The O and early B star winds show empirical correlations between X-ray (L_x) and Bolometric (L_Bol) luminosity as well as wind properties such as wind momentum and wind kinetic energy. Wolf-Rayet stars do not. We discuss scaling relations to qualitatively explain this lack of correlation among the WR winds and to quantitatively reproduce the observed ratio of X-ray luminosities between the N-rich WN types and C-rich WC types. If (a) the filling factor of hot X-ray emitting gas varies as (M⊙/v_\infty)(-1) for stars of different mass loss and terminal speed and (b) the ambient Wolf-Rayet wind component is optically thick to the hot gas X-rays, then a lack of correlation between L_x and wind parameters is to be expected. The emergent X-ray emission then depends only on factors relating to relative abundances and ionization. The observed ratio L_X(WN)/L_X(WC) is consistent with our scaling analysis using typical WN and WC abundances.