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Equation 1 · Part 2 · Building a Deployment Safety System That Actually Holds

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Precision=TPR⋅πTPR⋅π+FPR⋅(1−π),\text{Precision} = \frac{\mathrm{TPR} \cdot \pi}{\mathrm{TPR} \cdot \pi + \mathrm{FPR} \cdot (1 - \pi)},
=

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

The cost is measurable and it is not small, even for a genuinely well-built classifier, and the reason is arithmetic rather than a flaw in any particular model. Suppose a classifier catches 98% of genuinely harmful requests and wrongly flags only 1% of benign ones — numbers that would read, on a slide, as a strong result. If the true base rate of harmful requests in real traffic is low, say one in two thousand, which is the ordinary case for a general-purpose product, precision — the share of flagged requests that are actually harmful — is Precision=TPR⋅πTPR⋅π+FPR⋅(1−π)\text{Precision} = \frac{\mathrm{TPR} \cdot \pi}{\mathrm{TPR} \cdot \pi + \mathrm{FPR} \cdot (1 - \pi)}. where TPR\mathrm{TPR} and FPR\mathrm{FPR} are the true- and false-positive rates and π\pi is the base rate. Plugging in TPR\mathrm{TPR} = 0.98…

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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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