03 — confidence
The bootstrap: 1,000 resamples per rank.
For every phrase, we take the runs we actually collected and resample them — with replacement — 1,000 times, recomputing the ranking fresh each time. That gives us a distribution of ranks instead of a single guess.
100 runs →1,000 resamples →percentile interval→stability %
rank_stability_pct is the share of those resamples where a brand held the exact same position it holds in the headline ranking. A brand sitting at 96% stability held its spot in 962 of 1,000 resamples — it's a real result. A brand at 48% stability is telling you the ranking is close to a coin flip once you account for the noise inherent in a hundred samples. Both get shown as a plain rank number by every product we've seen except this one. Published research (arXiv:2606.24381 ↗) found the #1 spot in LLM brand rankings frequently flips once you resample at n≈100 — which is exactly the regime most rankings, including ours before resampling, get built in.
That's why every rank on this site carries its confidence band next to it, drawn, not just labelled — and there is one colour, ledger green, not a ramp. Uncertainty lives in two things instead: the band's width is the interval itself, wide when a rank is close to a coin flip and narrow when it isn't, and the marker's waver wobbles with an amplitude sized to how often that rank actually flipped across resamples — a locked #1 sits still, a contested #4 visibly refuses to settle. A rank you can't see the confidence of is a rank someone is asking you to trust for free.