How to put an interval on a hit rate (and why you should)

9 November 2026 · 5 min read · worked example

A hit rate on its own is a rumour. Add an interval and it becomes a measurement — including the part where the measurement admits it is uncertain.

Step 1: the standard error of a proportion

If you have n settled bets and h hits, the point estimate is p̂ = h/n. The standard error is

At 74 hits from 100 bets: se = √(0.74 × 0.26 / 100) = 0.0439, about 4.4 points.

Step 2: the rough 95% interval

Two standard errors either side:

That is the fast version and it is fine when n is large and p is away from the edges.

Step 3: why the fast version breaks on small samples

At 14 hits from 19 bets the point estimate is 73.7%. The naive interval is ± 2 × 0.101, which runs past 100%. Worse, it is not symmetric — a proportion cannot go below zero or above one.

The Wilson interval handles both problems. For 14 of 19 it gives roughly 51% to 88%. That is a large range, and it is the honest one.

Step 4: what the interval lets you say

Compare two claims:

Record	Point	95% interval	Can you claim an edge?
14 / 19	73.7%	51 – 88%	No. Break-even is inside.
74 / 100	74.0%	65 – 83%	Yes, if break-even is below 65%.
740 / 1000	74.0%	71 – 77%	Yes, comfortably.

Same hit rate three times. Only the third row is a measurement you can build on.

Step 5: the rule to remember

Precision scales with the square root of the sample. To halve the interval width you need four times as many bets. There is no clever analysis that produces precision the data does not contain.

This is why a public record should publish the interval, not just the percentage. A number without an interval is a claim; a number with one is a fact about a sample.