The math that determines whether your trading system makes money — risk/reward ratios, expectancy calculation, losing streak statistics, and the trading journal.
1. Calculate risk/reward ratio for any trade setup and set minimum thresholds.
2. Understand expectancy — the formula that determines whether your system makes money.
3. Recognize why win rate alone is meaningless without payoff context.
4. Model drawdowns and understand the statistics of losing streaks.
5. Build a trading journal that tracks the metrics that matter.
6. Use these concepts to filter out low-quality trades before entry.
The risk/reward ratio (R/R) compares how much you stand to make if the trade works versus how much you'll lose if it doesn't. If you enter at $50 with a stop at $48 (risking $2) and a target at $56 (potential gain of $6), your R/R is 6:2, or 3:1.
The minimum threshold: Never take a trade with less than 2:1 risk/reward. This is not a suggestion — it's a survival rule. At 2:1, you can be wrong 60% of the time and still break even. At 1:1, you need a 50%+ win rate just to tread water (and with commissions and slippage, you need even more). Higher R/R trades give your edge room to breathe.
| Risk/Reward | Win Rate Needed to Break Even | Quality |
|---|---|---|
| 1:1 | 50% | Poor — no room for error |
| 2:1 | 33% | Acceptable — minimum threshold |
| 3:1 | 25% | Good — comfortable margin |
| 4:1 | 20% | Excellent — significant edge |
| 5:1+ | 17% | Outstanding — rare but powerful |
Calculate R/R before entry, not after. The risk is your entry minus your stop. The reward is your target minus your entry. If the R/R is below 2:1, don't take the trade — regardless of how attractive the setup looks. Discipline on R/R is one of the most powerful filters for separating high-quality trades from mediocre ones. Module 4.6 (Building a Thesis) included exit criteria for exactly this purpose.
Expectancy is the average amount you make (or lose) per trade over time. It combines win rate, average win size, and average loss size into a single number:
Expectancy = (Win Rate × Avg Win) − (Loss Rate × Avg Loss)
Example: Win rate = 45%, avg win = $800, avg loss = $400.
Expectancy = (0.45 × $800) − (0.55 × $400) = $360 − $220 = +$140 per trade
This trader loses more often than they win (45% vs. 55%) but makes money because their winners are twice the size of their losers. Over 100 trades, they expect to make approximately $14,000. This is the power of R/R combined with reasonable accuracy — you don't need to be right most of the time as long as your winners are significantly larger than your losers.
Path 1: High win rate, modest R/R. Win 65% of the time with 1.5:1 average R/R. This feels psychologically comfortable (frequent wins) but requires consistent execution and gives less room for error.
Path 2: Moderate win rate, high R/R. Win 40% of the time with 3:1 average R/R. This feels psychologically challenging (frequent losses) but is mathematically robust and more forgiving of imperfect execution.
Most professional trend-following traders use Path 2. Most scalpers and mean-reversion traders use Path 1. Either can work — what matters is that expectancy is positive and that you're psychologically suited to your path's emotional demands (Module 7.4).
If you've been trading (even in paper trading from Module 2.3), pull up your last 20 trades. For each, record: win or loss, dollar amount won or lost. Then calculate: Win rate = wins ÷ total trades. Average win = total won ÷ number of wins. Average loss = total lost ÷ number of losses. Expectancy = (win rate × avg win) − (loss rate × avg loss). If expectancy is negative, your system needs work — either improve your win rate (better entries) or improve your R/R (better stop/target placement). If you have fewer than 20 trades, keep trading in paper until you have enough data to calculate meaningful statistics.
Every trader experiences losing streaks. They're not a sign of failure — they're a mathematical certainty. The question isn't whether you'll have a losing streak; it's whether your position sizing (Module 7.1) keeps you solvent through it.
| Win Rate | Expected Max Losing Streak (per 100 trades) | Probability of 5+ Consecutive Losses |
|---|---|---|
| 40% | 7–9 losses | ~78% |
| 50% | 6–7 losses | ~50% |
| 55% | 5–6 losses | ~37% |
| 60% | 4–5 losses | ~24% |
Even with a 60% win rate — which is very good — there's a 24% chance of 5+ consecutive losses in every 100-trade sample. This is why the 1% risk rule (Module 7.1) exists: it makes these inevitable losing streaks survivable.
Module 14.4 (The Trading Journal) builds a comprehensive tracking system for all these metrics. Module 2.3 (Paper Trading) introduced realistic performance benchmarks. Module 7.4 (Trading Psychology) addresses the emotional challenge of enduring losing streaks while maintaining discipline. These four modules together create the feedback loop that enables continuous improvement.
A trading journal is the most important self-improvement tool in a trader's arsenal. For every trade, record:
Pre-trade: Date, ticker, setup type, thesis (1 sentence), entry price, stop price, target price, R/R ratio, position size, conviction level.
Post-trade: Exit price, P&L (dollars and R-multiples), what you did well, what you'd change, emotional state during the trade.
After 50+ trades, your journal reveals patterns invisible in real time: which setups produce the best R/R, which market conditions lead to losing streaks, which emotional states lead to rule violations. This data-driven self-analysis is what separates traders who improve from those who repeat the same mistakes for years.
A trend-following trader tracked their results over one calendar year: 120 trades, 48 winners (40% win rate), 72 losers (60%). On the surface, this looks terrible — wrong most of the time. But the average winner was +3.2R (320% of the initial risk), while the average loss was −1.0R (the stop was hit). The small percentage of big trend-following winners — positions held for weeks to months using trailing stops (Module 7.2) — more than compensated for the many small losses from failed breakouts.
Expectancy per trade = (0.40 × 3.2R) − (0.60 × 1.0R) = 1.28R − 0.60R = +0.68R per trade. Over 120 trades at 1% risk per trade, the annual return was approximately 81.6R × 1% ≈ approximately 25% account growth (compounding effects make the actual return slightly higher).
The lesson: profitability is not about being right. It's about making more when you're right than you lose when you're wrong. This trader was wrong 60% of the time and still had an excellent year — because position sizing limited losses and trailing stops maximized winners.
1. A trade has $2 risk and $8 potential reward. The risk/reward ratio is:
2. A trader wins 40% of trades with an average win of $1,500 and loses 60% with an average loss of $500. Their expectancy is:
3. Why is a minimum 2:1 risk/reward important?
4. With a 55% win rate, what is the approximate probability of experiencing 5 or more consecutive losses in 100 trades?
5. A trader's journal shows that their 'revenge trades' (trades taken immediately after a loss to 'get it back') have −$2.10 expectancy per trade. What should they do?
6. What does a positive expectancy of +0.5R per trade mean in practical terms?