Why AsymptoticCalculator p0-values are constant = 0.5 outside peaks?

Dear experts,

for p0-values calculated by AsymptoticCalculator, in many areas outside the peaks, p0 = const = 0.5 (corresponding to significance = const = 0 sigma).
This may be seen e.g. already in the RooStats tutorial, Exercise 6b,

In principle, this might not be too important for physics, since it concerns areas where p0 are large. But nevertheless, why is that that p0 values become constant, shouldn’t there be some fluctuations, reflecting fluctuations which are always present in data?

Thank you in advance for your help, best regards,
Dima.

Hi @DmitryYuGolubkov; maybe @moneta or @jonas can help here.

Cheers,
J.

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