Yet Holmes’s vagueness and incompleteness on the page are what make him so irresistible as a pop figure, on whom we can project our own interpretation. A lot of what we know, or think we know, about him  the deerstalker hat, the cloaks, the catchphrase “Elementary, my dear Watson”  comes not from the texts at all but from subsequent imaginings of him, the movies especially. By now there have been more than 200 film or TV versions of Holmes, and the actors who have played him on screen or stage include John Barrymore, Raymond Massey, Ian Richardson, Jeremy Brett, George C. Scott, Stewart Granger, Charlton Heston, Roger Moore and, improbably, Larry Hagman and Leonard Nimoy.

The most influential, the one whose Holmes lingers in the mind as an anti-version of Mr. Downey’s, is Basil Rathbone, who was a movie Holmes from 1939 to 1946, and who imprinted on us such seemingly essential Holmesian traits as the high, brainy forehead; the slick, swept-back hair; the languid, aristocratic bearing; the supercilious putdowns. That’s the imperturbable image that remained more or less unshakable until Nicol Williamson cracked the mold with his hyper, drug-crazed Holmes in “The Seven-Per-Cent Solution,” Herbert Ross’s 1976 adaptation of the Nicholas Meyer novel.

Image ON TV Jeremy Brett as Holmes in a Granada Television series running from 1984 to 1994. Credit... Granada

In 1985 we got “Young Sherlock Holmes,” directed by Barry Levinson, in which the teenage Holmes turned out, in retrospect, to have been a sort of proto-Harry Potter. That movie was produced by Steven Spielberg, whose “Indiana Jones”-like fingerprints are all over the Ritchie film.

To say that our image of Holmes has evolved in ways that reflect changes in our understanding of the character is probably a stretch. More likely he has evolved simply because movies have evolved, and our appreciation of him now entails a large chunk of film history. The plot of the new movie echoes both “The Da Vinci Code” and the Nicolas Cage “National Treasure” movies. The wisecracking relationship between Holmes and Watson (here played engagingly, and not as an old duffer, by Jude Law) may now remind viewers of Butch Cassidy and Sundance. The pratfalling Mr. Downey, forgoing a deerstalker for a bowler or a slouch hat, inevitably evokes his earlier movie impersonation of Chaplin, who, as it happens, appeared in one of the early Holmes silents.

Mr. Ritchie’s London is a phony London, one where the wind on the Thames seems to blow in different directions at once. The real thing was never this rainy, murky or steampunky. But his is also the best-looking London that any on-screen Holmes has ever inhabited, and a reminder that part of the appeal of the books and stories was their atmosphere. On the other hand, the oddest thing about the movie is that Holmes is here lovable and endearing in a way that he has seldom, if ever, been before. Endearingness used to be the Watson trait  on film, anyway; in the books Watson is mostly just a straight man.

One of the characters in the Ritchie film remarks that there is a fragility beneath all Holmes’s logic and ratiocination, and it’s true. Mr. Downey’s character is as needy as he is superior. He still delights in showing off his cleverness but less out of snobbery than because he can’t help himself. He lives for an audience. The boredom, the lassitude, the hint of substance abuse, the violin playing (or plucking: for much of the time, Holmes seems to have lost his bow) are all here, but his problem appears to be less mental than physical.

He requires a case not so much to exercise his formidable intellect as to get himself out of the house so he can dart around, throw some punches, wear disguises, wind up nude and shackled to the bedposts. His frustration, you can’t help feeling, might stem from the fact that in the Victorian age, the proper vocation for him hasn’t yet been invented. He’s someone who needs to be in the movies.