Gold trading basics · Lesson 78 of 100

Gold Win Rates: Calculate a Confidence Interval and State Its Assumptions

Use an illustrative Wilson interval to describe uncertainty in a win proportion without confusing confidence coverage with a probability of profitability.

A Sample Rate Has Uncertainty: instructional diagram for lesson 78 — CYGURU GOLD · Original lesson schematic. Examples are illustrative.

A sample proportion is not a stable system property

A report of twelve winning trades out of twenty gives an observed win rate of 60%. That is a calculation about a defined sample, not a guarantee that the next twenty trades will reproduce it. Define a win after costs, identify how breakeven cases are treated and make the unit of observation explicit. Several partial exits from one market episode may not be independent trials. A confidence interval can describe estimation uncertainty under a model, but it cannot repair a biased selection of trades, a changing rule or an outcome definition chosen after examining the record.

Work through a Wilson interval with explicit inputs

For a teaching calculation, let p-hat=0.60, n=20 and z=1.96 for a nominal 95% two-sided Wilson interval. Its denominator is 1+z²/n=1.19208. The center is (p-hat+z²/(2n)) divided by that denominator. The half-width is z times sqrt(p-hat×(1−p-hat)/n+z²/(4n²)), also divided by the same denominator. The resulting lower and upper limits are approximately 0.3866 and 0.7812, or 38.66% to 78.12%. Retain unrounded intermediate values so a spreadsheet can reproduce the limits. This calculation uses the stated binomial-model assumptions rather than establishing them from twenty observations.

Explain confidence coverage without a probability shortcut

Under repeated samples satisfying the model and the method’s conditions, a nominal confidence procedure aims to produce intervals with its stated coverage behavior. The realized interval is not a guarantee about the next trade and is not automatically a 95% posterior probability statement about a fixed unknown parameter. Actual finite-sample coverage can differ from the nominal label. For this application, independence, comparable trial definitions and an approximately stable success probability require scrutiny. A group of signals triggered by the same gold release can provide less independent information than its raw ticket count suggests.

Wilson interval inputs and outputs
Quantity	Value
Wins / trials	12 / 20
Observed proportion	0.60
z	1.96
Denominator	1.19208
Lower limit	38.66%
Upper limit	78.12%

Nominal 95% binomial-model interval; independence and stability are assumptions.

Keep the payout distribution beside the interval

Even an exactly known win probability would not determine profitability without the size of winners, losers and costs. A method can win frequently while occasional losses exceed the accumulated gains. Conversely, a lower win proportion can coexist with a favorable payoff distribution. The Wilson interval estimates uncertainty in one proportion; it does not jointly estimate expectancy, drawdown or the distribution of net returns. Keep realized dollar or R outcomes visible and avoid comparing an interval boundary with an unrelated planned reward-to-risk ratio. Planned targets are not the same as the actual average payouts in the sample.

Do not repeatedly inspect until a claim looks significant

Watching an interval after every trade and stopping the experiment when a desirable boundary appears changes the evidence process. A fixed-sample confidence calculation does not automatically account for arbitrary sequential stopping or repeated strategy comparisons. Specify the review plan and use methods suited to the intended sampling design when formal inference matters. Also disclose missing or unresolved trades rather than omitting inconvenient cases. If the strategy version changes halfway through the record, a single constant-probability model may be inappropriate even when the arithmetic is correct. A larger sample does not erase systematic bias in how the observations were selected.

Practice task: write an uncertainty statement

Reproduce the 38.66%–78.12% interval and write a plain-language summary that names the twenty-trade sample, win definition, method and assumptions. Add a second paragraph explaining why the range is not a forecast of profitability. Identify overlapping episodes, exclusions and rule changes that would weaken the binomial interpretation. State the sample plan before extending the record. A defensible report can say that 60% was observed while acknowledging broad uncertainty; it should not turn the most favorable interval endpoint into an advertised success rate or a promise attached to future gold signals.

Gold Win Rates: Calculate a Confidence Interval and State Its Assumptions

A sample proportion is not a stable system property

Work through a Wilson interval with explicit inputs

Explain confidence coverage without a probability shortcut

Keep the payout distribution beside the interval

Do not repeatedly inspect until a claim looks significant

Practice task: write an uncertainty statement

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