Reconnection between the magnetosphere and magnetosheath at the dayside magnetopause is studied for southward IMF using high‐resolution 3‐D MHD simulations. The BATSRUS code is run at CCMC with a resistive spot added on the magnetopause to ensure that fast reconnection occurs and to control the reconnection physics. A large range of Mach numbers (1.9–15) are run. The reconnection rate at the nose of the magnetosphere is measured and compared with local plasma parameters and with upstream‐solar wind parameters. It is found that the reconnection rate is controlled by four local plasma parameters: Bs (the magnetic field strength in the magnetosheath), Bm (the magnetic field strength in the magnetosphere), ρs (the plasma mass density in the magnetosheath), and ρm (the plasma mass density in the magnetosphere). The Cassak‐Shay formula for fast reconnection was tested and found to successfully describe the reconnection rate on the dayside magnetopause. It was found that reconnection itself does not significantly modify the local plasma parameters that control dayside reconnection and argued that reconnection does not significantly alter the flow pattern of the magnetosheath. This means that dayside reconnection is not “driven” in the sense that plasma pileup occurs to change the local parameters to adjust the reconnection rate to balance the driving. A “plasmasphere effect” was observed in the simulations wherein high‐density magnetospheric plasma flows into the magnetopause reconnection site and mass loads the reconnection: a spatially localized plume of plasma was observed to locally reduce the reconnection rate by about a factor of 2.