Substorm initiation still remains an unsolved problem, even though there is a consensus among most researchers that its main stages include dayside reconnection and substorm expansion. Dayside reconnection results in magnetotail flux buildup to a certain critical level, after which [or after the interplanetary magnetic field (IMF) Bz turns northward] the substorm expansion begins. One problem with the above scenario is that the critical amount of magnetic flux differs from one substorm to another, and not every northward turning of the IMF Bz triggers a substorm. We suggest that an important factor in substorm dynamics may be the variable shape and alignment of the magnetospheric tail current sheet, which bends and warps in response to diurnal/seasonal changes of the Earth's dipole tilt angle and also in response to more rapid changes of the solar wind flow direction. Both of these factors may be important, if one assumes that the deformed current sheet becomes unstable at lower values of the tail lobe magnetic flux/pressure than the planar sheet. To investigate this idea, we examined large multi-year sets of THEMIS, Cluster, and Geotail data and established a relationship between the tail lobe Bx and the dipole tilt angle. Further examinations of substorm events during 2005-2010 supported the hypothesis that their probability and intensity indeed depended on the concurrent values of the tilt angle.