In a system where a boson (e.g., a phonon) of finite frequency omega(0) is coupled to electrons, two phenomena occur as the coupling is increased: electron pairing and polarization of the boson field. Within a path integral formalism and a dynamical mean-field approach, we introduce ad hoc distribution functions which allow us to pinpoint the two effects. When omega(0) is smaller than the bandwidth D, pairing and polarization occur for fairly similar couplings for all considered temperatures. When omega(0)>D, the two phenomena tend to coincide only for T >omega(0), but are no longer tied for low temperatures so that a state of paired particles with significant fluctuations but zero average polarization is stabilized. RI Capone, Massimo/A-7762-2008