Risk: streaks, expectancy, journal

In section 16 we learned to measure each trade's result in R. The next question is what a way of trading, repeated many times, brings — not one trade. The answer is expectancy:

expectancy = win rate × average win − loss rate × average loss, all in R.

Example: 40% of trades close at +2R on average, 60% at −1R. Expectancy = 0.4 × 2 − 0.6 × 1 = 0.8 − 0.6 = +0.2R. That means about +20R on average over a hundred such trades. At 1% risk per trade that is roughly +20% — but not as a straight line; with dips, which are the next lesson.

Another example: 65% wins at +0.5R and 35% losses at −1R. 0.65 × 0.5 − 0.35 × 1 = 0.325 − 0.35 = −0.025R. It wins almost two trades out of three — and still slowly loses.

Hence the key point: win rate on its own says nothing, and neither does the average win on its own. What matters is their ratio. It helps to know the break-even win rate — the one at which expectancy is zero:

break-even win rate = average loss / (average win + average loss).

• +1R / −1R → 1 / 2 = 50%;
• +2R / −1R → 1 / 3 ≈ 33.3%;
• +3R / −1R → 1 / 4 = 25%;
• +0.5R / −1R → 1 / 1.5 ≈ 66.7%.

A system with +3R wins is profitable already at 26% winners, while a system with +0.5R wins loses money even at 66%.

Fees and slippage live inside expectancy. Every trade, winning or not, pays for entry and exit. If that averages 0.1R per trade, a +0.2R expectancy becomes +0.1R — half of the edge goes to the exchange. With a +0.05R expectancy the same 0.1R makes the trading unprofitable.

Averages must be measured, not planned. “Target +2R” and “average win +2R” are different things. If you close half of the winners early, “before it turns”, the average win may come out at +1.2R. Then with the same 40% winners expectancy = 0.4 × 1.2 − 0.6 × 1 = −0.12R: a system profitable on paper becomes a losing one in your hands.

How little “tens” is. Take a system with a true 40% of wins at +2R and 60% of losses at −1R (expectancy +0.2R) and look at a stretch of 20 trades. The probability of seeing 5 wins or fewer is about 13%, of 11 or more — also about 13%. And the probability that the 20 trades end at zero or below (6 wins or fewer) is 25%: one such stretch in four ends flat or negative for a profitable system.

Conclusion: twenty trades cannot honestly tell you either “the system works” or “the system is broken”. The smaller the sample, the more chance there is in it.

If trades are independent and the loss rate is q, the probability that the next N trades all lose is q to the power N. At q = 60%: two in a row — 36%, three — 21.6%, four — 12.96%, five — 7.78%. At q = 55%: four in a row — 0.55⁴ ≈ 9.15%. At q = 50%: six in a row — 1.56%.

That is the probability for a specific place — “these five trades”. It is small, and so a streak feels like a rare event. But people trade hundreds of trades, not five.

A completely different question is whether at least one run of N losses in a row will occur somewhere among 100 trades. Here the probabilities are large (the exact computation is in the section's script):

• 60% losers: a run of 5 or more — 97.6%, of 6 — 87.3%, of 8 — 49.0%, of 10 — 20.5%;
• 50% losers: of 5 — 81.0%, of 6 — 54.6%, of 8 — 17.0%;
• 40% losers (60% winners): of 5 — 45.9%, of 6 — 21.2%, of 8 — 3.6%.

A “40% winners at +2R” system is profitable (+0.2R per trade), yet over a hundred trades it will almost certainly live through six losses in a row, and with a probability of about one half — eight. That is not the system breaking; it is its normal life.

The past does not change the next trade. If trades are independent, after five losses in a row the chance of winning the sixth is the same as it was. The feeling “now I'm surely due” is the well-known gambler's fallacy. The reverse holds too: after five wins in a row the next trade is not “bound” to lose.

An honest caveat: in real life trades are not perfectly independent. The market changes its character, and a losing streak sometimes means that the conditions the entry was designed for are not present right now. But that can only be judged from records and on a sufficient sample (lesson 4), not from a feeling after three failures.

