It’s semi-ironic that Police Story kept its own name, given how generic that name is. The film arrived at a time when Chan and his home studio Golden Harvest were dealing with rivals who’d fish around for hints about his latest projects, so that they could try to beat them to the market with something similar. Chan picked nondescript titles like Project A and Police Story to keep his competitors in the dark about what his movies were going to be about.

It would’ve been difficult for anyone to copy Police Story anyway, since its plot is essentially an afterthought. Chan’s first brief stab at American stardom taught him two valuable lessons: that Hollywood movies are too tightly controlled, and that in international markets, big stunts sell better than hand-to-hand/foot-to-face combat. So for Police Story (Chan’s first big picture back home after making the misbegotten The Protector), he conceived of a few grand set pieces—filled with a ridiculous amount of property damage—and then told his screenwriter Edward Tang to figure out how to connect them up.

Action geeks who rented Police Story on VHS back in the early ’90s could tell when the good parts were going to start, because that’s when the tracking would get fuzzy, from all the previous renters rewinding and re-watching the same scenes, over and over. No Jackie Chan best-of reel would be complete without three Police Story highlights: the scene where a car chase down a steep hill destroys a shantytown; the bit where Chan first hangs off of a city bus and then plants himself in the middle of the street to stop it; and the final shopping mall standoff, where bad guys and good guys alike go flying through glass windows and destroy about a kajillion light fixtures (give or take a zillion). Some of these gags don’t seem as immediately impressive today, because so many subsequent action pictures ripped off their broader strokes. But with repetition, the impossible physics and logistics of what Chan and his stunt team did really starts to sink in.

Yet even though Tang’s script really didn’t matter much, the first Police Story is still the series’ smoothest ride from start to finish, just as a piece of storytelling. It deftly introduces the characters and concepts that anchored the first four films (and one spinoff). Chan plays Chan Ka-Kui—sometimes dubbed as “Kevin” or “Jackie”—a courageous, temperamental Hong Kong cop who frequently gets in trouble with his superiors, “Uncle” Bill Wong (Bill Tung) and Superintendent Raymond Li (Lam Kwok-Hung). His job also complicates his relationship with his long-suffering girlfriend May, played by Maggie Cheung—who was destined for greater things than pouting her way through the background of someone else’s movie. Police Story has a satisfyingly twisty story, with Sgt. Chan suffering a professional disgrace and then making a comeback. Even its slapstick interludes (like one sequence were Chan answers about a half-dozen phone calls at once) are slickly staged and fairly funny.

The same can’t be said of 1988’s Police Story 2, which opens with a montage of thrilling clips from its predecessor, then hits all the same notes, harder and duller. Again, the hero’s humiliated then redeemed. Again, he dashes and leaps through fast-moving traffic. Again, the villain wrecks a shopping mall. The big additions are a hep-looking younger squad of plainclothes detectives, a greater emphasis on crude humor (including one random fart joke), and more explosions and chases than acrobatic fisticuffs. The movie still has plenty of great moments—including a warehouse standoff that’s like a live-action game of Donkey Kong—but after a mid-’80s burst of creativity that saw Chan directing and starring in the action classics Project A, Police Story, and Armour Of God, he seemed a little exhausted and under-inspired at the end of the decade.

He’d rebound strongly in the ’90s, during the years immediately before he broke through in the American market. Between 1991 and 1994, Chan got into a groove, directing and starring in two more essential martial arts epics: Armour Of God II: Operation Condor (released just as Operation Condor in the U.S.) and Drunken Master II (confusingly released stateside as The Legend Of Drunken Master). In between those, he turned the Police Story series over to director Stanley Tong, who made its most spectacular entry.

Story-wise, Police Story 3: Super Cop (or just Supercop, as it was called in America) isn’t as seamless as the franchise’s first installment. Poor Maggie Cheung has her worst part yet as May, in what would be her last PS appearance. And the plot’s focus on a partnership linking Chan to the mainland authorities and everyone’s favorite catch-all crime-fighting organization Interpol is very much a product of its time, rooted in the cultural anxiety over the U.K.’s impending handover of Hong Kong.

But the Chinese connection does allow for the addition of the amazingly agile Michelle Yeoh as Inspector Jessica Yang, as well as a return to the elaborate stunts and fights of chapter one. During his heyday, Chan notoriously wasn’t so keen on working with female action stars. But he respected Yeoh, and when the two of them fight side-by-side against drug lords, their comic and choreographic timing is peerless. They move in uncanny unison, like the interlocking pieces of a wind-up toy. Meanwhile, as Chan wound up for another pitch at becoming viable in the American market, he worked with live sound instead of dubbing, and he varied his locations, working in Malaysia and mainland China as well as Hong Kong.

