Well, let us consider methyl radical....#dotCH_3# or hydrogen radical #dotH# or halogen radical #dotX# or benzyl radical #C_6H_5dotCH_2#....you want to know the oxidation numbers of the radical species in each beast?
Oxidation number is the charge left on the atom of interest when all the bonding pairs of electrons are broken, with the charge, the electron assigned to the MORE electronegative atom.
And so if we do this for #H-Cl#, a real molecule, since chlorine is MORE electronegative than hydrogen, we go thru the rigmarole ad get...
#H-X rarr H^(+) + X^(-)#.
And so here we gots formal oxidation states of #H(+I)#, and #X(-I)#. And I stress that these are formal charges, i.e. charges of convenience that can help us rationalize reactivity. And the use of oxidation numbers comes into its own when we consider redox chemistry.
Now radicals GENERALLY form from homolysis...:
#H_3C-H rarr H_3dotC +dotH#...
with respect to methyl and hydrogen radical we gots formal oxidation states of #C(-III)# and #H(0)#. Here the bonding electrons are SHARED rather than transferred...leaving neutral species.
And for #X_2rarr2dotX(0)#, we got formally zerovalent halogen.
Capisce?
