The effectiveness of spatial averaging in an ideal diffuse field is examined, with intended application to pure-tone reverberant sound power measurement. A theoretical measure of spatial averaging effectiveness is proposed, based on the variance of the spatial average, which is determined analytically from the shape and size of the intended path. Three cases, examined here in detail, are: continuous averaging on a line, a circle, and the surface of a disk. Results show that for greatest effectiveness, the path of averaging must extend over a region of space whose dimensions are large with respect to a wavelength. In particular, it is shown that averaging on a line segment of given length will be more effective if the line is straight rather than circular. Surprisingly, it is also shown that averaging on the surface of a disk will be less effective than averaging on its perimeter if the disk is small compared to a wavelength. This last result is employed to illustrate the dangers of oversampling (the use of highly correlated samples) which might otherwise go unrecognized.