Leading edge statistics are obtained by direct numerical simulation(DNS) of freely propagating incompressible and stagnating compressible turbulent premixed flames. Conditional averages of velocities in terms of reaction progress variable, c, and local flame surface density, ${sum}^{prime}_f$, are defined and compared through the flame brush. It holds asymptotically that $_f=_f$ and $_u-_b=D_t/L_w$ with the characteristic length scale of $ar{c}$ variation, $L_w$. It also holds that $_b=_f$ for a freely propagating flame under no mean strain rate. The turbulent burning velocity, $S_T$, is determined by the conditional statistics at the leading edge under large activation energy.