What is it about Sherlock that has the nation turning on in their millions? Surely it can't be for hokey stories about massive dogs or dominatrixes who enjoy booting feminism back to the dark ages. Or direction that majors heavily on floating words, or confusingly outdated references to "cameraphones". No, the reason that people watch Sherlock is because of the interplay between Martin Freeman and Benedict Cumberbatch – who might just qualify as one of the greatest TV double acts of all time.

The relationship between Sherlock Holmes and Doctor Watson has always been important, but past representations of Holmes have often erred on the side of the staid, logical pipe-smoking period detective, with more space given over to the case than the character. This ossification of what began as a genuinely eccentric figure left little room for Watson to react to Holmes, which is basically the only reason he exists.

Guy Richie's Sherlock Holmes movies did more to coax out the sexually ambiguous, almost husband-and-wife dynamic between Holmes and Watson, although in a such a cartoonishly heavy-handed way that the latest film even makes a point of dressing Robert Downey Jr up as a woman to thump the message home. But Gatiss and Moffat's Sherlock has given us a zippier, much more modern version of the relationship.

In their take, we need Watson even more than Holmes does. Without him, Sherlock would just be another Jonathan Creek-style mystery series where an idiosyncratic bloke in a big coat goes around solving complex riddles and then explaining them with a flourish at the end, albeit with more fiddly shots of him looking at people and working out what they ate for breakfast. But Freeman's Watson grounds Holmes's lovelessly abstract reasoning and highfalutin' talk of "mind palaces" for us, giving us a human side to engage with.

Here, performance is key. Martin Freeman's Watson – like Martin Freeman's Tim from The Office, Martin Freeman's Mike from Hardware, Martin Freeman's reaction to TOWIE winning a Bafta and doubtlessly Martin Freeman's Bilbo Baggins – trades on a kind of everyman bewilderment at whatever extraordinary nonsense happens to be exploding around him. It's not just a role he's played a billion times before; it's pretty much the only role he's ever played. But this also makes him the perfect Watson to play off Benedict Cumberbatch's deliberately attention-seeking, scenery chewing Sherlock.

He's also the perfect foil for Gatiss and Moffat. Watson has always been used to show how clever the writers can be, because after Sherlock has dashed around solving complicated crimes with all sorts of daring last-minute reveals, you can get Watson to pop up and ask for a slower idiot's guide to what just happened and then congratulate Holmes – and therefore the writers – for being so brilliant. In the wrong hands this would be an insufferable gimmick, but Freeman's Watson has just the right mix of innocence and doubt to make it look seamless.

Last night's Hounds of Baskervilles wasn't quite as rapturously received as other adventures, perhaps because of the amount of time that Cumberbatch and Freeman spent apart. The whole middle section, where Watson stormed off in a huff after being subjected to another one of Sherlock's baroque "that man is left-handed and also has dog hair on one of his socks" monologues, felt slow and flat precisely because there was none of the chemistry between the two leads that we've come to expect from Sherlock.

Hopefully Sunday's The Reichenbach Fall will have much more of Watson and Holmes affectionately prodding at one another, because their singular relationship – more than anything else – is the true key to the show's success.