The Saha Equation describes the ratio of the the number of atoms in stage (i+1) to the number of atoms in stage (i) using the partition function. It describes the ratio of ionized atoms to neutral atoms as a function of temperature.
The Saha equation is inversely proportional to the number density of electrons based on the idea of the packing parameter. Physically, the packing parameter describes how much phase space volume is available to the electrons. As we increase the number density of electrons, we decrease the volume available to free electrons which forces some of them to recombine to create neutral atoms.