Previous angle-resolved photoemission spectroscopy experiments in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ reported both a strongly renormalized bandwidth near the Fermi level and moderately renormalized Fermi velocities, leaving it unclear whether the correlations are weak or strong and how they could be quantified. We explain why this situation occurs and solve the problem by extracting clearly the coherent and incoherent parts of the band crossing the Fermi level. We show that one can use their relative weight to estimate self-consistently a quasiparticle weight $Z=0.15\pm 0.05$. We suggest this method could be a reliable way to study the evolution of correlations in cobaltates and for comparison with other strongly correlated systems.

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