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Trading Expectancy, Sample Size and Sizing Beyond the 1% Rule
The fixed 1% rule is a beginner's safety net, not a sizing model. Here is the arithmetic that replaces it, including how to tell whether your edge is real or noise.
The 1% rule exists because it is very hard to destroy an account with it. That makes it an excellent place to start and a strange place to stop.
What follows is arithmetic most traders never do. It is not difficult, and it answers a question most never think to ask: how confident am I that the edge I think I have is real? Once you have a trade log worth analysing, sizing becomes a question with an answer, and the first step is establishing whether the edge you are sizing exists at all.
Expectancy, properly stated
Convert every closed trade into an R multiple: the result divided by the amount risked. A full stop-out is −1R. A trade that made twice the risk is +2R.
Expectancy = the mean of your R multiples
That one number is your average result per trade, and it is comparable across instruments, account sizes and time periods in a way dollars and percentages are not.
A worked example from a 100-trade log:
| Count | Average R | |
|---|---|---|
| Winners | 38 | +2.4R |
| Losers | 62 | −0.95R |
Expectancy = (0.38 × 2.4) − (0.62 × 0.95) = +0.323R per trade
At $250 of risk per trade that is about $81 per trade, or $8,100 over the hundred. Which looks decisive, and is not.
The question almost nobody asks: how confident are you?
Expectancy is a sample mean, and sample means have error bars.
Standard error = standard deviation of R multiples ÷ √n
Suppose those R multiples have a standard deviation of 1.6R, which is entirely typical when winners run to +4R and losers cluster near −1R.
- Standard error = 1.6 ÷ √100 = 0.16R
- 95% confidence interval ≈ 0.323 ± (1.96 × 0.16) = +0.01R to +0.64R
The edge is only just clear of zero after a hundred trades. Run the same arithmetic on a 30-trade sample and the interval comfortably contains zero, meaning the data cannot distinguish that strategy from a coin flip.
To halve the width of that interval you need four times the trades, because the error shrinks with the square root of n. Strategy evaluation is slow for mathematical reasons, not because you lack discipline.
The Kelly criterion, and why not to use it in full
Kelly gives the fraction of capital that maximises long-run growth. In trading terms:
f = W − (1 − W) ÷ R
where W is the win rate and R is average win divided by average loss.
Using the log above: W = 0.38, R = 2.4 ÷ 0.95 = 2.53
f = 0.38 − (0.62 ÷ 2.53) = 0.38 − 0.245 = 0.135
Kelly says risk 13.5% of capital per trade. That is thirteen times a 1% habit, and it is not an arithmetic error.
It is still a bad idea in practice, for three reasons.
- It assumes your edge estimate is exact. It is not. You just calculated a confidence interval from +0.01R to +0.64R. Kelly sized on the optimistic end of that range is catastrophically oversized.
- The drawdowns are unexecutable. Full Kelly routinely produces 50%+ drawdowns even when the edge is genuine. Almost nobody keeps executing through that.
- Overbetting is asymmetric. Sizing above optimal reduces growth and raises risk of ruin. Sizing below optimal only reduces growth. The error worth making is the conservative one.
Half Kelly captures roughly three quarters of the growth rate with about half the volatility. Quarter Kelly is closer to what institutional frameworks run: 3.4% on the numbers above, still well above most retail practice and far below the raw formula.
Volatility-adjusted sizing
A flat percentage stop treats a utility and a biotech as equivalent. They are not.
Using ATR as the unit fixes it. Instead of “stop 5% below entry”, the rule becomes “stop 2 ATR below entry”:
| Stock A | Stock B | |
|---|---|---|
| Price | $50 | $50 |
| 14-day ATR | $0.60 | $3.20 |
| 2-ATR stop distance | $1.20 | $6.40 |
| Shares at $250 risk | 208 | 39 |
Both positions now carry the same statistical risk, and both are stopped out by roughly the same amount of abnormal movement. A flat 5% stop would have been far too tight on Stock B and needlessly wide on Stock A.
The arithmetic afterwards is unchanged. Run it through the position size calculator; only the stop distance is derived differently.
A framework that survives contact with reality
- Fixed fractional as the base. 0.5–1% while your sample is under roughly 200 trades.
- Volatility-adjusted stops. ATR multiples, not flat percentages.
- Scale with confidence, not conviction. Size up only when the lower bound of your expectancy interval rises, never because the last three trades won.
- Cap at a fraction of Kelly. Quarter Kelly as a ceiling, and only once n is large.
- Portfolio heat limit. Total open risk capped at 5–6% regardless of what per-trade sizing suggests, because correlated positions behave as one position.
Sequencing matters. A sizing model applied to an unvalidated edge amplifies a mistake. Get the sample first, the confidence interval second, the sizing model third.
Next: backtesting without fooling yourself for why the edge you measured is probably smaller than it looks.
Frequently asked questions
How do you calculate trading expectancy?
Express every closed trade as an R multiple, where R is the amount you risked, then take the mean. A trade that made twice your risk is +2R and a full stop-out is minus 1R. The average across all trades is your expectancy per trade, and it is the only performance number that is comparable across different position sizes.
How many trades do you need to know if a strategy works?
More than most traders assume. The standard error of your expectancy is the standard deviation of your R multiples divided by the square root of the trade count. With a typical spread of outcomes, 100 trades often leaves a confidence interval wide enough to include zero, meaning the sample cannot distinguish a winning system from a losing one.
What is the Kelly criterion for trading?
A formula giving the fraction of capital that maximises long-run growth. For trading it can be written as f = W minus (1 minus W) divided by R, where W is the win rate and R is the ratio of average win to average loss. It assumes your edge estimate is exact, which is why full Kelly is almost never appropriate in practice.
Why not use full Kelly sizing?
Because it is extremely sensitive to estimation error and produces drawdowns most people cannot execute through. Overestimating your edge causes Kelly to size above optimal, where growth falls and risk of ruin rises sharply. Half-Kelly captures roughly three quarters of the growth rate with about half the volatility, which is a far better trade in practice.
What is volatility-adjusted position sizing?
Setting the stop distance from a volatility measure such as ATR rather than a fixed percentage, so each position carries comparable risk regardless of how much the instrument typically moves. A 2-ATR stop on a quiet stock and a 2-ATR stop on a volatile one represent the same statistical distance, which a flat 5% stop does not.