Two bells — the well and the sick — cut by the same line: the sick's tail past it is the sensitivity, the well's is the false-positive rate, and their ratio is one number the test owns whatever the base rate. Evidence: the same ratio moving a low prior far less than a middling one; the ladder is how independent results stack on a log scale.
How much MORE often?
When your brother has been in the garden, his boots are almost always muddy. When he has been in his room, they hardly ever are. Muddy boots don't prove anything — they just make 'garden' ten times more likely than it was a minute ago.
A clue is worth how much more often it shows up when the story is true.
O(D|+) = O(D) × LR⁺ where LR⁺ = P(+|D) / P(+|¬D)
One positive
LR⁺ ≈ 10
×10
Two positives
10 × 10
×100
Three positives
10 × 10 × 10
×1,000
Two, then a no
100 × 0.1
×10
Bars are log₁₀ of the combined likelihood ratio — independent results multiply, so on this scale they add; a negative result (LR⁻ ≈ 0.1) is one step back