Spatial variation of nonlinear wave groups with different initial envelope shapes is numerically studied by the nonlinear Schrödinger (NLS) equation, confirming that the simplest nonlinear theoretical model can describe the evolution of propagating wave packets reasonably well in deep water. Moreover, three groups of laboratory experiments run in the wave basin are systematically compared with the numerical simulations of the NLS equation. Although a little overestimation is detected, especially in the set of experiments characterized by higher initial wave steepness, the numerical simulation still displays a high degree of agreement with the laboratory experiments. Therefore, the third-order NLS model can catch the essential characteristics of the extreme waves and provides an important physical insight into their generation. The modulation instability, resulting from the quasi-resonant four-wave interaction in a unidirectional sea state, can be indicated by the coefficient of kurtosis, which shows an appreciable correlation with the extreme wave height and hence is used in the modified Edgeworth–Rayleigh distribution. Finally, some statistical properties on the maximum wave heights in different sea states have been related with the initial Benjamin–Feir index.