Equation 15 · Part 4 · Ten Ways an Agent Evaluation Can Mislead You Even When It's Working Correctly
√
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4. Insufficient trial counts producing false confidence. A success rate reported from a small number of trials carries a much wider margin of error than the single reported number suggests, and the interval widens fast as the trial count shrinks. For a naive binomial estimate — treating each trial as an independent coin flip with unknown success probability p — the 95 percent confidence interval around an observed rate from n trials is approximately . At ten trials and an observed 90 percent success rate, that formula gives an interval of roughly plus or minus nineteen percentage points — an agent genuinely succeeding anywhere from about 71 percent to essentially…
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