There are few Hollywood directors from whom "event cinema" is personally expected, but Paul Thomas Anderson is one. This year, he brought his reputation and prestige closer to Kubrick levels with this film, an epic based loosely on the early life of the Scientology founder L Ron Hubbard. Philip Seymour Hoffman plays Lancaster Dodd, a homespun philosopher and cult leader in postwar America. He is a bullish and conceited actor-manager figure who one evening chances upon a semi-homeless alcoholic called Freddie Quell who was invalided out of the US Navy with a nervous breakdown after VJ Day. Quell is played, unforgettably, by Joaquin Phoenix.

Dodd decides to make poor, muddled Freddie a special project of his, but his failure to indoctrinate his new disciple, to exert his mastery over this troubled man's mind forms the backbone of this gripping and deeply mysterious drama. Just as in Anderson's previous film There Will Be Blood, the movie suggests a secret history or prehistory of the US; just as in that film, a troubled quasi-father-son relationship is all important. And there is also another bizarre, absurdist flourish in the dialogue. As Daniel Day-Lewis's rapacious oilman, Plainview, boasted about sucking up another man's milkshake, so Hoffman's Dodd starts singing (I'd Like To Get You On) a Slow Boat To China – at great and uncomfortable length.

There Will Be Blood was about entrepreneurial capitalism; The Master was about entrepreneurial religion, gimcrack philosophy, prospecting for snake oil. Dodd is giving America a new vernacular belief, or rather self-belief, with a little of this and a little of that. Bits and pieces are taken from religion and pop science and science fiction of the sort written by Hubbard and his contemporary, Philip K Dick. And Quell, intoxicated by the Master's rhetoric, shows his own parallel genius for being the life and soul of the party by brewing up booze. Almost by magic, he can create fiendishly addictive hooch from fruit, bread, bathroom medicaments – anything. Dodd and Quell have a match made in sociopath heaven, and there is a kind of covert, erotic excitement in their association. One of the most startling scenes is the one in which Dodd starts singing I'll Go No More a Roving in polite company, and we see – through Quell's eyes, and perhaps through Dodd's – the women there unclothed.

It is a difficult, challenging and, at times, opaque movie, which does not have the story arc of a conventional Hollywood biopic. Unconvinced audiences have praised the performances but complained about the lack of "story". It's an understandable reservation, but I think Anderson is offering something closer to a colossally ambitious portrait, or dual portrait, perhaps comparable to Don DeLillo's depiction of Lee Harvey Oswald in his novel Libra, or the woman with polio lying in the tawny grass in Andrew Wyeth's painting Christina's World. And Phoenix's agonisingly intense and blazingly committed performance makes this our film of the year.