Excess Chemical Potential Widom's fix

Hi All, I am a beginner user for lammps and I want to use the widom’s insertion method.

I have some doubts regarding the output excess chemical potential. It says it is average excess chemical potential, but the definition of excess chemical potential already has log of average boltzmann factor for the number of insertions made. Then what exactly are we averaging the excess chemical potential in this case?

Thanks in advance.

It is averaged over the insertion attempts.

But we obtain excess chemical potential by averaging the boltzmann factor (e^(-(delta U))) over the number of insertions.

So, are we dividing the excess chemical potential again by number of insertions?