Why is the first peak of Franck–Hertz experiment at 4.9 eV, and not shifted by 4.9 eV from the maxima of the energy vs emitted electrons distribution?

I suppose that in the Franck–Hertz experiment, the electrons emitted naturally (without any potential applied) from the hot cathode would have a particular distribution for the electron energy vs. number of electrons emitted in a particular direction, for a given cathode, temperature and the particular geometry of the anode/cathode setup. The electrons emitted from the hot cathode would have some initial thermal energy due to the cathode being hot.

My question then is, shouldn't the first current peak be shifted by 4.9 eV from the energy of maxima of the above-mentioned distribution?

4.9 eV is the energy difference of the ground state and the first excited energy state of Hg atoms.