We examine the Butcher-Oemler effect and its cluster richness dependence in the largest sample studied to date: 295 Abell clusters. We find a strong correlation between cluster richness and the fraction of blue galaxies, f_B, at every redshift. The slope of the f_B(z) relation is similar for all richnesses, but at a given redshift, f_B is systematically higher for poor clusters. This is the chief cause of scatter in the f_B vs. z diagram: the spread caused by the richness dependence is comparable to the trend in f_B over a typical redshift baseline, so that conclusions drawn from smaller samples have varied widely. The two parameters, z, and a consistently defined projected galaxy number density, N, together account for all of the observed variation in f_B within the measurement errors. The redshift evolution of f_B is real, and occurs at approximately the same rate for clusters of all richness classes. ; Comment: 6 pages, 2 Postscript figures, uses emulateapj.sty. Accepted for publication in the Astrophysical Journal Letters