Calculate the negative predictive value from a confusion matrix.
Negative Predictive Value (NPV) measures how many of the predictions labeled negative were actually correct: NPV = TN / (TN + FN). It answers 'if the model says negative, how likely is that true?' — the mirror image of precision (which answers the same question for positive predictions). NPV is heavily influenced by prevalence: even a highly sensitive test can have low NPV in a population where the condition is very common, because false negatives become relatively more likely.
NPV = TN / (TN + FN)
Specificity = TN / (TN + FP) measures correctness among actual negatives, while NPV = TN / (TN + FN) measures correctness among predicted negatives — different denominators, and NPV is more sensitive to the underlying prevalence.
When a condition is rare, most negative predictions really are negative, boosting NPV; when a condition is common, more of the 'negative' predictions turn out to be false negatives, lowering NPV even with the same sensitivity and specificity.
NPV doesn't have as common a machine-learning-specific renaming as sensitivity/specificity do (recall/TPR, TNR), but it's sometimes referred to as 'negative class precision' by analogy to standard precision for the positive class.