The structure of velocity in the outer region of turbulent channel flow (y+ [gsim ] 100) is examined statistically to determine the average flow field associated with spanwise vortical motions. Particle image velocimetry measurements of the streamwise and wall-normal velocity components are correlated with a vortex marker (swirling strength) in the streamwise–wall-normal plane, and linear stochastic estimation is used to estimate the conditional average of the two-dimensional velocity field associated with a swirling motion. The mean structure consists of a series of swirling motions located along a line inclined at 12°–13° from the wall. The pattern is consistent with the observations of outer-layer wall turbulence in which groups of hairpin vortices occur aligned in the streamwise direction. While the observational evidence for the aforementioned model was based upon both experimental and computational visualization of instantaneous structures, the present results show that, on average, the instantaneous structures occur with sufficient frequency, strength, and order to leave an imprint on the statistics of the flow as well. Results at Reτ = 547 and 1734 are presented.