Geomagnetic storms start with activity on the Sun that causes propagation of magnetized plasma structures in the solar wind. The type of solar activity is used to classify the plasma structures as being either interplanetary coronal mass ejection (ICME) or corotating interaction region (CIR)-driven. The ICME-driven events are further classified as either magnetic cloud (MC)-driven or sheath (SH)-driven by the geoeffective structure responsible for the peak of the storm. The geoeffective solar wind flow then interacts with the magnetosphere producing a disturbance in near-Earth space. It is commonly believed that a SH-driven event behaves more like a CIR-driven event than a MC-driven event; however, in our analysis this is not the case. In this study, geomagnetic storms are investigated statistically with respect to the solar wind driver and the intensity of the events. We use the Hot Electron and Ion Drift Integrator (HEIDI) model to simulate the inner magnetospheric hot ion population during all of the storms classified as intense (Dstmin ≤ - 100 nT) within solar cycle 23 (1996-2005). HEIDI is configured four different ways using either the Volland-Stern or self-consistent electric field and either event-based Los Alamos National Lab (LANL) magnetospheric plasma analyzer (MPA) data or a reanalyzed lower resolution version of the data that provides spatial resolution. Presenting the simulation results, geomagnetic data, and solar wind data along a normalized epoch timeline shows the average behavior throughout a typical storm of each classification. The error along the epoch timeline for each HEIDI configuration is used to rate the model's performance. We also subgrouped the storms based on the magnitude of the minimum Dst. We found that typically the LANL MPA data provides the best outer boundary condition. Additionally, the self-consistent electric field better reproduces SH and MC-driven events throughout most of the storm timeline but the Volland-Stern electric field better reproduces CIR-driven events. Contrary to what we expect, examination of the HEIDI model results and solar wind data show that SH-driven events behave more like MC-driven events than CIR-driven storms.