Small sample, wide uncertainty: inspect a completed-outcome Wilson interval

Six successes out of ten is a description of ten records

An observed proportion is easy to calculate and easy to overinterpret. Six labelled successes among ten included completed records gives 60%. It does not establish that the next record has a 60% chance of success, that a trading method is profitable or that the ten records represent every relevant outcome.

This worksheet first shows which supplied rows enter the denominator. It then offers a conditional Wilson interval for an explicitly assumed binary model. You can leave those assumptions unconfirmed and still inspect the descriptive count. The calculation is available without signing up or presenting account credentials.

Define success before counting it

Write a fixed outcome rule in the form. For the fictional example, success means a strictly positive net realised result under one documented convention; a zero result is classified as failure. This is an example classification, not a universal definition of a winning trade. The tool does not calculate P&L or check that fees were included.

If your own rule treats break-even records as void, state that before examining results and keep the void rows visible. Changing the definition after seeing the count creates a different sample. The exported rule makes that choice inspectable; it does not prove that the choice was made in advance.

Use a local completion-date window consistently

The selected dates are inclusive calendar dates in America/New_York. Each completion timestamp must contain seconds and a known offset or Z. The tool converts the instant to a New York date before deciding whether it lies inside the window. It does not compare the first ten characters of a UTC timestamp.

For the worked example, 2026-10-21T03:59:59Z still belongs to 20 October in New York, while 04:00:00Z belongs to 21 October. A one-second boundary change can therefore change the included count. This is a declared research convention, not an exchange session calendar or a rule for a tax return.

Do not keep a fixed Eastern offset for every date

NIST’s 2026 guidance gives 8 March through 1 November as the US daylight-saving period and describes the repeated hour on the return to standard time. A local-date workflow must therefore use a named zone rather than permanently subtracting four hours from UTC.

The worksheet uses the runtime’s America/New_York time-zone data. It requires an unambiguous input instant and does not verify the source clock. If a saved local timestamp has no offset during a repeated hour, obtain the missing information before including it; guessing an hour can place a record in the wrong evidence sequence.

Sources: NIST — Daylight Saving Time Rules.

A pending outcome is not a failure

Rows are classified as success, failure, pending or void. Only completed success/failure rows with a time and saved reference can enter the date-filtered denominator. Pending and void rows remain visible, but they are not quietly turned into losses or deleted from the export.

A completed row with a missing instant or saved reference blocks the interval, even though the known descriptive subtotal remains visible. The block is conservative: the tool cannot establish a complete supported sample from that input. An empty included sample yields an unknown proportion rather than 0%, because there is no denominator.

What the optional interval represents

The NIST handbook gives the two-sided Wilson construction for a binomial proportion. This tool uses that formula with fixed 90%, 95% or 99% normal critical values. The model assumes a fixed sample of independent binary trials with one unchanged success probability. It does not provide exact finite-sample coverage.

Here the observed proportion p is successes divided by included completed records n. With critical value z, the centre is (p + z²/(2n))/(1 + z²/n). The half-width is z × sqrt(p(1 − p)/n + z²/(4n²))/(1 + z²/n). The displayed limits are centre minus and plus that half-width; boundary samples are handled explicitly.

Sources: NIST/SEMATECH e-Handbook — 7.2.4.1 Confidence intervals.

Read the default result without turning it into a promise

The ten completed fictional records produce 6/10. With the 95% setting, the lower limit rounds to 31.27% and the upper limit to 83.18%. The interval is broad because the sample supplies limited information under the selected model. P01 stays pending, and NEXT is excluded by its New York completion date.

Switching the confidence level changes the mathematical interval, not the records. Switching the date window changes the records and therefore requires a new calculation. The tool clears old results whenever inputs change. Keep the chosen confidence level and date convention with any screenshot or exported comparison.

Coverage is not a probability attached to this realised interval

A frequentist confidence procedure is interpreted through repeated samples under its model. It is not a direct probability that a future trade succeeds, nor a posterior probability for the unknown parameter. Once your sample has been observed, its computed endpoints are fixed numbers.

