More incidents followed, and Mr. Reilly’s skepticism grew. “This phenomenon of fake hate crimes did not appear to be small-scale or regionally based,” he writes. A gay pastor in Texas accused a Whole Foods store of selling him a cake with a slur written in icing. The store produced video evidence that the pastor was lying. A white woman in Oregon disfigured her own face with acid and claimed a black man had attacked her. Later, she admitted fabricating the entire story. After signs that read “blacks only” and “whites only” were found at bathroom entrances on the University at Buffalo campus in upstate New York, a black graduate student confessed to posting them.

Mr. Reilly eventually compiled a database of 346 hate-crime allegations and determined that less than a third were genuine. Turning his attention to the hoaxes, he put together a data set of more than 400 confirmed cases of fake allegations that were reported to authorities between 2010 and 2017. He allows that the exact number of false reports is probably unknowable, but what can be said “with absolute confidence is that the actual number of hate crime hoaxes is indisputably large,” he writes. “We are not speaking here of just a few bad apples.”