Context. Among massive stars, binary interaction is the rule rather than the exception. The closest binaries – those with periods of less than ∼10 days – undergo mass transfer during core-hydrogen burning, with many of them experiencing a nuclear-timescale contact phase. Current binary population synthesis models predict the mass-ratio distribution of contact binaries to be heavily skewed toward a mass ratio of unity, which is inconsistent with observations. It has been shown that effects of tidal deformation due to the Roche potential and energy transfer in the common layers of a contact binary alter the internal structure of close binary components. However, previous population studies neglected these effects. Aims. We aim to model a population of massive binary stars that undergo mass transfer during core-hydrogen burning, while consistently considering the effects of tidal deformation and energy transfer in contact phases. Methods. We used the MESA binary-evolution code to compute large grids of models with primary star masses of 8 − 70 M⊙ at solar metallicity. We then performed a population-synthesis study to predict distribution functions of the observational properties of close binary systems, focusing in particular on the mass and luminosity ratio distribution. Results. We find that the effects of tidal deformation and energy transfer have a limited effect on the predicted mass-ratio distribution of massive contact binaries. Only a small fraction of the population have their mass ratio significantly shifted toward a more unequal configuration. However, we suggest that orbital hardening could affect the evolution of contact binaries and their progenitors, and we advocate for a homogeneous set of observed contact binary parameters.