What an Edge Feels Like

Eight losses in a row at a 45 per cent win rate is not evidence of anything: it turns up in more than half of all two-hundred-trade samples, and it depends on your win rate alone and not at all on how much your winners pay. What actually threatens the account is the drawdown, which is a different and larger number. Both are computable before you meet them, and both take one evening and a spreadsheet.

Prerequisites: Lesson 17, which gave you p and b and the +0.35R a trade that every figure below is a consequence of, and lesson 10, for R, which is the unit they are written in.

The drawdown you have not met yet

Take the system from lesson 17’s table: a 45 per cent win rate at b = 2, so an expectancy of +0.35R a trade. A good system, and one most traders would sign for. Here is what it does to you along the way.

There is no closed form for this one, so it is simulated: two hundred thousand independent runs of two hundred trades each, outcomes drawn at a 45 per cent win rate, seed 20260901. The second column is the distribution of the worst peak-to-trough drawdown in each run. The last two columns are those same runs measured in money instead of in R: among every run that fell exactly that far, what an account risking a fixed fraction of its current equity was typically down at the bottom. Every outcome here is +2R or −1R, so the equity is a whole number at every step and the R drawdown is too; re-running under other seeds returns the same integers, give or take one at the far tail.

How unlucky	Worst drawdown in 200 trades	Fall in the account at 1% risk a trade	Fall at 3%
Typical — the median run	9R	8.7%	24.4%
One run in four	12R	11.5%	31.3%
One in twenty	16R	15.0%	39.5%
One in a hundred	21R	19.2%	48.5%

The sentence worth keeping is this. A 16R drawdown in this system is not evidence of anything either. It is the one-in-twenty outcome of a method that makes money, and one in twenty is not rare — it is a normal year in a career of twenty. If your risk limits are set so that 16R forces you to stop, you have built a system that switches itself off during an ordinary year, and you will experience that shutdown as proof the edge died.

The last two columns are where sizing stops being theoretical, and they are worth reading across rather than down. Nothing differs between them except the fraction of the account you put behind each trade. Same method, same edge, same trades in the same order: one trader is down 15 per cent in the one-in-twenty year and is level again on an 18 per cent gain, the other is down nearly 40 and needs 65 per cent to get back. Neither figure is sixteen straight losses compounded, which comes to 14.9 and 38.6 per cent, because a 16R fall is a longer stretch than sixteen trades and contains winners as well; the shortcut runs a tenth of a point light at 1 per cent risk and nearly a point light at 3. Lesson 20 is where that decision gets made properly, and where the gap between those two arithmetics turns out to matter; the point here is only that the depth of a normal bad run is a number you choose, and the frequency of one is not.

Which brings the two halves together. Your deepest drawdown to date is almost certainly not the deepest this method will hand you. If you have taken two hundred trades, the arithmetic above says a typical worst is around 9R and the one-in-twenty case is 16R — and if you have taken fewer than two hundred, you have not yet had the chance to meet either. Being surprised by a 12R drawdown after 150 trades is not information about the method. It is information about which part of the distribution you happen to have visited.

What this does not settle

That these are your numbers. Everything above is computed for a 45 per cent win rate at b = 2, and the whole point of the exercise is that you replace both with your own. Do not borrow the nearest row either: two points of win rate move the eight-loss cell nine points, down to 44 per cent if you are better than 45 and up to 62 if you are worse, and the direction you are wrong in is the one you would not have guessed. And the two tables answer to different inputs, which is the thing to carry away from having them side by side — the streak table does not move with b at all, while the drawdown distribution moves with both p and b. The problems below are how you get your own, and neither calculation needs anything more than a spreadsheet.

Nor is the win rate you are about to plug in a fact. It is an estimate, and on a short record a poor one: forty trades that came out at 45 per cent are consistent with a true rate of roughly anywhere from 30 to 60, and across that range the eight-loss cell runs from 98 per cent down to 7. Which means the card you write in the first problem below is, early on, uncertain by more than the entire spread of the table it came from. That is not a reason to skip the calculation. It is the reason the next lesson exists, and it is why the card is worth rewriting every fifty trades rather than once.

Nor does it say that a bad run is always variance. That is the opposite error and it is just as expensive. What the table establishes is which run lengths are ordinary for your own win rate; a run well outside them is a different conversation, and so is a drawdown past your own one-in-a-hundred. The value of computing the distribution in advance is precisely that it tells you where the boundary is, and a boundary you have not computed cannot be crossed knowingly.

The simulation also assumes your trades are independent and identically distributed, which real records are not. Positions taken on the same idea lose together, which makes the fall steeper than the model says; a change of regime clusters the losses rather than spreading them, which does the same. Both violations push the drawdown deeper than the table, so treat every figure in it as the optimistic case.

And none of this tells you when to stop. It tells you what is ordinary, which is the input to that decision and not the decision itself. The rule for stopping has to be written before the drawdown rather than during it, which is lesson 24, and how likely a drawdown is to end the account outright is lesson 22. Whether the edge you are drawing down on was ever real is the next lesson, and it is the slower question of the two.

A working method still hands you runs long enough to make you doubt it. The only thing that separates a normal bad run from a broken system is arithmetic you did before you needed it.

Problems

1. Compute your own row. Take your own win rate rather than the 45 per cent the first table uses, and work out the probability of at least one losing run of 5, 6, 7, 8 and 10 inside two hundred trades. One column per current-run-length state, one row per trade, a win sends the whole probability back to state zero and a loss shifts it along by one. Write the row on a card and keep it where you will see it during a drawdown, because that is the only moment it is worth anything.
2. Ask how often, not just whether. Using the same win rate, compute (1 − q^k) ÷ (p × q^k) for the run length that would genuinely worry you. Divide by how many trades you take in a week. If the answer is a number of months rather than a number of years, you are going to meet that run, and you now know roughly when.
3. Find your own distribution, then check yourself against it. Simulate ten thousand runs of two hundred trades at your own p and b, record the worst drawdown in each, and take the median and the ninety-fifth percentile. Now put your actual worst drawdown to date beside those two numbers. If yours sits below the median, the honest reading is not that the method is safe. It is that you have not yet been trading long enough to have met the ordinary case.

Sources. William Feller, An Introduction to Probability Theory and Its Applications, Volume I (3rd edition, 1968), chapter XIII, which is the classical treatment of success runs and where the recursion behind the first table comes from. Malik Magdon-Ismail and Amir Atiya, “Maximum Drawdown” (Risk 17, 2004), which derives the expected maximum drawdown of a process with positive drift and establishes the uncomfortable half of it: a profitable process still has an expected worst drawdown that keeps growing as you keep going. Ilia D. Dichev, “What Are Stock Investors’ Actual Historical Returns?” (American Economic Review 97, 2007), which measures the gap between what markets returned and what investors in them actually earned, and locates it in the timing of money arriving and leaving — which is this lesson’s subject, priced across a whole population.

You now know what a working method feels like from the inside, and how to compute it for your own two numbers. The next lesson asks the question a bad run makes urgent: if the edge really has gone, how long would it take before your results could show it?

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.