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Published equation contexts

Precision=TPR⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}

Why this formula appears here

A simple way to see why the base rate of genuine misuse matters as much as the detector’s accuracy is the standard result relating a detector’s precision to how rare the thing it is looking for actually is. If a detection system has a true-positive rate TPR\text{TPR} and false-positive rate FPR\text{FPR} , and the true prevalence of the underlying misuse event in the traffic it sees is p , the fraction of flagged events that are genuinely misuse — the precision an analyst actually experiences — is Precision=TPR⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}. When p is small, which it almost always is for genuine, successful misuse against a well-defended system, precision collapses toward zero even for a detector with a very low…

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TPR⋅p+FPR⋅(1−p)\text{TPR} \cdot p + \text{FPR} \cdot (1-p)

Denominator: TPR × p + FPR × (1-p)

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⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}

Equation 4 · Security

How AI and Cybersecurity Actually Work

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

A simple way to see why the base rate of genuine misuse matters as much as the detector’s accuracy is the standard result relating a detector’s precision to how rare the thing it is looking for actually is. If a detection system has a true-positive rate TPR\text{TPR} and false-positive rate FPR\text{FPR} , and the true prevalence of the underlying misuse event in the traffic it sees is p , the fraction of flagged events that are genuinely misuse — the precision an analyst actually experiences — is Precision=TPR⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}. When p is small, which it almost always is for genuine, successful misuse against a well-defended system, precision collapses toward zero even for a detector with a very low…

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