How do you fix a precision-based factuality metric that...

A precision-based metric often fails because precision divided by a shrinking claim count trends toward a perfect score as the count approaches one true claim. By introducing a recall term, you anchor the evaluation against a fixed reference constant. This forces the model to maintain a balance between accuracy and the expected volume of information, preventing the metric from rewarding models that simply write shorter, safer, or hedged responses to avoid making errors.