℓ
Step 1 — average of anything = probability-weighted sum of outcomes.
E = ( P(win) × avg win ) + ( P(loss) × avg loss ) E = (\text{P(win)} \times \text{avg win}) + (\text{P(loss)} \times \text{avg loss}) E = ( P(win) × avg win ) + ( P(loss) × avg loss )
Step 2 — plug in our symbols.
E = W ⋅ A w − ( 1 − W ) ⋅ A ℓ [ in units of R ] \boxed{E = W \cdot A_w - (1-W)\cdot A_\ell} \quad [\text{in units of } R] E = W ⋅ A w − ( 1 − W ) ⋅ A ℓ [ in units of R ]
Why the minus sign? Losing trades subtract R, so their contribution is negative. A ℓ A_\ell A ℓ magnitude ; the sign is carried explicitly.
Intuition Predict before you computeA system wins 40% of the time. Winners average + 2 R +2R + 2 R − 1 R -1R − 1 R Guess: profitable or not? Many people say "loses 60% of the time → bad system."
Now verify:
E = 0.40 ( 2 ) − 0.60 ( 1 ) = 0.8 − 0.6 = + 0.2 R E = 0.40(2) - 0.60(1) = 0.8 - 0.6 = +0.2R E = 0.40 ( 2 ) − 0.60 ( 1 ) = 0.8 − 0.6 = + 0.2 R Positive! Over 100 trades with R = ₹ 1000 R = ₹1000 R = ₹1000 ≈ 0.2 × 1000 × 100 = ₹ 20,000 \approx 0.2 \times 1000 \times 100 = ₹20{,}000 ≈ 0.2 × 1000 × 100 = ₹20 , 000
Worked example A high win-rate LOSERA system wins 90% of the time (+0.5R winners) but the 10% losers are − 6 R -6R − 6 R E = 0.90 ( 0.5 ) − 0.10 ( 6 ) = 0.45 − 0.60 = − 0.15 R E = 0.90(0.5) - 0.10(6) = 0.45 - 0.60 = -0.15R E = 0.90 ( 0.5 ) − 0.10 ( 6 ) = 0.45 − 0.60 = − 0.15 R Why this matters: Feeling "right 9 out of 10 times" is emotionally addictive but the rare huge losses destroy the account. This is why cutting losses (keeping A ℓ A_\ell A ℓ
Common mistake "High win rate = good system."Why it feels right: Being correct often feels like skill, and we hate losing streaks. The fix: Win rate alone is meaningless. Expectancy = win rate weighted by the size of wins vs losses. A 40% system with 3:1 payoff beats a 90% system with tiny wins and giant losses.
Common mistake Measuring R from the entry price instead of the stop.Why it feels right: The entry price is the number you "paid," so it seems central. The fix: R is the distance to your stop × size. It's the money at risk, not the money invested.
Common mistake Changing R after entry (moving the stop away to avoid a loss).Why it feels right: "The trade will come back." The fix: R is fixed at entry. Widening the stop secretly turns a − 1 R -1R − 1 R − 3 R -3R − 3 R
Common mistake Confusing per-trade expectancy with per-day profit.Why it feels right: You want to know daily income. The fix: Expectancy is per trade averaged over MANY trades . Small samples swing wildly; the number only shows up over dozens/hundreds of trades.
Recall Feynman: explain to a 12-year-oldImagine every bet you make risks exactly one candy. Sometimes you win 2 candies, sometimes you lose your 1 candy. If you play a hundred times, expectancy tells you how many candies you'll have on average at the end for each game you played. Even if you lose more games than you win, if your wins give you big candy piles and your losses only cost one candy, you go home with more candy. The trick is: never let one bad game cost you a whole bag of candy — always risk just one.
"Win Big, Lose One R." — Keep every loss at − 1 R -1R − 1 R W inners W eighted minus L osers L oaded → W A w − ( 1 − W ) A ℓ W A_w - (1-W)A_\ell W A w − ( 1 − W ) A ℓ
What is R in trading? The fixed amount of money you're willing to lose if your stop is hit;
R = ( Entry − Stop ) × Size R = (\text{Entry}-\text{Stop}) \times \text{Size} R = ( Entry − Stop ) × Size . It's your 1-unit of risk.
