Suppose that X1, ···, Xkare mutually independent observations from populations π1, ···, πkand that Xihas a density fxi(·)(1 ≤ i ≤ k). For i = 1, ···, k let pi= P[Xi> maxj ≠ iXj], and let p[k] = max (p1, ···, pk). Bechhofer and Sobel [4] have proposed a nonparametric selection procedure based on multinomial random variables for the problem of selecting a population which has the highest probability, p[k], of producing the largest observation. (The density fxi(·) may be different for each i(i = 1, ···, k) and unknown.) If the k distribution functions have the same form, differing only in location, a population with the highest probability of yielding the largest observation corresponds to a population with the largest location parameter. This latter situation allows use of certain alternative procedures designed for specific parametric cases, and the present article studies the relative efficiency (in terms of fixed sample sizes required to guarantee a given probability of a correct selection in certain specified parametric subspaces) of the Bechhofer-Sobel procedure with respect to some competing selection procedures. These competitors were designed specifically for the normal case by Bechhofer [2], and for the uniform case by the present author. The relative efficiency of the Bechhofer-Sobel procedure, in the cases studied, ranges from .27 to .74.