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Equation 1 · Part 8 · Building a Deployment Safety System That Actually Holds

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

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

What this part means

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

Its job in the formula

TPR × pi + FPR × (1 - pi) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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