Why Win-Rate Lies: the Wilson Lower Bound

The Seduction of a Big Percentage

A win-rate is the most quoted and least trustworthy number in trading. "This signal wins 80% of the time" sounds decisive. But 80% from 5 trades (4 of 5) and 80% from 200 trades (160 of 200) are not the same claim at all. The first is barely distinguishable from luck; the second is a real pattern.

The raw percentage erases the one thing that determines whether you should believe it: how much evidence is behind it. A point estimate with no sense of its own uncertainty is a number pretending to be a fact.

Sample Size Is the Hidden Variable

Statisticians deal with this by reporting a confidence interval instead of a single number — a range the true rate plausibly lives in. The smaller your sample, the wider that range.

Four wins from five trades might have a true success rate anywhere from roughly 38% to 99%. That interval is so wide it tells you almost nothing. Take the same 80% from two hundred trades and the interval tightens to something like 74%–85% — now you have a claim worth acting on. Same headline percentage, completely different amount of trust warranted. The width of the interval is the information.

Enter the Wilson Lower Bound

The Wilson score interval is a well-established way to put a confidence interval around a proportion that behaves correctly even for small samples and extreme rates (near 0% or 100%), where the naive formula falls apart.

Probalist reports its lower bound: the pessimistic edge of that interval at a chosen confidence level. In plain terms it answers, "given how many signals I have actually seen, what is the worst the true win-rate is plausibly likely to be?" A small sample is automatically penalised — the lower bound sits far below the raw rate until enough evidence accumulates to pull it up. It is built to be conservative on purpose.

How Probalist Uses It

This is the engine behind the glyphs you see on signals:

• ● solid — the Wilson lower bound clears the bar at the chosen confidence. The edge is not just present, it is backed by enough evidence to trust.
• ◐ half — building; the long-run sample supports it but the recent window does not yet clear the bound.
• ○ open — the lower bound does not clear the bar. Treat it as noise.

The evidence-gated alerts follow the identical rule: they fire only when a signal is recently backed, not on every raw trigger. So you are never alerted on a flashy percentage that rests on three lucky samples.

Reading It in Practice

When you look at a signal, ignore the gross hit-rate and look at the backed verdict. A signal showing 65% with a solid glyph is worth more than one showing 90% with an open glyph — the first has cleared the evidence test, the second has not.

This also explains why a brand-new symbol or a fresh timeframe starts cautious: there simply are not enough closed-bar signals yet for the lower bound to rise. That is not the tool being shy; it is the tool being honest about how little it has seen so far. Edge that has not earned confidence does not get a solid mark.