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 The book I use is "Statistical Distributions, 2nd Edition" by Evans, Hastings, and Peacock. They define r as the number of successes, and p as P(success). They also define q=(1-p) which shortens all the formulas. They say the mean is rq/p, and the variance is mean/p. This makes sense to me. Suppose "success" is "being a genius". Suppose p is 10^-6 or one in a million. That means if you want r geniuses, you need about r/10^-6 = r × 10^6 = r million people. So the smaller p is, the bigger the mean has to be. And of course, the smaller p is, the less relevant q is, because it's basically one.