How Many Degrees of Freedom Has the Gluon?

In constituent models, glueballs are described as bound states of effective gluons. The dynamical mass generation lead to a gluon mass without violating gauge invariance. One can then consider three degrees of freedom for those effective massive gluons. However, models with only two degrees of freedom are shown to be in better agreement with the lattice glueball spectrum. I review both models for two- and three-gluon models and explain why even though the gluon gains a mass, it behaves as a massless particle with only two degrees of freedom.