Law of Large Numbers & Confidence Intervals
Trading Intelligence
11 min read
Build statistical confidence in your edge by understanding sample sizes, confidence intervals, and why 10 trades prove nothing.
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11 min read
Build statistical confidence in your edge by understanding sample sizes, confidence intervals, and why 10 trades prove nothing.
You can’t trust a strategy based on 10 trades. Here’s how to build statistical confidence in your edge.
Many traders fall into this trap:
“I just had 3 winners in a row — my system’s working!” “I hit a 6-trade losing streak — it’s broken!”
But those reactions ignore something critical:
A strategy’s performance only becomes meaningful after a large enough sample size.
This is the Law of Large Numbers — and it explains:
In probability:
As the number of trials increases, the average result approaches the true expected value.
In trading:
Until then — you’re mostly seeing randomness.
| Sample Size | What It Tells You |
|---|---|
| 10–20 | Noise. Not statistically meaningful |
| 50 | Early directional signal |
| 100 | Minimum for confidence in win rate/EV |
| 200–300 | Reasonable confirmation of robustness |
| 500+ | Strong evidence for long-term consistency |
The more variance and skew in your system → the larger the sample size required.
Imagine this strategy:
But you only log 10 trades:
You might quit at trade #6 — never reaching the edge that would appear by trade #100.
A confidence interval shows the likely range where your true performance lies, based on your sample.
Example:
That means:
You're 95% confident your true win rate is somewhere between 35–55%.
The more trades you log, the narrower this range becomes — and the more stable your metrics become.
To calculate a 95% confidence interval for your win rate:
CI = p ± z * √[ (p(1 – p)) / n ]
Where:
p = observed win rate (as a decimal)z = z-score for confidence level (for 95%, z ≈ 1.96)n = number of tradesYou’ve taken 100 trades, and 45 were winners.
p = 0.45n = 100z = 1.96Plug into formula:
CI = 0.45 ± 1.96 × √[ (0.45 × 0.55) / 100 ]
CI = 0.45 ± 1.96 × √(0.2475 / 100)
CI = 0.45 ± 1.96 × 0.0497
CI = 0.45 ± 0.0974
Confidence Interval = [0.3526, 0.5474] or [35.3%, 54.7%]
This means:
You’re 95% confident your true win rate is between 35.3% and 54.7%.
The more trades you add (larger n), the narrower your confidence interval becomes — and the more precise your system measurement gets.
You can also apply confidence intervals to other metrics like:
Only consistent, full tracking can:
Instead of judging trade-by-trade, look at:
A strategy that makes +0.4R over 100 trades is likely better than one that makes +3R in 10.
Many traders:
…after just 5–20 trades.
You’re optimizing for noise — not truth.
Wait for a meaningful sample. Then evaluate with:
Trading results are deceptive — unless you give the math enough time to speak.
The Law of Large Numbers reminds you:
Great traders think in series. They trade through noise, journal consistently, and only make decisions when the math is loud enough to hear.