Previous results from this parameter space numerical study have shown that convective storm downdraft speeds are relatively difficult to explain in terms of the background environmental conditions. Linear regressions between storm properties and environmental parameters also perform relatively poorly when describing horizontal wind speeds at the lowest model level (126 m AGL), with only 40 percent of the inter-experiment variance explained by the convective available potential energy (CAPE) and the idealized hodograph radius, which is analogous to the amount of deep layer tropospheric wind shear. The amount of variance explained increases to 46 percent when downdraft CAPE is used in lieu of pseudoadiabatic CAPE, which is a better descriptor of updraft behavior. However, using the difference between equivalent potential temperature at the middle levels and the surface, in combination with the hodograph radius, significantly increases the amount of explained variance (70 percent) in 60-120 minute averaged outflow peak wind speeds. The present results offer insight into the environmental conditions that are supportive of strong convective winds at the surface and may be useful to forecasters and researchers in developing algorithms used to predict damaging convective wind gusts.