The aim of this work is to test the hypothesis by Kivelson and Hughes (Kivelson and Hughes in Planet. Space Sci. 38:211–220, 1990), according to which, for asymmetric configurations with a curved current sheet and large curvature of magnetic field lines in the tail of the magnetosphere, the substorm breakdown threshold decreases. The work used two databases on the substorms onset: (1) (Frey et al. in J. Geophys. Res. 109:A10304, 2004)—4700 events for 2000–2005, and (2) SUPERMAG—18,800 events for 2000–2010 (Gjerloev in J. Geophys. Res. 117:A09213, 2012). OMNI data was used for the solar wind parameters. We try to answer the question what solar wind parameters are responsible for the bending of the current sheet in the tail of the magnetosphere, how these parameters affect the number of emerging substorms, and what structures of the solar wind are capable of carrying them. Among these possible factors of symmetry break, we explore the alfvénic-type excitations, the dipole tilt, and the direction of solar wind flow, which were traced within the solar activity cycle. As a result, we found a notable correlation (R = 0.65) of yearly substorm occurrence rate and the yearly amount of earthward propagating alfvénic disturbances, while no correlation (R = 0.01) was observed for substorms and sunward propagating alfvénic fluctuations. We also found that the yearly averaged absolute value of dipole tilt at a substorm explosion is always larger (by 0.5°–2.0°) than the mean value of absolute dipole tilt and the difference is larger during the solar cycle maximum when substorm occurrence rate also maximizes. The above difference becomes about 0.5° larger if we take into account the effective tilt angle and consider the input of solar wind flow direction to the actual dipole tilt. We also show that the averaged AL-index for a portion of substorms, which occurred under the dipole tilt less than 8° was −244 nT, and the AL-index for substorms with larger tilt (20°–30°) was −192 nT, which gives more than 20% difference.