Expectancy Is the Only Verdict

Expectancy, in R

Everything in this subject is measured in **R**, where one R is the amount risked on the trade. A trade that gains three times its risk is +3R; a trade stopped out for the planned loss is −1R. Measuring in R rather than dollars does two things at once: it makes trades of different sizes comparable, and it separates the quality of the decision from the size of the account, because a system that earns 0.4R a trade earns it at any account size while a system that earns $400 a trade earns it at exactly one. Expectancy is then the average of the outcomes in R: **win rate × average win − loss rate × average loss.** With 40% wins at +2.5R and 60% losses at −1R, that is 1.00 − 0.60 = **+0.40R per trade**. With 85% wins at +0.4R and 15% losses at −3R it is 0.34 − 0.45 = **−0.11R**. The second system wins four trades out of five and loses money, and the reason is arithmetic rather than paradoxical: a win rate tells you how often something happens and the payoff tells you how much it is worth. This is why a quoted win rate is close to useless on its own, and why the strategies that advertise high win rates are usually the ones with hidden negative skew. A system that collects a small premium most months and pays a large loss occasionally has a 90% win rate and can still be a losing proposition; the losses are rare, so they do not show up in the sample you were shown, and they are enormous, so they swamp everything when they arrive. The one-line test is the two products above: multiply the win rate by the win and compare it with the loss rate times the loss. Two systems, both measured in R — System A: 40% × 2.5R − 60% × 1R: +0.40R a trade · System B: 85% × 0.4R − 15% × 3R: −0.11R a trade ← · Break-even win rate at a 2:1 payoff: 33.33% · What System A earns at $500 a risk unit: $20,000 over 100 trades The break-even win rate at any payoff is 1 ÷ (1 + payoff ratio): at 2:1 you need to win a third of the time, at 3:1 a quarter, at 1:1 half. Below that, the payoff has to make up the difference.

An edge needs a few hundred trades to show itself

A positive expectancy is a statement about an average, and an average takes a sample to appear. Run a 45% system long enough and losing streaks of eight, ten or twelve trades are not a malfunction but the ordinary weather: at a 45% win rate the chance of at least one eight-loss run somewhere in five hundred trades is about **85%**, and the chance of a ten-loss run is about 43%. At the more comfortable-sounding 55% win rate the eight-loss run still turns up in about 37% of five-hundred-trade samples. Nothing has gone wrong in those stretches; the sample is simply small enough for the variance to dominate. This has two consequences that decide whether a strategy is ever allowed to pay. The first is that a losing streak is not evidence about expectancy until the sample is large enough to distinguish the two, which is typically fifty trades at a minimum and several hundred for a confident statement. The second is far more practical: **survival is the precondition for expectancy to matter.** A system earning +0.125R a trade over two hundred trades has to live long enough to have those trades, and the sizing rule is what buys the time. A strategy is therefore not just an edge — it is an edge plus a size that lets the edge be expressed. Expectancy also gives the correct answer to a question people ask after a bad month: is this system broken? The test is not the streak, it is whether the realised expectancy over a decent sample has moved outside what the sample size can explain. Judging a 0.4R system on ten trades is not analysis; it is reading noise, and it produces exactly one behaviour — abandoning a working system at the bottom of its normal range. The subject comes back to this in R7 and R15, where streaks and sample size get their own arithmetic. How often a normal streak happens — 8 losses in a row, 45% win rate, in 500 trades: about 85% · 10 losses in a row, 45% win rate, in 500 trades: about 43% · 8 losses in a row, 55% win rate, in 500 trades: about 37% · 8 losses in a row at 1% risk: a 7.7% drawdown · 8 losses in a row at 10% risk: a 57% drawdown ← The same streak is a bad month or the end of the account depending entirely on the risk fraction. The streak is not the risk; the size is.

