When a standard action-thriller has as many chaotically moving parts as Jason Statham’s “Safe,’’ you might think the filmmakers lost a handle on their narrative somewhere along the way. Not so in this case. Writer-director Boaz Yakin (“Remember the Titans’’) delivers his conflicting elements mostly as intended, and with obvious ambition. But he fails to take care of certain fundamentals - most problematically, coaxing out the emotion he’s seeking from Statham and young newcomer Catherine Chan.

Statham plays Luke Wright, a cage fighter who runs afoul of the Russian mob and winds up a broken man. (Actually, the fighting background feels like something just thrown in for the trailers; Yakin’s script gives uber-hyphenate Luke a CV that also lists him as sanitation worker, ex-cop, and hobo. Statham pulls on his longshoreman’s cap to sell this last part.) Chan is Mei, a Beijing math prodigy abducted by Han (James Hong, “Seinfeld’’) and his Triad to keep an untraceable accounting of their New York rackets.

It takes a good half hour for the storylines to link together, but once they do, the logic is pretty straightforward: They’re all crooks. If the Chinese have something, the Russians want it, and vice versa. Ditto for corrupt cop Wolf (Robert John Burke) and his crew. All that Luke wants is to help Mei, who has unexpectedly given him reason to live. But hey, if he takes out a lowlife or 20 in the process, so much the better.

This is certainly the sort of setup that’s been entertainingly effective for Statham before. But Yakin tries for more, calling on his tough-guy star to play despondent, even tearful, with awkward results. The movie features a couple of firefights inventively shot from inside cars, giving the visuals an arresting, boxed-in feeling, but then dilutes things elsewhere with monotonously routine gunplay and bone-crunching. And Yakin does some dizzying timeline shuffling early on, but finally takes it nowhere. It’s like another “Transporter’’ installment trying to be something slightly more - and not quite delivering the goods.

Tom Russo can be reached at trusso2222@gmail.com.