“My win rate is 58%.” No, it isn’t. It’s somewhere around 58%, and the width of that “around” is the single most important number your journal never shows you.
Point estimates lie: the case for error bars
When you report a win rate of 58%, you’re stating a point estimate — one number computed from your closed trades. But that number is a sample drawn from an underlying process, and the sample is never the truth. Report it alone and you’ve thrown away the most useful information you have: how uncertain you are.
A confidence interval fixes this by handing you a range instead of a point — a band that, with some stated confidence (usually 95%), contains your true long-run win rate. “58% ± 3%” and “58% ± 18%” are wildly different situations, but the bare point estimate hides which one you’re in. The first is an edge you can size on. The second is barely distinguishable from a coin.
Error bars turn “I think I have an edge” into “here’s the plausible range of my edge, and here’s the worst case I should plan around.”
The Wilson interval vs the naive normal approximation
The obvious way to build the interval is the normal approximation (Wald): take your win rate p, compute p ± 1.96 × √(p(1−p)/n), done. It’s taught everywhere and it’s wrong exactly when traders need it most — at small samples and at extreme win rates.
The Wald interval can produce nonsense like a lower bound below 0% or an upper bound above 100%, and it’s badly miscalibrated when n is small. That’s the regime a trader evaluating a new strategy lives in.
The Wilson score interval fixes this. It’s slightly more involved but well-behaved: it never escapes the 0-100% range, and it stays accurate at small samples and near the extremes. The formula for a win rate p over n trades, with z = 1.96 for 95% confidence:
center = (p + z²/2n) / (1 + z²/n)
margin = (z/(1 + z²/n)) × √( p(1−p)/n + z²/4n² )
interval = center ± marginYou don’t need to memorize it — you need to know that it exists, that it’s the right tool, and that it behaves sensibly where the naive version falls apart. This is the interval Shibiki uses under the hood to put a confidence band on your live edge, precisely because it stays honest at the small samples where funded traders make their biggest sizing decisions.
Worked example at 30, 100, and 300 trades
Hold the observed win rate fixed at 55% and watch what more trades do to the band (95% Wilson, approximate):
| Trades | Win rate | ~95% Wilson interval | Interval width |
|---|---|---|---|
| 30 | 55% | 37% – 72% | ~35 pts |
| 100 | 55% | 45% – 64% | ~19 pts |
| 300 | 55% | 49% – 61% | ~12 pts |
Read this carefully. At 30 trades, your true win rate could plausibly be anywhere from 37% to 72% — the interval includes 50%, meaning you cannot statistically rule out that you have no directional edge at all. At 100 trades the band pulls in and finally clears 50% on the low side. At 300 it’s tight enough to plan around.
Same headline number, three completely different levels of knowledge. The point estimate never moved; only the honesty did.
Reading the lower bound as your conservative edge
Here’s the practical move that changes how you trade: plan around the lower bound, not the point estimate.
The lower bound of your confidence interval is your conservative edge — the win rate you can be reasonably sure you’re at least as good as. If your 95% interval is 45%-64%, you don’t get to assume 55%. You assume something closer to 45% and let reality pleasantly surprise you.
This does two things. It keeps your position sizing anchored to a defensible estimate instead of an optimistic one, and it makes you robust to the ordinary bad luck that would otherwise feel like a broken strategy. Combine the lower-bound win rate with your payoff ratio in an expectancy calculator and you get a pessimistic expectancy — the number you should actually be sizing against. If you’re still profitable at the lower bound, you have a real edge. If you’re only profitable at the point estimate, you have a hope.
Why the interval narrows as trades accumulate
The band tightens with the square root of your trade count — the same square-root law that governs all sampling. Quadruple your trades and the interval roughly halves. That’s why the jump from 30 to 100 trades in the table shrinks the width so much, while the jump from 100 to 300 helps less per trade.
The consequence for how you work:
- Early on, the interval is wide no matter how clean your recent trades look. Accept it. There is no metric that manufactures certainty the sample doesn’t contain.
- The interval is your progress bar. Watching it narrow is watching your edge estimate earn trust in real time — far more meaningful than watching the raw win rate wobble up and down.
- A strategy tools like Edgewonk will happily report a precise win rate on 25 trades; the discipline that keeps you funded is refusing to act on it until the band is tight enough.
Using the band to decide when to size up
Turn the interval into a sizing rule:
- Wait for the lower bound to clear break-even. Until the bottom of your interval sits above the win rate your R:R requires, treat the edge as unproven and keep size minimal.
- Size to the lower bound. Once it clears, position as if your true win rate is the lower bound, not the middle.
- Add size as the band tightens, not as the point estimate rises. A win rate ticking up on a still-wide interval is noise; a stable estimate on a narrowing interval is signal.
- Watch for the band shifting, not just narrowing. If more trades pull the whole interval down, that’s your edge decaying — act on it before a drawdown forces the issue.
A live confidence interval on your edge — recomputed as each auto-journaled trade lands — turns this from a monthly spreadsheet chore into an always-current read on whether your win rate is real or you’ve just been lucky.
Related: Trading expectancy · Expectancy calculator · Shibiki vs Edgewonk