A significant amount of the fuel consumed by marine vehicles is expended to overcome skin-friction drag resulting from turbulent boundary layer flows. Hence, a substantial reduction in this frictional drag would notably reduce cost and environmental impact. Superhydrophobic surfaces (SHSs), which entrap a layer of air underwater, have shown promise in reducing drag in small-scale applications and/or in laminar flow conditions. Recently, the efficacy of these surfaces in reducing drag resulting from turbulent flows has been shown. In this work we examine four different, mechanically durable, large-scale SHSs. When evaluated in fully developed turbulent flow, in the height-based Reynolds number range of 10 000 to 30 000, significant drag reduction was observed on some of the surfaces, dependent on their exact morphology. We then discuss how neither the roughness of the SHSs, nor the conventional contact angle goniometry method of evaluating the non-wettability of SHSs at ambient pressure, can predict their drag reduction under turbulent flow conditions. Instead, we propose a new characterization parameter, based on the contact angle hysteresis at higher pressure, which aids in the rational design of randomly rough, friction-reducing SHSs. Overall, we find that both the contact angle hysteresis at higher pressure, and the non-dimensionalized surface roughness, must be minimized to achieve meaningful turbulent drag reduction. Further, we show that even SHSs that are considered hydrodynamically smooth can cause significant drag increase if these two parameters are not sufficiently minimized.