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Equation 4 · Part 1 · How AI and Cybersecurity Actually Work

Symbol p

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

What this part means

the when.

Its job in the formula

p is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

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 false-positive rate, simply because the pool of benign traffic the false-positive rate applies to is so much larger than the pool of real events.

The passage around this formula

…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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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