Expectancy is not a constant

The expectancy of a system is computed from a sample, and the sample came from a market that was in a particular state. A trend-following system measured through a trending decade shows a high expectancy; the same rules measured through a range-bound one show a low or negative one. The number is a property of the *system in a regime*, not of the system in general, and treating it as a constant is how a strategy that “worked” stops working while its users keep trading it. Two consequences follow for how the number should be used. First, the sample size that makes an expectancy reliable is larger than most traders assume, and it must span more than one kind of market — a few hundred trades across at least one full cycle, not a few hundred trades in a bull market. Second, the expectancy should be tracked *live*, as a rolling estimate, with a written rule for what a decay in the number means. A system whose live expectancy has fallen below its break-even win rate is telling you the regime has changed. There is also a distinction the arithmetic hides: expectancy per trade is not the same as return per unit of capital per unit of time. A system with a modest expectancy that trades often, at low risk, can compound faster than one with a large expectancy that ties up capital for months. Comparing systems on expectancy alone ignores opportunity cost and capital efficiency, which matter as soon as you have more than one idea competing for the same account. Date the sample that produced an expectancy. A number from one regime is a description of that regime, and it is not a promise about the next one.

How many trades before the verdict is a verdict

The previous read said an edge needs a few hundred trades and that a losing streak proves nothing. This is the arithmetic behind both statements, and it turns “how many trades” from an opinion into a calculation. An expectancy is an average of the R-multiples of a sample, so it carries a standard error like any average: the standard deviation of the trade outcomes divided by the square root of the number of trades. The **standard deviation of R outcomes** for a typical system — winners around two to three R, losers at minus one — is roughly 1.5 to 2R, which is the number to remember. If the expectancy is +0.15R and the standard deviation of outcomes is 1.8R, then after a hundred trades the standard error of the expectancy is 1.8 ÷ 10 = 0.18R, which is larger than the edge itself. After four hundred trades it is 0.09R, still roughly two thirds of the edge. Only at around two thousand trades does the estimate get tight enough for the sign of the edge to be beyond reasonable doubt. That is the arithmetic that makes “my system works, I am up over thirty trades” a sentence about luck rather than about a system. The same calculation gives a usable diagnostic, and it is the t-statistic: expectancy divided by its standard error. Two is the conventional threshold for “probably not noise”, and it is worth internalising what it costs to reach. With an expectancy of 0.15R and a standard deviation of 1.8R, t equals 0.15 ÷ (1.8 ÷ √N), which is 0.0833 × √N — so t reaches two at roughly five hundred and eighty trades. Halve the edge and the requirement quadruples. It is the same square-root law as the ratio error in R15, and it is why a system with a small edge is a long-horizon commitment: the first year of live trading on a real but modest edge is mostly a measurement exercise, not a harvest. Two further distinctions keep the test honest. The first is between the **arithmetic expectancy** and the **median outcome**: expectancy is the mean of the outcomes, and with a right-skewed payoff distribution the mean is well above the median. A system that earns +0.15R a trade on average may have a median trade near zero and a median account path that is flatter than the number suggests — which is not a contradiction, it is the definition of a system whose money comes from the tail. Reporting only the mean overstates what a typical month looks like; reporting only the median understates the edge. Both are needed. The second is the **sequence**: the t-test above assumes the trades are independent, and the same system run twice produces two different paths with the same expectancy. The correct reading of a live track record is not “has it earned what the backtest said”, it is “is the realised expectancy inside the interval the sample size can explain” — and the interval is being computed on the run, every day, whether or not anyone writes it down. How the verdict tightens with the sample — 100 trades: SE = 1.8 ÷ √100 = 0.18R — larger than a 0.15R edge · 400 trades: SE = 0.09R — the edge is twice the error, and still not settled ← · ~580 trades: t = 2 with a 0.15R edge — the conventional threshold for “probably not noise” ← · 2,000 trades: SE = 0.04R — the sign of a modest edge is finally beyond reasonable doubt The practical implication is uncomfortable and worth stating plainly: a trader with a genuine but small edge cannot distinguish it from luck inside a year, and the only rational response is to size so that being wrong is survivable and to keep the sample rather than the opinion. The journal from TR21 exists precisely because memory keeps a losing streak and a working system in the same drawer.

Sources

• Expectancy and R-multiples as the unit of comparisonVan Tharp, "Trade Your Way to Financial Freedom"
• Why win rate is the least informative summary of a strategyStandard trading-system literature; Elder, "Trading for a Living"
• Streak probabilities and how often a real edge loses several in a rowIndependent-trials probability; risk-of-ruin literature
• The short-volatility trap: high hit rate, negative skewTaleb, "Dynamic Hedging"; the 2018 volatility-product terminal events