Of all the things this world absolutely needs more of (peace, love, common sense) it would be difficult to argue that another Sherlock Holmes adaptation ranks very high on the list. The great detective rarely goes long without getting reimagined yet again; it has, in fact, only been a few months since the Sherlock-based modern-day medical drama Watson, not to be confused with that other, older Sherlock-based modern-day medical drama House.

Now comes The CW’s Sherlock & Daughter, whose innovation on the mythology is right there in the title. As a mystery, it’s no great shakes; at least in the early episodes sent to critics, it’s missing that satisfying snap of clues falling into place in clever ways. But the Brendan Foley-created drama is bolstered by enough winning performances ­— starting with David Thewlis as the first half of that title — that it’s mostly just nice...