Symbol p
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At p = 0.60 and k = 8 , that model predicts roughly 1.7%. The reported figure — under 25% — sits well above that naive prediction, and the direction of the gap is informative on its own: it is only possible if outcomes are not independent draws from one fixed probability, but rather reflect a task population that splits into instances the agent reliably solves and instances it reliably does not, with the reported 60% average blending the two. The practical consequence is that a single success-rate figure understates how often a system that “usually works” will keep failing on the same class of request every single time it is asked, and overstates how often a system that “usually fails” might…
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Equation 4 · AI Infrastructure
Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty
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At p = 0.60 and k = 8 , that model predicts roughly 1.7%. The reported figure — under 25% — sits well above that naive prediction, and the direction of the gap is informative on its own: it is only possible if outcomes are not independent draws from one fixed probability, but rather reflect a task population that splits into instances the agent reliably solves and instances it reliably does not, with the reported 60% average blending the two. The practical consequence is that a single success-rate figure understates how often a system that “usually works” will keep failing on the same class of request every single time it is asked, and overstates how often a system that “usually fails” might…
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