The basic idea of the Sharpe ratio or of any of it's cousins is to get a single number that is a sort of figure of merit for the performance of a portfolio— whether the portfolio is actively managed or not. And so that should involve not only a bigger figure of merit for better returns but also some sort of penalty being applied to the more volatile portfolios, volatility being not desired. The Sharpe ratio is a suitable figure of merit because it is a ratio of a measure of the return on an investment to a measure of its volatility. It therefore implies less merit when the volatility, the denominator, is large.
The question is exactly how do we compute the ratio... the details. This concern isn't only or particularly about whether or not a specific way of computing the ratio makes it into a more innately worthwhile figure of merit than another, as the various specifications of the ratio that have been put forward are not so very different in that regard; it's mainly about wanting to avoid taking an approach that hardly anyone else is using, for the sake of communicating results fairly to broad audiences. So what are others doing? What is William F. Sharpe doing? Incredibly, he's being vague about how his ratio should be computed— that's what he's doing. Read on!