ABSTRACT This work studies the significance of light-curve intrinsic variability in the numerical modelling of contact binaries. Using synthetic light curves, we show that the starspot-based intrinsic variability increases the apparent mass ratio by $\Delta q=5{{\ \rm per\ cent}}$. For systems with orbital period P > 0.3 d, the effects of intrinsic variability averaged over a long time are compensated by Kepler-mission-like phase smearing. Further, we analyse 47 totally eclipsing Kepler mission contact binaries. We find a sharp cut-off of the intrinsic variability at P = 0.45 d. With light-curve numerical modelling and observational relations, we derive the physical parameters of 47 systems. At least 53 per cent of binaries have a possible third companion. 21 binaries show the O’Connell effect in the averaged phase curve. 19 of them have a primary maximum lower than the secondary, suggesting a stationary dark region on the trailing side. Using the P = 0.45 d cut-off, we propose a new approach to the period–colour relation. The only parameter correlating with the magnitude of the intrinsic variability is the apparent effective temperature ratio. We conclude that, instead of describing the system parameters, the A/W subtype division should be applicable only to the light curves, as a tentative phenomenon.