The calculation also says nothing about the size of wins and losses. A high success proportion can coexist with unfavourable average monetary outcomes, while a lower one can coexist with another payoff structure. This resource deliberately omits expectancy, position sizing, return forecasts and strategy ranking so those separate questions are not hidden behind a percentage.

The log cannot establish independence or a fixed sampling plan

Several trades can react to the same market event, use overlapping positions or share a decision rule. Such dependence is not detected by this worksheet. Continuing to collect records until a desirable percentage appears is also different from the fixed-sample model. A simple checkbox cannot repair either problem.

The model selector records your assumption; it does not certify it. Pending outcomes may be outcome-dependent, and analysing only the quickly completed subset can be selective. Before interpreting the interval, explain the collection rule, exclusions and stopping rule outside the arithmetic. If those conditions are not supportable, use the descriptive audit and leave the interval withheld.

Make the denominator inspectable

Each exported row carries its exact ID, original completion timestamp, New York date, supplied outcome, reference and inclusion status. Duplicate IDs are rejected. References are local evidence labels, not verified URLs. The export keeps missing values explicit and protects spreadsheet-sensitive text without claiming that every importer behaves identically.

No account is read and no calculation result is sent to a service. The tool has a visible manual CSV fallback if downloading or copying is unavailable. Its optional link leads to the site’s English-language signals and updates offer after the result; that link is not an endorsement by NIST or a claim of US availability.

Worked examples

Example 1

The fictional New York-date sample contains 10 completed records: 6 successes and 4 failures, an observed proportion of 60%. At 95% two-sided confidence, the Wilson interval is approximately 31.27% to 83.18%, conditional on the stated fixed independent binary model. P01 remains pending and is not counted as a failure. NEXT completes at 00:00 on 21 October in New York and is outside the chosen 20 October window. No future success probability or profitability is established.

Inspect example inputs

{
  "start_date": "2026-10-20",
  "end_date": "2026-10-20",
  "outcome_rule": "DEMO success means strictly positive net realised result under one fixed documented rule; failure includes zero",
  "confidence": "95",
  "model": "fixed_independent_binary",
  "rows": "id|closed_at|outcome|reference\nR01|2026-10-20T11:00:00-04:00|success|DEMO completed record 1\nR02|2026-10-20T12:00:00-04:00|success|DEMO completed record 2\nR03|2026-10-20T13:00:00-04:00|success|DEMO completed record 3\nR04|2026-10-20T14:00:00-04:00|success|DEMO completed record 4\nR05|2026-10-20T15:00:00-04:00|success|DEMO completed record 5\nR06|2026-10-20T16:00:00-04:00|success|DEMO completed record 6\nR07|2026-10-20T17:00:00-04:00|failure|DEMO completed record 7\nR08|2026-10-20T18:00:00-04:00|failure|DEMO completed record 8\nR09|2026-10-20T19:00:00-04:00|failure|DEMO completed record 9\nR10|2026-10-20T20:00:00-04:00|failure|DEMO completed record 10\nP01||pending|DEMO unfinished record\nNEXT|2026-10-21T04:00:00Z|success|DEMO next New York day"
}

Questions about the method

Does 95% confidence mean the next trade succeeds with 95% probability?

No. The level describes a statistical procedure under its assumptions, not a future outcome or profitability.

Why not count pending records as losses?

Their binary outcomes are not known. They remain visible and excluded; treating them as losses fabricates data.

Can the interval show that a strategy is ready to trade?

No. The tool does not validate the sample design, independence, costs, payoff size or future conditions.

Primary sources and scope

NIST/SEMATECH e-Handbook — 7.2.4.1 Confidence intervalsChecked 2026-10-21. Two-sided Wilson score formula for a binomial proportion and distinction from exact binomial intervals. No trading performance or future-return conclusion.
NIST — Daylight Saving Time RulesChecked 2026-10-21. The 2026 US DST period is 8 March to 1 November, with a repeated hour on rollback. Time-zone conversion is supplied by local runtime data, not a live NIST clock query.

Examples explain a method. They do not predict prices or establish where a trading service is available. Check the named source before relying on future schedules.