We investigated the stretched dynamics of the structural relaxation in molecular glass formers by using dielectric and thermal (or enthalpic) relaxations. The dielectric stretching exponents βdie are determined by the Havriliak-Negami function, while the enthalpic βTNMH is quantified by using the Tool-Narayanaswamy-Moynihan-Hodge formalism. We found βTNMH is anticorrelated with the degree of freedom, a molecule addressed by the concept of beads. Referring to the reported relation of βdie to the dipole moment μ, we proposed a combined parameter of μ2*beads, which can rationalize the difference in stretching exponents obtained by dielectric and enthalpic relaxations. For the majority of glass-forming molecules, the difference is trivial, but for those molecules with both unusually high dipole moments and flexibility, a large difference is obvious. The interplay of the degree of freedom and dielectric dipole-dipole interaction in molecular dynamics is addressed.