Given @sabinekraml's good GitHub Discussion question (that we've seen before in Issues) scikit-hep/pyhf#1619, along with scikit-hep/pyhf#1620 we should make this more explicit by adding a notebook that demonstrates the differences between the expected and observed CLs values given
If you switch from observed data to expected data — your background-only model will have NPs centered at different values because they're fit to different datasets. The expected CLs has to be different.
cc @kratsg @lukasheinrich