How to use this. A streak cannot be predicted, but its length can be estimated in advance and prepared for. The order is: how many trades you make in a quarter → what your loss rate is according to your records → what streak is ordinary for that number of trades. Per the table above, with 60% losers a run of 8 or longer happens within a hundred trades in almost half of cases (49.0%).

Then a simple calculation: eight losses in a row at 1% risk of the current account leave 0.99⁸ ≈ 92.3% of the account, at 2% — 0.98⁸ ≈ 85.1%. If the second number is unbearable for you, 2% risk is not for you, and it is better to find that out before the streak than in the middle of it.

Another rule worth writing down in advance: “if a streak is longer than so many — I stop for a day and review my records”. Not “I increase size”, not “I change the entry”, but a pause and a review: that way a streak becomes a reason to check yourself rather than a reason to break the rules.

A drawdown is the account's fall from its peak to the subsequent low, in percent. The account grew to $12,000, then fell to $9,000 — a drawdown of (12,000 − 9,000) / 12,000 = 25%.

The main trouble with a drawdown is its asymmetry. Having lost half, you need not +50% but +100%: $10,000 → $5,000, and to get back you must make $5,000 — that is 100% of the remaining $5,000. The general formula: required gain = d / (1 − d), where d is the drawdown as a fraction.

• −10% → +11.1%;
• −20% → +25%;
• −30% → +42.9%;
• −40% → +66.7%;
• −50% → +100%;
• −75% → +300%.

Small drawdowns come back almost “one for one”. Deep ones require growth that most ways of trading simply do not deliver in a reasonable time.

Risk from the current account. If risk per trade is a fixed percentage of the account as it is now, the next dollar risk is slightly smaller after each loss. After k losses in a row (1 − r) to the power k remains:

• r = 1%: 6 losses → 94.15%, 10 → 90.44%;
• r = 2%: 6 → 88.58%, 10 → 81.71%;
• r = 5%: 6 → 73.51%, 10 → 59.87%;
• r = 10%: 6 → 53.14%, 10 → 34.87%.

The link to the previous lesson is direct: a run of six losses within a hundred trades is ordinary for a system with 60% losers. At 1% risk it costs about 6% of the account and needs +6.2% to recover. At 10% risk it costs about 47% of the account and needs +88%.

Everything above — expectancy, average win, win rate, streak length — cannot be learned from memory. Memory keeps bright wins and losses explained after the fact. That is why you need a trading journal: a record of every trade, made right away, in the same format.

What to record:

• date and time of entry and exit, the coin, the side (long or short);
• entry, the initial stop and the target — before entry, not after;
• position size and the dollar risk — that is, this trade's 1R;
• exit and the result in R, fees;
• the reason for entry — which type of entry (setup), one word from your fixed list;
• what the market showed at entry: flow, book, the nearest levels;
• mistakes — honestly: moved the stop, entered without a plan, increased size, closed early.

Without the initial stop the result in R cannot be computed at all: R is the distance to the stop set before entry. If the stop was moved later, R stays the same, and the result honestly shows what the move cost.

How to read what has accumulated. After a month or two the journal answers questions that memory answers wrongly:

• what my real expectancy in R is — not planned but measured, fees included;
• which type of entry makes money and which gives it away: the most useful thing is to find the worst one — it is easier to drop than to learn to do the best one more often;
• what my mistakes cost: the sum of R over trades marked “moved the stop” is often larger than the whole month's profit;
• what shape the equity curve has: a steady rise and the same total made in one burst after a long drawdown are different ways of trading, even though the total is the same.

And always look at the number of trades next to every conclusion: a difference between two entry types over five trades is almost certainly chance (lesson 1).

In EVA the journal is kept on the «Statistics» tab: a trade is logged with a «Position» from the chart or by hand, results are counted in R, there is an equity curve, breakdowns by setup, coin and time, and the «Mistakes you tagged» block — their price in R. Details are in section 18.