Cheap Seats

How many runs do you need to trust an AI visibility number?

· Chad Metcalf

Ask an assistant the same question twice and you’ll get two different answers. So when an AI visibility tool says you’re named in 40% of answers this week and 30% last week, the first question isn’t “what did we break?” It’s “is that a change at all?” Usually, at the sample sizes most people run, it isn’t.

The research

Four findings worth knowing:

The arithmetic for one rate

Start with the simplest case: a rate near 50%, from n independent answers. The 95% margin is about 1.96 × √(0.25 / n):

answersmargin
10±31 pts
30±18 pts
100±10 pts
400±5 pts

To tell two such readings apart, the margin on the difference is √2 times wider. Detecting a 10-point change between two weeks needs about 2 × 0.25 × (1.96 / 0.10)² ≈ 192 answers on each side; a 5-point change, about 768. Few prompt sets get there in a single run.

Prompts are the units

Answers to the same prompt aren’t independent draws about your whole category. They’re repeated draws on one question, so Cheap Seats treats each prompt as the unit: a trend’s rate is the mean of each prompt’s own rate, and each prompt’s sampling variance is

var = p̃ (1 − p̃) / n, with p̃ = (h + 0.5) / (n + 1)

for h hits in n answers. Over K prompts, a day’s margin is 1.96 · √(Σ var) / K.

Cheap Seats’ own Choosing an AI visibility tool set has 17 prompts and two answerers, each answering once on each track. On one track, each prompt gets n = 2 answers a run. At a rate near 50%:

p̃ = (1 + 0.5) / 3 = 0.5, var = 0.25 / 2 = 0.125 per prompt

Σ var = 17 × 0.125 = 2.125, √2.125 = 1.458

one run: ± 1.96 × 1.458 / 17 = ±16.8 points

one run against the next: ± 1.96 × √(2 × 2.125) / 17 = ±23.8 points

A week of daily runs pooled gives each prompt n = 14:

var = 0.25 / 14 = 0.0179 per prompt, Σ var = 0.304, √0.304 = 0.551

one week: ± 1.96 × 0.551 / 17 = ±6.4 points

one week against another: ±9.0 points

The same arithmetic for other set-ups:

answers per prompt on the trackhow you get thereone readinga change between two
2one run, 2 answerers × 1 sample±17 pts±24 pts
4one run with 2 samples, or two runs±12 pts±17 pts
8four weekly runs (a 28-day window)±8 pts±12 pts
14seven daily runs (a 7-day window)±6 pts±9 pts

So a swing of 10 points between two single runs is well inside the noise, and a week against a week can just about see it.

What to do about it

A change beyond the margin still isn’t proof that your work caused it: a model update or the web changing can move a rate too. But a change inside the margin isn’t evidence of anything, and treating it as a win or a loss is how teams end up chasing noise.

How big a change Cheap Seats can detect has the full method: the two kinds of interval on the rankings, the paired test for a change, rank moves, fix outcomes and adaptive sampling. For why the same answers can give different numbers in different tools, see Why AI visibility scores differ between tools.

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