Start with the arithmetic, because it sets the budget. Run one prompt 30 times, count 10 answers that mention your brand, and the point estimate is 33.3%. Put a 95% Wald interval on it, p plus or minus 1.96 times the square root of p(1-p)/n, and the range is 16.5% to 50.2%, a width of 33.7 points [2]. Keep the same hit rate and take 300 runs instead, and it tightens to 28.0% to 38.7%, a width of 10.7 points [3]. Width scales as one over the square root of n, so halving it costs four times the calls [4].
Then multiply by surfaces. The writeup names five distinct answer surfaces [1], and it says the research ran prompt sets dozens to hundreds of times [3]. At 100 runs each, that is 500 observations for one prompt in one reporting period [5], before you have measured a single competitor. A single screenshot documents one run, not a measured rate with confidence bounds attached.
There's an assumption underneath the interval worth checking. The dev.to summary reports that the same prompts returned changing brand recommendations [3] but does not say what generates the variance, and that gap matters, because a binomial interval assumes the runs are independent draws from one fixed distribution [6]. If a model version rolls out across your sampling window, or a retrieval index refreshes mid-week, consecutive runs are correlated and the interval you print is narrower than the uncertainty you actually have. The cheap defence is already in the source's governance list: record collection dates [9], then plot the daily rate rather than the pooled one, so a step change shows up as a step instead of dissolving into the mean.
Per-surface separation is not a presentation preference either. The source's position is that each surface is its own measurement environment, and that blending ChatGPT, the Google experiences, Perplexity and Gemini into one unexplained number hides the differences you were paying to see [10]. Same logic applies to the counting rule. "Mentioned" and "recommended" are different Bernoulli variables [9], and if you switch between them between quarters, your trend line is measuring your own definition.
This is where someone else's number stops transferring. A published mention rate is a claim about a specific prompt list, a specific surface, a specific sampling window, and a specific rule for what counted as a hit [9]. Changing the prompt wording changes the population, and changing the surface changes the instrument [10]. The source is explicit that results from one surface should not be assumed to represent another [7], which is a polite way of saying that a vendor's cross-platform score is not comparable to your own unless you can read their method.
What follows is narrow and practical. A single run is fine evidence of an opportunity or a content gap [6], and useless as a position. If two brands' intervals overlap, the gap between them is not a budget input [8]. And a period-over-period change is unfalsifiable unless the prompt file, the run count, the dates and the counting rule shipped with the percentage [7][9]. Without the method sitting next to the number, the number is just a screenshot with more decimal places.
