Sample Size and Confidence Intervals

What Is a Confidence Interval?

A confidence interval tells you the range within which your true win rate (or any metric) is likely to fall, given your sample.

The key insight: your measured win rate is not the same as your true win rate. It's an estimate. The confidence interval shows how wide or narrow that estimate is.

A Practical Example

You have 50 trades with a 58% win rate. What's your 95% confidence interval?

Formula: CI = p ± 1.96 × √(p × (1-p) / n)

Where p = win rate = 0.58, n = 50

CI = 0.58 ± 1.96 × √(0.58 × 0.42 / 50)

= 0.58 ± 1.96 × 0.070

= 0.58 ± 0.137

95% confidence interval: 44.3% to 71.7%

Your true win rate is somewhere between 44% and 72% — that's a huge range. Your system might actually be 44% win rate (barely profitable) or 72% (highly profitable). You don't have enough trades yet to know.

How Sample Size Narrows the Interval

At 200 trades:

CI = 0.58 ± 1.96 × √(0.58 × 0.42 / 200)

= 0.58 ± 1.96 × 0.035

= 51.1% to 64.9%

At 500 trades:

55.3% to 60.7%

Notice how the range shrinks dramatically as sample size grows. This is why more trades equal more certainty.

Using Confidence Intervals for Decision-Making

When evaluating whether a setup has a real edge:

1. 1Calculate your win rate
2. 2Calculate the 95% confidence interval
3. 3Check whether the entire interval is above your break-even win rate

If the lower bound of your interval is still above break-even, you have statistical evidence of edge. If the lower bound is below break-even, your sample is insufficient to confirm edge.

Translating to Tradapt

While Tradapt doesn't display formal confidence intervals (yet), you can use these thresholds:

• Fewer than 50 trades: wide uncertainty — avoid major decisions
• 50–100 trades: moderate certainty — adjust setup criteria cautiously
• 100+ trades: meaningful certainty — make significant system decisions