Magnitude and frequency are prominent features of river floods informing design of engineering structures, insurance premiums and adaptation strategies. Recent advances yielding a formal characterization of these variables from a joint description of soil moisture and daily runoff dynamics in river basins are here systematized to highlight their chief outcome: the PHysically-based Extreme Value (PHEV) distribution of river flows. This is a physically-based alternative to empirical estimates and purely statistical methods hitherto used to characterize extremes of hydro-meteorological variables. Capabilities of PHEV for predicting flood magnitude and frequency are benchmarked against a standard distribution and the latest statistical approach for extreme estimation in two ways. The methods are first applied to an extensive dataset to compare their skills for predicting observed flood quantiles in a wide range of case studies. Synthetic time series of streamflow, generated for select river basins from contrasting hydro-climatic regions, are later used to assess performances for rare events. Both analyses reveal fairly unbiased capabilities of PHEV to estimate flood magnitudes corresponding to return periods much longer than the sample size used for calibration. The results also emphasize reduced prediction uncertainty of PHEV for rare floods when the mechanistic hypotheses postulated by the method are fulfilled, notably if the flood magnitude-frequency curve displays an inflection point. These features, arising from the mechanistic understanding embedded in the novel distribution of the largest river flows, are key for a reliable assessment of the actual flooding hazard associated to poorly sampled rare events, especially when lacking long observational records.