As for Tong, he pushed his star even further than Chan would’ve pushed himself (which is saying something). On the Dragon Dynasty DVD edition of Supercop, Tong talks about how he wanted to avoid the martial arts movie cliché ending of “five guys fighting in a warehouse.” Police Story 3 climaxes with an elaborately constructed sequence that set Chan dangling from the ladder of helicopter, while Yeoh races through the city on a motorcycle—until they both converge on the enemy and take them down, in a fight on top of a speeding train. The series never got any better than the last 20 minutes of its third movie.

Two more Police Story films came out in the ’90s, of wildly varying quality. The 1996 era-ender Police Story 4: First Strike overplays the comic humiliation that’s often a key part of Chan’s onscreen persona, by dropping his now-internationally known cop into situations where he ends up underdressed and even naked. Also, the Ukraine-to-Russia-to-Australia arc of the story doesn’t make a lot of sense—though to be fair, the American version, known just as First Strike, was even more butchered than usual by New Line. (On the Supercop DVD, Chan complains that his Hollywood hosts would talk about how much they loved his work and then would immediately hack it to bits and change all the music, to justify their paychecks.)

But returning director Tong again works magic with Police Story 4’s action sequences. None of them is an all-timer like the copter/train craziness of Supercop, but Chan does get involved in a chilly snowboard chase, and a battle in a shark tank. And he has one of his better actual martial arts sequences of this series when he wields a stepladder as both a weapon and a shield.

At the least, First Strike is an improvement over 1992’s Once A Cop (sometimes known as Project S, or Supercop 2). Though it was directed by Tong, and put the charismatic, capable Yeoh front and center, the lone Police Story spinoff has none of the charm of the earlier movies. Fans of the franchise—and of Chan in general—came to expect stunts that were practical and plausible, carried out by a skilled team that risked grievous injury for the honor of ending up in a bloody, wince-inducing “blooper reel” over the closing credits. But Once A Cop includes a couple of instances of egregious green-screen, wrecking the reality of some of the splashier action sequences. And Yeoh didn’t get the same opportunities to show off her dancer’s flexibility and speed that she had in Police Story 3.

Chan and Tung have a painfully unfunny scene together in Once A Cop, dressed in women’s clothes—complete with “comically” fake boobs—as part of an undercover operation. Otherwise, the film is curiously maudlin, saddling Yeoh with a semi-romantic subplot that takes a dark turn. More than anything, the issue with Once A Cop is that it lacks the joyousness of the earlier Police Storys. The much lighter First Strike arrived four years later, but Yeoh’s spinoff still marked an unfortunate turning point in the franchise.

There’s some debate among Chan fans about whether 2004’s New Police Story or 2013’s Police Story 2013 (a.k.a. Police Story: Lockdown) really count as part of the series, or if they’re a more modern example of Hong Kong producers slapping familiar titles onto non-sequels. Neither are about the character who appeared in the first four core films. In New Police Story, Chan plays a depressed, drunken detective named Chan Kwok-Wing; in Police Story 2013, he’s a sullen widower father/cop named Zhong Wen. And neither film could be called “an action-comedy”—although New Police Story does at least have a few winking callbacks to its lineage, including a mall fight and a big bus chase.

Both movies are mostly useful just as contrasts to the earlier Police Storys—as grim counterpoints that end up making the originals look all the brighter. The first four subtly capture changes in culture and cinema, from evolving technology (corded land-line phones to cells) to shifts in action styles (punch-outs to explosions). But none are as jarringly of their time as New Police Story’s extreme sports villains, who go roller-blading down the sides of buildings, or as Lockdown’s Taken-esque “tough-guy father tries to rescue his daughter” plot.

Taken on its own merits, Police Story 2013 isn’t so bad. Writer-director Ding Sheng plays around with narrative structure in a way that’s highly unusual for the series, jumping right into a hostage situation and then having Zhong and his captors tell stories about themselves that serve as little flashback vignettes. New Police Story, though, is fairly hard to take. The bad guys are dopey, the stunts are too special-effects-driven, and it’s unpleasant to watch Chan play a character whose self-loathing is profound. One of the hallmarks of Chan’s best work is that he’s willing to let his heroes get knocked around before they go on the aggressive. But those are supposed to be physical beatings, not psychological.

The problem with the two most recent Police Storys is that they’re just not cool—and if nothing else, Chan’s breakthrough hits were always cool. At the time when Rumble In The Bronx became a modest success in the United States, it’d been a while since an Asian martial arts star took the lead in a widely released import, so a lot of younger moviegoers went to see it out of curiosity, with only their experiences with kung fu parodies to cue them as to what to expect. They may have figured on enjoying Chan ironically. (This was the ’90s, after all.) But he won them over with his exuberance, his athleticism, and his panache. A good Police Story made even Chan neophytes say, “Oh, now I get what this guy’s all about.”

Final ranking:

1. Police Story 3: Super Cop (1992)
2. Police Story (1985)
3. Police Story 4: First Strike (1996)
4. Police Story 2 (1988)
5. Police Story 2013 (2013)
6. New Police Story (2004)
7. Once A Cop (1993)