What does this equation mean?

Even when a team does report a rate rather than a single anecdote, a rate on its own understates how uncertain that number is. Evan Miller’s statistical treatment of language-model evaluation makes an argument borrowed from experimental science generally: an evaluation score is an estimate drawn from a finite, noisy sample, not a fact about the system, and it should be reported the way any other science reports a measurement — with an uncertainty attached [ 4 ] . His worked illustration is a useful gut check on how much data “enough” actually requires. To reliably detect an absolute difference of three percentage points between two systems, with conventional statistical standards for false positives and false negatives, the calculation runs as follows. Plugging in a 5% false-positive rate, 80% power, and a three-point difference gives roughly 969 independent questions — not thirty, not one hundred, close to a thousand [ 4 ] . Most published agent evaluations, run against benchmarks with a few dozen to a few hundred tasks because each task requires an expensive, stateful, sometimes hours-long rollout, fall well short of that bar by construction, which means many of the differences reported between agent versions or between competing systems are, on this analysis, indistinguishable from noise even when they are reported as a clean percentage-point win. Miller’s own demonstration on real evaluation data found gaps of 3.1 and 2.7 percentage points on two separate benchmarks that did not clear statistical significance once treated properly, and he further showed that once repeated comparisons on the same fixed question set are accounted for with clustered standard errors, the true uncertainty can run more than three times larger than the naive calculation suggests [ 4 ] . His practical recommendation is unglamorous: report the standard error next to the mean, the way other sciences do, rather than a bare percentage that invites over-reading.