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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)}

Why this formula appears here

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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TPR⋅π+FPR⋅(1−π)\mathrm{TPR} \cdot \pi + \mathrm{FPR} \cdot (1 - \pi)

Denominator: TPR × pi + FPR × (1 - pi)

The complete quantity below the fraction bar; it must be nonzero for this division.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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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)},

Equation 1 · AI Safety

Building a Deployment Safety System That Actually Holds

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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