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Equation 5 · Part 2 · Measuring Tool Protocols and the Model Context Protocol: Evidence, Benchmarks, and Uncertainty

=

k=8k = 8
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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