A community-clinic no-show predictor is given the identical booking twice and returns two nearby scores. A conventional scheduler would have repeated exactly. Why do testers look at distributions and confidence instead of a single expected bit?

The same booking twice, two nearby scores: that is non-determinism and a probabilistic mapping. Testers look at distributions and confidence, not a single expected bit. Nearby scores are not a one-shot defect, and a clinic predictor is not a conventional scheduler.