Dear Professor Kasman,
I have been reading through your website, and came across the description of the 1947 story "The Law" (which I have read, but far too long ago to remember). It put me in mind of a 1954 essay by Joseph Wood Krutch (a naturalist), "How Probable Is Probability?", which begins:
"Some years ago an ingenious journalist filled his column with speculation about the people who would jump from the Brooklyn Bridge during the twelve months to come. At the moment probably none of them knew that he was going to have to do anything of the kind. Probably at the moment each would have been appalled by the fate in store for him. But somebody would be compelled to jump because statistics prove that somebody always does.
"When the time came each would suppose that he had his private reasons. But the real reason would be that the Law must be obeyed. The question is merely: Who will be picked out by the God of Mathematics to demonstrate His infallibility? Will it be, perhaps, you or I? In any event it will be some of us, and the number will not be much larger or much smaller than usual. Figures don't lie and some will have to be sacrificed to prove that they do not."
The coincidence of the writings of Robert M. Coates, the unnamed jokester columnist, and Joseph Wood Krutch seems to indicate that the topic of the Law of Averages was "in the air" about that time. Krutch's essay suggests some reasons why. This was the era when market research, polling, viewership ratings (Nielsen began business in 1950), and such like really took off (to my surprise, none of this really existed much before the 1920s). Likewise, social scientists were in the process of developing statistical tools for their research (done since the 18th century but greatly expanded in the 20th). So you have the public starting to become aware that their lives are being described by numbers and that policymakers and marketers are using these numbers. No wonder that anxiety arose, aided by a shaky understanding of statistics. Krutch attempted to clear up some misunderstandings, to show what the fallacy of the introductory example was. But he concludes that "an individual is free, but the group of which he is a part is not. Any given man's destiny is to some extent in his own hands; but the destiny of mankind is predetermined."
Anyway, I'll bet there were yet other writers grappling with that issue in similar ways at that time, since the social and scientific factors I mentioned all came together then.