Effects of large-scale stretching of premixed turbulent flames on flame speed are discussed and an extension of the classical Markstein number concept is proposed to parameterize flame speed modifications by the stretch rate. The concept is applied to fit various experimental data on the growth of the radius of expanding, statistically spherical, premixed, turbulent flames, obtained by different groups under different conditions. In all the cases studied, the suggested extension approximates the experimental data very well. It is shown also that this phenomenological approach may be utilized to determine the values of unperturbed turbulent flame speeds, S-t(0), by processing the experimental data for spherical flames. The difference between the obtained values of unperturbed S-t(0) and the mean speeds of spherical flames, observed during expansion, may be as large as 200-300%. The strong influence of the perturbations discussed shows that such effects should be properly addressed when analyzing experimental data or invoking a presumed turbulent flame speed in simulations, for example, in large-eddy simulation based on the G-equation approach.