After “The Hangover Part II,” more than one critic took filmmaker Todd Phillips to task for too slavishly following the first movie’s winning formula, ingredient for ingredient. For a story so heavily dependent on the element of surprise why couldn’t he manage to nudge things in a slightly different direction?

With “The Hangover Part III,” he’s taken that advice to heart. And that’s the problem.

The second movie was little more than a retread of the first, with a change of venue and a bit more outrageous extremity loss. (A missing tooth in the first film became a severed finger in the second.) “The Hangover Part III,” on the other hand, is such a departure from the franchise that there’s not even a hangover. That’s right, there’s no drunken blackout, the events of which must be pieced together retroactively, forming the plot of the film.

To the contrary, the action here is precipitated by an intervention.

It starts on a road trip to Arizona, where the deranged man-child Alan (Zach Galifianakis) — whose careless drug dispensing gets everything going so horribly wrong in movies I and II — is being taken to a rehab facility by his reluctant friends Phil (Bradley Cooper), Stu (Ed Helms) and Doug (Justin Bartha) — collectively known as the Wolfpack. While en route, the four of them are ambushed by thugs working for the gangster Marshall (John Goodman), who wants to exploit the men’s connections to Leslie Chow (Ken Jeong) to retrieve some stolen gold.

Jeong, of course, was memorably manic in the first two films as a criminal who is both dangerously unhinged and bizarrely charming, delivering a foul-mouthed, more than slightly frightening, yet also terribly funny performance. In this film, he’s stashed several million dollars worth of gold bricks that he took from Marshall, who now wants them back. The Wolfpack’s assignment is to track down Chow and get back the gold. In order to ensure their compliance, Marshall takes Doug hostage.

So, no drugs, no booze, no hangover. It’s part manhunt, part heist. And it takes them, at first, to Mexico, and then — sigh — back to Vegas in pursuit of the gold and Chow, who ultimately proves as slippery and unreliable as in the first two films.

Does the change-up work? Sadly, it does not.

On the one hand, Phillips and co-writer Craig Mazin (“The Hangover Part II”) have wisely realized that what made the first film work — as well as, to a lesser degree, the second — wasn’t plot so much as character. Helms’ straightlaced everyman dentist made a nice foil to Cooper’s glib, calm-in-the-face of disaster libertine, with Galifianakis’s unpredictable lunatic thrown in as a wild card. Bartha, as the milquetoast-y Doug, pretty much sits out all three films, as well he should.

On the other hand, if you’re going to mine humor from well-established characters, you ought to at least have the good sense to respect those characters. “The Hangover Part III” starts to get off track as soon as it shows the Wolfpack in league with Chow, their former nemesis.

First off, he’s a snake, so why should they trust anything he says? Secondly, they’re about to turn him and his gold over to Marshall, who will probably kill Chow as soon as he gets his loot back. So why should he trust them?

None of it makes sense.

At least in “Part II,” the Wolfpack’s unwise decision to hang out with Chow could be chalked up to judgment impaired by drugs and drink. Here, they’re stone-cold sober. The film needs something, even if it’s only one line of dialogue, to indicate that someone — Phil, Stu, Alan or even Chow — is aware of the inherent instability of their strange alliance. There is none.

And then when, duh, everything goes kablooey again, there are no intoxicants to blame, only lazy screenwriters.

To make matters worse, this third “Hangover” is dull. Coupled with its logic headaches, it left me feeling like I needed an Alka-Seltzer Plus. Anything to add a little fizzy relief to these flat and unfunny proceedings.

(100 minutes, at area theaters) is rated R for obscenity, nudity, violence, crude humor, offensive ethnic stereotypes and mistreatment of animals.