How do you compute an R-multiple? Trade profit or loss divided by R. A full stop-out =
− 1 R -1R − 1 R ; a win of twice your risk =
+ 2 R +2R + 2 R .
Write the expectancy formula in R. E = W ⋅ A w − ( 1 − W ) ⋅ A ℓ E = W\cdot A_w - (1-W)\cdot A_\ell E = W ⋅ A w − ( 1 − W ) ⋅ A ℓ , where
W W W = win rate,
A w A_w A w = avg win in R,
A ℓ A_\ell A ℓ = avg loss magnitude in R.
Can a system with a 40% win rate be profitable? Yes. E.g.
0.4 ( 2 R ) − 0.6 ( 1 R ) = + 0.2 R 0.4(2R) - 0.6(1R) = +0.2R 0.4 ( 2 R ) − 0.6 ( 1 R ) = + 0.2 R . Win rate alone doesn't determine profitability.
Why measure results in R instead of rupees? To put every trade on the same risk scale regardless of price, share count, or account size, so outcomes are comparable.
What does positive expectancy mean? Each trade returns positive R on average, so over many trades
E × R × N E\times R\times N E × R × N money is expected — profitable long-run.
Over N trades, expected profit ≈ ? E × R × N E \times R \times N E × R × N (expectancy per trade × risk unit × number of trades).
Why can a 90% win-rate system still lose money? If the rare 10% losers are huge (e.g.
− 6 R -6R − 6 R ), they overwhelm the many small wins:
0.9 ( 0.5 ) − 0.1 ( 6 ) = − 0.15 R 0.9(0.5)-0.1(6)=-0.15R 0.9 ( 0.5 ) − 0.1 ( 6 ) = − 0.15 R .
What happens to expectancy if you widen your stop after entry? Your real R grows, turning a
− 1 R -1R − 1 R into a bigger loss, poisoning expectancy and the account. R must be fixed at entry.
Break-even expectancy value? E = 0 E = 0 E = 0 (before costs). Below 0 you lose money; no position sizing fixes negative expectancy.
Position Sizing — R determines how many shares to buy for a fixed % risk.Stop-Loss Placement — the stop defines R; bad stops distort everything.Risk-Reward Ratio — the ratio A w : A ℓ A_w : A_\ell A w : A ℓ Win Rate vs Payoff — the trade-off that makes low-win systems viable.Trading Journal — where R-multiples are logged to measure real expectancy.Law of Large Numbers — why expectancy only manifests over many trades.
System profits over many trades
Win rate below 50 percent
Intuition Hinglish mein samjhoDekho, trading mein har ek trade ka result predict karna impossible hai — woh random noise hai. Lekin ek cheez tum control kar sakte ho: kitna paisa risk karoge . Usko bolte hain R . R matlab entry price aur stop-loss ke beech ka distance × kitne shares. Agar entry ₹200, stop ₹190, aur 100 share liye, toh R = ₹1000. Yehi tumhara ek "risk unit" hai.
Ab har trade ka result rupees mein mat socho, R ke multiple mein socho . Agar ₹3000 profit hua toh woh + 3 R +3R + 3 R − 1 R -1R − 1 R
Expectancy batati hai ki average mein per trade tum kitne R banaoge: E = W ⋅ A w − ( 1 − W ) ⋅ A ℓ E = W \cdot A_w - (1-W)\cdot A_\ell E = W ⋅ A w − ( 1 − W ) ⋅ A ℓ W W W A w A_w A w A ℓ A_\ell A ℓ E E E loss ko 1R par control rakho aur jeet ko badi hone do.
Yaad rakho: expectancy ek din ya do trade mein nahi dikhti — 100-200 trades ke baad dikhti hai (Law of Large Numbers). Isliye discipline rakho, stop mat hilao, aur R fix rakho. "Win Big, Lose One R" — bas yehi mantra hai.
