In this work, we focus on the analysis of a coronal mass ejection (CME) driven shock observed by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph Experiment. We show that white-light coronagraphic images can be employed to estimate the compression ratio X = ρ d /ρ u all along the front of CME-driven shocks. X increases from the shock flanks (where X ~= 1.2) to the shock center (where X ~= 3.0 is maximum). From the estimated X values, we infer the Alfvén Mach number for the general case of an oblique shock. It turns out that only a small region around the shock center is supercritical at earlier times, while higher up in the corona the whole shock becomes subcritical. This suggests that CME-driven shocks could be efficient particle accelerators at the initiation phases of the event, while at later times they progressively loose energy, also losing their capability to accelerate high-energy particles. This result has important implications on the localization of particle acceleration sites and in the context of predictive space weather studies.