This paper investigates the average shape of the largest waves arising in finite water depths. Specifically, the largest waves recorded in time-histories of the water surface elevation at a single point have been examined. These are compared to commonly applied theories in engineering and oceanographic practice. To achieve this both field observations and a new set of laboratory measurements are considered. The latter concern long random simulations of directionally spread sea-states generated using realistic JONSWAP frequency spectra. It is shown that approximations related to the linear theory of Quasi-Determinism (QD) cannot describe some key characteristics of the largest waves. While second-order corrections to the QD predictions provide an improvement, key effects arising in very steep or shallow water sea-states are not captured. While studies involving idealised wave groups have demonstrated significant changes arising as a result of higher-order nonlinear wave-wave interactions, these have not been observed in random sea-states.The present paper addresses this discrepancy by decomposing random wave measurements into separate populations of breaking and non-breaking waves. The characteristics of average wave shapes in the two populations are examined and their key differences discussed. These explain the mismatch between findings in earlier random and deterministic wave studies.